BEHIND THE VEIL THE REFORM OF ISLAM IN INTER-WAR ALBANIA OR THE SEARCH FOR A "MODERN" AND "EUROPEAN" ISLAM Nathalie Clayer

The Albanian case is unique. When the independence of this young European country was again recognized by the International Community in 1920, 1 Islam was the religion of the majority of the population (around 70% of an estimated 800,000 inhabitants). Albania was thus the only predominantly Muslim European state. Unlike the majority of Muslims in Western Europe, Albanian Muslims were neither immigrants nor recent converts to Islam. Nor did they form a "surviving minority,"2 as was the case with Muslim groups living in other Balkan countries ; rather we could say that they made up a "surviving majority." One of the components of the national identity building process had been to legitimize the existence of a sovereign nation, even if predominantly Muslim, in Europe, in case of the collapse of the Ottoman Empire. 3 Despite this Muslim majority, from 1920 onwards the Albanian state was immediately defined by its political leaders as afetar ("without religion"), that is to say "without any official religion". The aim was to strengthen national feeling among a population divided between different denominations, Muslims, Catholic Christians and Orthodox Christians. 4 In fact, the state was multi-denominational rather than a-denominational. The "a-denominational" character of the state also fitted the wishes of secularist intellectuals and civil servants, who were non-Muslims as well as Muslims -Sunnis or members of the heterodox Islamic brotherhood of the Bektashis. These secularists dominated the intellectual life and the state apparatus, and were working for what they called the "modernization" and the "Europeanization" of the country.

The dominant role of secularist elites paved the way for the "reform of Islam." This process was made easier by the nationalization of the Islamic religious institutions and by the progressive control exerted over them by the state. Indeed, the Albanian state played an important role in the organization and reform of official religious institutions. For example, it interfered in the organization of the first national Islamic Congress which took place in 1923, issuing orders concerning the choice of the delegates. It was not essential that they were clerics, but above all they had to be "patriots" and "more or less liberal." The civil authorities themselves even choose some of the delegates, who were supposed to represent one province or another. 5 Government representatives were also present during the meetings. Apart from the congresses, the political view of clerics was closely controlled. Their nomination had to be accepted, and was sometimes even decided by the civil authorities who also dismissed some of clerics. Finally, with the further reform and centralization of religious institutions in 1929, the state came to provide a substantial part of the Islamic Community"s budget. 6 The "reform of Islam" was also facilitated by the fact that the authority of the official religious leaders was sometimes even imposed through the intervention of the civil authorities. For instance, in 1926 the head of the Islamic Community informed the Ministry of the Interior that a propaganda had been launched in Shkodër against the New Madrasa established in that city, as well as against the new organization of the Jemaat and the collection of money that it implied. The Ministry therefore ordered the head of the Community not to allow sermons to be delivered in mosques without the authorization of the Community, and promised that the civil authorities would taken action against offenders. 7 The links between the political authorities and the Islamic Community were especially close since Islam and the Islamic religious institutions were also used by the government for social control. As early as 1922, sermons (vaz) were used to persuade parents to send their children to school, and to strengthen national fraternity and loyalty to the government. Even in 1936, the official aim of the Islamic Community was to contribute by means of sermons and lectures to the strengthening of national fraternity and national feeling, as well as to advise Muslims to conform to progress and "true civilization." Islam was also particularly used in the context of the economic crisis. During Ramadan in 1931, for example, preachers had to address this problem, and Islamic charity was encouraged in order to help solve the social crisis. In 1937, the leaders of the Islamic Community called upon wealthy Muslims to give to the poor who were suffering from unemployment in order to show that there was no need for socialism and bolshevism. Indeed, Islam was certainly considered by the Albanian political authorities as a tool against the diffusion of Communist ideas, which, at that time, were attractive especially for young people. 8 The "harmful nature" of Communism was denounced by Muslim clerics in numerous articles and booklets. 9

Among the "reforms of Islam" that were introduced in this context, we should mention firstly the autonomy granted to the Sufi brotherhoods, in particular to the Bektashiyya, which had already been promoted by some Albanian nationalists at the end of the Ottoman period as a liberal form of Islam. These changes, imposed by the political power against the wishes of the leaders of the Islamic Community, were quite different from the developments taking place in Turkey where Sufi orders were banned. Nevertheless, from 1936 onwards, four Sufi networksthe Kadiriyya, the Rifaiyya, the Sadiyya and the Tijaniyyawere grouped within a special organization, under the umbrella of the Islamic Community. 10 Another important reform was the suppression of the Shari"a courts, following the adoption of the Civil Code in 1928-1929. Their abolition was only reluctantly accepted by the leaders of the Islamic Community because it erased the religious character of marriages and introduced some provisions concerning inheritance and divorce that were contrary to the Sacred Law. On the other hand, other reforms proposed by the political authorities were well accepted, because they were in accordance with the ideas promoted by reformist ulemas. F. 882, v. 1923, D. 1. 11 As in Turkey, religious reformists and political reformers had a common goal, to elaborate a "true spiritual Islam," cleansed of its impurities.

was set up in the capital, in order to train a new staff of religious officials, in a "modern" spirit.12 However, by using the example of another reform, the ban on the veil, I want to highlight the mechanisms of such reforms and the relations between the various actors involved. More generally, I want to show how these mechanisms reveal the place of Islam within Albanian society during the inter-war period.

The progressive lifting of the veil

The ban on the veil only occurred step by step. 13 Between 1920 and 1928, such a reform was only evoked or asked for by some actorsintellectuals and politiciansin the press or in parliament, particularly when important political decisions were to be taken. This was the case between 1920 and 1923, a period which represents the beginning of a difficult state building process. 14 This was also the case in 1924, during the short government of Fan Noli, established after the so-called "June Revolution." The question was again debated in 1928, when the Civil Code was introduced and when the political system was transformed from a republic to a monarchy. But during this first phase, no action was actually taken, either by the political authorities, or by religious leaders.

In 1929, at a time of political change and of religious re-organization under state control, however, the ban on the veil became part of the radical measures requested by Behxhet Shapati, the new head of the Islamic Community, elected at the close of the national Islamic Congress. Indeed, it has been suggested that B.

Shapati asked the Minister of Justice to ban the perçe (veil) and requested that, through the police, he advice the population to abandon the veil by prohibiting husbands and fathers to go in the company of veiled women. 15 However, it seems doubtful that the new head of the Islamic Community would have taken this initiative which was probably the work of the political authorities. Indeed, the ministerial Council banned not only the perçe (veil), but also the ferexhe (a dustcoat worn by women when they went out). The Minister of Justice nevertheless recommended to police stations that they should be very careful not to offend the people, and to try to convince them by working together with the district councils responsible for explaining to women why the ban was necessary. 16 At the same time, during the following years, the political authorities used various means in order to impose this decision : propaganda in newspapers, lectures and, above all, to insist that women working for the state, such as midwifes and teachers, comply. In fact, at least in 1935, punitive measures were taken against those women who did not respect the ban.17 In addition, initiatives were sometimes taken by local authorities, such as the mayors of Gjirokastër and Tirana. 18 But the question of the ban on the veil gained new impetus in 1936-1937, during a new period of political crisis. At that time, the country"s sovereignty was more and more openly challenged by Italy. A liberal government had been set up in October 1935, but lasted only until November 1936. During this "liberal government" led by Mehdi Frashëri, the debate on the veil was relaunched in the press, especially between the Islamic Community"s journal and the newspapers of some young intellectuals. Then, in 1937, when an important set of reforms was launched by the Albanian authorities to assert the country"s sovereignty, the ban on the veil became the subject of a law.

Here again, the initiative was supposed to have been taken by the official religious authorities. According to this version, the two muftis of the Southern provinces asked the General Council of the Islamic Community to ban the veil.

Following this request, the head of the Islamic Community, B. Shapati, wrote a report, containing among others a fatwa by him stating that, it was not haram (forbidden by religion), for a woman to show her face. On 1st March 1937, the General Council of the Community agreed with this report and the fatwa, and decided to make the decision known on one hand to the population by means of sermons, and on the other to the government. The latter immediately presented a draft law to parliament that was approved on 8th March 1937. Under the title « Law on the ban on face covering », it stipulated that it was forbidden for a woman to cover her face, totally or partially, with any kind of veil. The offenders, as well as the husbands, fathers or guardians who had not exerted their authority and those who were making a propaganda in favor of the veil, incurred a fine. 19 In reality, this initiative probably originated in political circles, and it seems that a kind of compromise was achieved between the political and the religious authorities. Indeed, the law concerned only the covering of the face and remained silent about the wearing of the ferexhe, a garment that the police was supposed to have banned since 1929.

What is important to note is that this law had a strong echo abroad, and this had certainly been the true aim of the political authority. In fact, the ban on the veil aimed at symbolizing the westernization of the country, by making it possible for women to have a place in economic and social life. As a Western country, Albania should be a sovereign country among the other Western countries. 20 However, in the country itself, the veil did not totally disappear for two reasons. On one hand, there was popular opposition and, on the other, the government remained very cautious. A resistance developed especially in Shkodër, the stronghold of Islam in Northern Albania, and in small cities of Central Albania, such as Tirana, Kavajë, Elbasan and Durrës. Despite the example given by high religious officials and the order given to civil servants concerning their wives, the veil reappeared after a short period. In some places, women began to wear a xhari, a piece of material which allowed them to uncover their face when meeting a policeman, and quickly to recover it afterwards. Still in 1940, problems were noticed in Kavajë by the civil authorities. 21 In fact, these authorities had received instructions that when applying the law they should not act brutally.

Politically, it was better to convince than to forbid. At the beginning of the campaign, King Zog had sent his three sisters unveiled to Shkodër, along with the Minister of the Interior and other officials, in order to convince the population. 22 Persuasion was also part of the programme of the Albanian Woman Association"s local groups, that were in charge of the organization of conferences. 2319 Zani i naltë [The supreme voice], XII/3, March 1937, pp. 65-73. The law was published in the Official Journal (Fletorja Zyrtare, Tiranë, XVI/15, 10/3/1937, p. 1). 20 A special file in the archives of the Albanian Ministry of Foreign Affairs is devoted to the articles collected in the press of various countries on that reform launched in Albania (AQSh, F. 151, V. 1937, D. 75). See F. Musaj, op.cit., pp. 319-321. 21 F. Musaj, op.cit., pp. 316-319 ;AQSh, F. 882, V. 1937, D. 88, fl.1 ;F. 152, V. 1940, D. 86. 22

The debate and its actors

A multiplicity of actors, with various positions and interests, were involved in this reform, as well as in the debate that surrounded it. There were three categories of actors, all of whom had to take into account the fact that the population was severely affected by the economic and social crisis and that religion was an important reference for the people. These categories, which were not always very clearly separated, were : state representatives, secularist intellectuals and Muslim clerics. In fact, these different actors together represented only a tiny proportion of the population. As in the case of the question of the Civil Code, some non-Muslims participated in the debate, while they interfered to a lesser extent in other reforms of Islam. Nevertheless, the main actors remained Muslims. This reveals that the social division implied by the multi-denominational character of the population was still very important, except for a section of the younger generation. 24 The state representatives

The state representatives did not intervene much in the debate, but they played an important role in the field, because they were responsible for the enforcement of the ban at different levels. In general, the policy they had to implement was dictated by a desire for reform. The aim was to "modernize" the country, but above all to built a "faithful nation" and to assert the sovereignty of the country. However, in concrete terms, the realization of this policy was changing with time and circumstances. Furthermore, the civil servants in charge of its implementation had their own views that could have an impact upon their actions. Mayors, officials, teachers, policemen could act locally according to their own feeling, either enforcing or not the orders received from above. Some of the state representatives were Muslim conservatives who were against the ban. In this case they could be still "more cautious" vis-à-vis the population in implementing the ban. But it seems that, as officials, they were often obliged to set an example. It seems also that, in fact, most of the civil servants even anticipated the government initiatives ; I have already referred to the local initiatives in favor of the ban taken in 1929 by the mayor of Gjirokastër. He asked the city"s population to abandon the veil, because it was the cause of women"s isolation. 25 Teachers, especially those belonging the younger generation, were often more eager for reforms than the government itself. In particular, some of them seem to have called for a clearer and quicker disappearance of religion, and especially of Islam, from the public sphere. 26 This was the case for non-Muslims, but also for young Muslims trained in Western countries or in new schools in Albania. Their attitude reflects both the social competition in which they were involved vis-à-vis the older elites and especially the clerics who had previously exerted a monopoly over education, and the effects of ideas developed by secularist intellectuals. 27 The secularist intellectuals

The secularist intellectuals, who voiced opposition to the veil in the press (or in the parliament) from 1920 onwards, were often guided by a European-centered vision of Islam. They used the question of the veil as a component in the debate on "modernization," "Westernization," "secularization" and strengthening of the state. They generally belonged to the younger generation. Most of them were of Muslim origin, but others were Christians. However, as they were all secularist, their religious origin did not matter so much. Among non-Muslims, there was no specific discourse, even if for them secularization meant not only the separation of state and religion, but also the end of the hegemony of Islam in society. 28 The young Albanians of Muslim origin who took the floor had a different profile. Some were born in important notable families, such as Ali Këlcyra and Namik Delvina. They had studied in the West or in Istanbul, in modern schools where positivism was quite widespread. Other secularist intellectuals were of more modest social origin. They had studied in Western Europe or in Albania. Some of them were attracted by communism, such as Halim Xhelo and Selim Shpuza. 29 25 F. Musaj,op.cit., In April 1928, the cadi of Delvinë (in the South-West of the country) complained that the director of a primary school was opposing the teaching of religion at school (AQSh, F. 882, V. 1928, D. 95). 27 See, for example the case of Safet Butka (1901-1943), trained in Austria (Uran Butka, Safet Butka, Tiranë 2003, cf. pp. 31-34 and 98). 28 In September 1924, the editors of a Catholic newspaper in Shkodër asked the Democratic government to ban the veil in the name of democracy, politics and morality (Ora e maleve, II/37, 6/9/1924, p. 3). 29 The set of articles which I took into consideration is that used by F. Musaj for the period 1922-1923, with articles from the journal Drita (Gjirokastër, edited by a Muslim), Agimi (Shkodër, edited by a Catholic), Mbrojtja kombtare (Halim Xhelo) and Kombi në rrezik (Musaj, op.cit., p.

However, they all were fighting against the "Eastern mentality and habits," and wanted their country to turn to the West, even though they were debating how to do this and some of them were trying to build a specifically Albanian way to "westernization." 30 For the secularist intellectuals, the veil (as well as the ferexhe) was linked with notions of seclusion, servitude and slavery of women. It was associated, not with the outside Muslim world as in the current debate concerning the veil in Western Europe, but with the Ottoman past, seen as synonymous with "yoke," "barbarism," "backwardness," "fanaticism" and "Asia." It was also closely associated with the socio-political decline of the Islamic community and the backwardness of the nation. Indeed the veil was described by such intellectuals as the cause of the backwardness of the whole nation, because Muslims were the majority of the population, and because girls were not educated and did not participate sufficiently in economic life. But, for them, the question was not only intrinsic. There was also the problem of foreign perceptions, and concern that the first impressions gained by "European tourists" (as they wrote) would be to see veiled women in all Albanian cities. These intellectuals considered that the ban on the veil was necessary in order to make Albania a European country or at least to portray it as such. It could lead Albania towards progress and show that Albanians deserved to live as a free people in the middle of Europe. They considered that the geographical location of Albania in Europe, as well as the fact that the country was living in the 20 th century, were two reasons for the ban on the veil. Lastly, they used the example given by Kemalist Turkey, or by other Muslim countries (like Iran and Afghanistan), which had made similar reforms. For instance, in 1923, the deputy Ali Këlcyra declared in the middle of the Albanian Parliament that Mustafa Kemal went to the Turkish Parliament with his unveiled fiancée and that newspaper photographs showed the faces of Mustafa Kemal and "his wife." 31 The case of Mehdi Frashëri Among this group of secularist intellectuals, the figure of Mehdi Frashëri In 1928, the question of the veil enabled him to contrast Bektashism, portrayed as "liberal," with Sunnism, presented as "fanatical" and the enemy of progress. Indeed, in the introduction of his book about the Ancient History of Albania, he tackled the question of religion. He depicted Sunnism as a fanatical form of Islam, which considered every type of progress and every change as a threat to religion, while presenting Bektashism as a "protest" against this type of Islam. According to Mehdi Frashëri, Bektashism prohibited polygamy and, whereas Sunni Islam required women to be veiled, Bektashis considered that women had to be veiled only with the "veil of honour," which was not a material veil. Women therefore were only required to be honorable, and were not required to cover their face. 33 In a long text published the same year as a serial in a newspaper aimed at "intellectuals and patriots," Mehdi Frashëri explained his ideas about "Muslim reforms." 34 He presented the position of the woman and the question of the veil, as well as the perception of Christians by Muslims, as the two revealing factors of the evolution of Islam. The veil appeared with the decline of Islam. Therefore, the most radical reform required was the one concerning the position of women. 35 He claimed that such a reform was necessary in order for Albanians to be included 32 Schmidt-Neke, op.cit., pp. 335-336. 33 M. Frashëri, Historia e lashtë e Shqipërisë dhe e Shqipëtarëve, Tirana 2000 (1928 1 ), pp. 44-45 and 46-47. 34 "Reformat Myslimane në Shqipëri," in Gazeta e re (Tiranë), n°17, 20/11/1928, p. 1 ;n°26, 1/12/1928, p. 2 ;n°27, 2/12/1928, p. 4 ;n°30, 6/12/1928, p. 2 ;n°31, 7/12/1936, p. 3 ;n°35, 12/12/1928, p. 2 ;n°36, 13/12/1929, p. 2 ;n°37, 14/12/1937, p. 2 ;n°39, 16/12/1928, p. 2. 35 Mehdi Frashëri also suggested making other reforms concerning the way of performing prayers and the diffusion of knowledge. In a later article, published in 1931, concerning the economic situation of the country and the lack of development of agriculture, he suggested that one of the factors was that the Islamic religion was humiliating women in numerous ways ("Aveniri I Shqipërisë në pikpamje bujqësore," in Bujqsija, III/1-2, January-February 1931, p. 17).

among "European people." Since Albanians wanted to live free, independent and advanced lives, Mehdi Frashëri saw only two solutions for Albanian Muslims who represented the part of the Muslim world that was face to face with Christian people : either make reforms or Islam would have to disappear from the face of Albania. 36 Only radical reforms like those of Mustafa Kemal in Turkey could bring civilization and independence, as the Christian people experienced four centuries before, with the Protestant reform.

At that time, Mehdi Frashëri was preparing new legislation covering all fields, including family law, previously covered by the Shari"a courts. Thus, his approach to the reform of Islam had another important aspect : that of religious authority. In fact, in the same article, 37 he advocated returning to the sources without the intermediary of an authority, in accordance with Luther"s principle.

Moreover, he claimed that even some features of the Islamic religion urged him to follow this line. Indeed for Mehdi Frashëri, the Prophet himself did not assume authority ; and Islam, as a general principle, opted to have no clergy. Because the educational level of the clerics was too low, and until the arrival of a new educated generation, clerics should confine themselves to the practice of religion, whereas the Muslim councils established all over the country should be made up of educated people, doctors, lawyers, agronomists, professors, etc. Mehdi Frashëri went so far in this direction, that he proposed a totally new training for muftis. He stated that all the country"s madrasas should be closed, and replaced by the establishment of two colleges (one in the South, the other in the North), with a new educational system where Arabic should be taught according to the American Berlitz method. The best students should be sent to Europe to study philosophy, as well as the Arabic language in the departments of foreign languages. On their return, they should be appointed muftis, since, in Islam, those who are more learned are in a better position to interpret the texts and since muftis do not need to wear turbans and jubes.

The "Ulama

It is easy to understand that people holding religious authority reacted to a debate in which Islam was often disparaged and their authority challenged. They were also reacting to the measures taken by the state and its representatives to ban 36 Mehdi Frashëri considered that the other Balkan Muslims, who were under the domination of the Balkan states, were condemned to emigrate to Anatolia. 37 See footnote 34. the veil. However the reactions were expressed in various ways, often depending on the social position of those concerned.

A first group of Muslim clerics was made up of the leaders of the Islamic Community, i.e. of the official religious institutions. These people were themselves reformists. For instance, in 1925, when a national Islamic Congress was convened, they declared that Albania was taking part in the "revival" of Islamic civilization inaugurated by Muhammad Abduh. They wanted to introduce reforms in order to achieve culture, civilization and progress. As a result, the political authorities looked favourably on them. Nevertheless they only had a limited room to manoeuvre vis-à-vis these political authorities, and when they had differences of opinion with them, especially when reforms implied restrictions to their own authority, they had great difficulty imposing their view.38 They themselves did not form a totally homogeneous group. For instance, in 1926, when the students of Tirana"s madrasa asked for authorization to create a sports association, only one member of the High Council of the Shari"a was in favour of this idea. 39 The attitude of the leaders of the Islamic Community concerning the veil had been fluctuating according to their place in the debate and in the process. Until 1929, they generally defended the veil, or at least opposed criticism against it using two arguments -a woman"s honour and religious authority. 40 In 1929 and in 1937, when official measures were taken concerning the ban on the veil, the leaders of the Islamic Community were supposed to have taken the initiative, but, as I have argued, this does not seem very plausible. In 1929, the argument they used to justify the measures taken by the civil authorities, was that the wearing of the veil was not a Qur"anic prescription and that the Islamic religion did not insist on covering the face. Some months later, the Islamic Community published in its journal the translation of a lecture given in the Berlin mosque on a woman"s position in Islam. Here again the interpretation of the Qur"an, inspired by the leader of the Lahori Ahmadiyya, Muhammad Ali, led to the conclusion that uncovering of a woman"s face and hands was lawful. 41 When the veil debate livened up again in the press in 1936, as representatives of the Islamic Community, they choose above all to defend the Islamic religion and, for that, to denounce the criticisms made against the veil, since it was associated by their adversaries with Islam. In the Community"s journal, they denounced the idea that the veiland the Islamic religionwas the cause of the lack of progress of the Albanian nation and accused their adversaries of wanting to force Albanian women to live in excessive luxury. In doing so, they inevitably appeared all the more as the champions of the veil. Yet, relying on the Qur"an, the article concluded that a woman could go out with her face unveiled, but without any make-up, and with a cloak (jilbab) leaving only the face and the hands uncovered. 42 It shows the ambiguity of their discourse.

With the decision of the political authorities to impose the ban on the veil at the beginning of 1937, the leaders of the Islamic Community were placed in a different position. Again they had to justify, at the religious level, such a decision and even to appear to promote it. The arguments presented in these new circumstances were in fact of various types. 43 Some were of course religious. B.

Shapati explained that, according to verses 31-32 of Surat XXIV of the Qur"an, a woman had to be covered in front of foreigners. But according to Imam Azam, this prescription excluded the face and hands. All the Hanafi "ulama preached this interpretation. Later on, because of the problems that appeared in Muslim societies, Muslim jurists had prohibited women from showing their face. 44 According to fiqh books, a Muslim woman had the right to work outside the home, to trade, to be a witness at the court, etc. Then B . Shapati wrote :

"Ibn Abidin said that the fact that a free woman shows her face is not haram [unlawful], but it is not necessary, it is meqruh [not forbidden by God, but looked upon by Muslim teachers with disgust] ; According to this prescription, we issue the following fatwa : The foreigner, Zeyd, when he sees the face of a foreign woman, Hindi, is it haram ? Answer : it is not haram." 45 41 "Gjendja e Grues n"Islamizmë," Zani i naltë, VI/4, March 1930, pp. 966-976. 42 "Zbulimi u Grues Muslimane," Zani i naltë, XI/5, May 1936, pp. 142-149. One of the arguments used against their adversaries was also that the latter wanted the unveiling only because of the shame vis-à-vis foreigners. So they accused the secularist intellectuals of wanting "to destroy the country in order to please the foreigners." 43 Zani i naltë, XII/3, March 1937, pp. 65-77. 44 B. Shapati argued that some regions, in particular mountainous areas, continued to observe the true prescriptions of the Prophet and did not veil women. Thus, for nationalists, mountainous areas appeared as the bastion of tradition. 45 Ibid.

Apart from the religious justification, the leaders of the Islamic Community also used the rhetoric of the civil authorities, and eventually that of the secularist intellectuals they had opposed. They presented abandoning the veil as a "social measure." They explained that its main aim was to improve the position of Muslim women within Albanian society, because the fatherland needed such an investment of women in social life in order to achieve, as soon as possible, the level of cultural progress and economic development of a civilized country. Moreover, they did not forget to mention that the measure was taken just at the time when the King promised a set of reforms.

Like the secularist intellectuals, their arguments were also structured round the question of perception. The veil had become a problem because it was misused by some people, and, because it was considered as a prescription of the Islamic religion, the result was a criticism of the Islamic religion itself. Abandoning the veil was therefore necessary to enlighten the true nature of Islam in the mind of public opinion. The fact that Albanians, particularly Muslims, wore different clothes made others laugh at them. Every day, "foreign tourists" were taking photographs of Muslim women, showing them to the rest of the world as testimony to the barbarian nature of the Muslim religion. Just like the secularist intellectuals, the leaders of the Islamic Community declared lastly that in the 20 th century and in the middle of Europe Albanians had to adapt themselves to all the "good customs" of the civilized nations.

In this way, urged on by the political authorities, the leaders of the Islamic Community, henceforth seemed to agree with the young religious Muslims sent to Lahore (India), who had expressed a different position during the debate in 1936. This small group of future "ulama, who were not yet involved in the leadership of religious affairs, had published at that time an article about the veil in their small journala supplement to the journal of the Lahori Ahmadiyya, The Light. 46 Like the leaders of the Islamic Community, the authors criticized those who wanted unlimited freedom for women to mix with any foreigner. They also drew the same conclusions from the analysis of the Qur"an, which they considered as giving the principles of religion and civilization : there was no prescription concerning the 46 Sherif Putra, "Moda e mbulesës dhe veçimi i grave," in Drita (Lahore), n°6-8, June-July-August 1936, pp. 6-19. In fact, this text was a translation of an article written by the head of the Lahori Ahmadiyya, Muhammad Ali, and published in 1905 in The Review of Religions. This appears in the second part of the text which was published in the journal of the Albanian Islamic Community in 1937, after the ban on the veil (Zani i naltë, XII/5, May 1937, pp. 202-213).

covering of the face and the hands. However, they seemed to hold an opposite position in the debate. Indeed, they were convinced that the progress of Muslims was closely related to "solving the problem of the veil." Like the secularist intellectuals, they even declared that the veil was responsible for the educational backwardness of Muslim women.

But the real difference was between the leaders of the Islamic Community and other "ulama who were against lifting the veil. These people did not use the press or any printed matter to express themselves in public space. Nevertheless, we know that the leaders of the Islamic Community had to face opposition from such "ulama, which they tried to hide 47 . In fact, a blurred frontier existed between these "ulama and those belonging to the official Community who only reluctantly accepted the lifting of the veil. But the "ulama who opposed the ban on the veil had been against both the other reforms (introduction of the Civil Code and closing down of Shari"a courts and local madrasas) and the new religious hierarchy close to the political power. Apart from their real opinion concerning the veil, it provided a good opportunity to oppose the fatwa and the law.

It would have been interesting to know how a reformist "ulama like Hafiz Abdullah Zëmblaku, who choose to have no relations with the authorities and who remained outside the new religious institutions, reacted in the 1937"s debate. A former reader of the Turkish Islamist journals Beyanülhak and Sebilürreşad, in the 1920s he took as a model the missionaries of the Lahori Ahmadiyya, with whom he was in contact. He claimed to have the same objectives as this network : to make accessible to everybody the religious prescriptions and texts in vernacular languages, to work against the superstitions that entered into religion, to defend the Shari"a and to reinforce the bonds between Muslims, to show that Islam was a modern religion and that the clerics were also acting on the path to civilization, as well as to oppose the intense activity of Christian missionaries. That is why he worked for the teaching of religion and true beliefs in the Albanian language, through courses, preaching and a set of booklets. He even invented a transcription of the Arabic language in Latin script in order to make it more accessible. 48 We know that at the beginning of 1938 Hafiz Abdullah Zëmblaku was confined by the political authorities in the city of Vlorë, but we do not know the 47 Whereas a report from Elbasan shows that there were opponents (AQSh, F. 882, V. 1937, D. 88, fl.1), the journal of the Islamic Community published a false report showing that there was no opposition to unveiling (Zani i naltë, XII/3, March 1937, p. 96). 48 See, for example, H.A. Sëmlaku, Bilbil i gjashtë. Kanarja, 1930, Korçë, p. 41-43, Bilbil i shtatë, 1931, Korçë, p. 15, 24-26, Bilbil i tetë, Korçë, 1931, p. 15-21. reason for this.49 Some years before, however, he seems to have had an intermediary position on the question of the veil, between the young students in Lahore and the leaders of the Islamic Community. He criticized those who were against the veil, as well as those who were in favour of it for the wrong reasons.

He considered that religious prescriptions obliged a woman to wear a complete veil, but that the old ferexhe was not necessary ; a modern thick coat was much better, with a headscarf (shami) on the head and a kind of shawl.50 Three years later, like the leaders of the Islamic Community, he appeared to deny the right of newspapers to address the question of the veil which he saw as an issue that concerned only the "ulama, thus reducing the debate to the question of the religious authority. 51

Therefore, we can see that multiple issues appeared throughout the debate and the way the question was tackled by the different categories of actors.

The stakes behind the veil

In the first place, it is clear that the debate and the measures concerning the veil had their climax when political and social events or crisis occurred : at key moments in the state building process, at times when the country"s sovereignty was questioned, and during economical and social crises. Whereas Islam was a mean of social control for the political authorities against the spread of Communist ideology in society, notably among young people, the question of the veil had a particular meaning. In 1937 it became a tool of foreign policy deployed to assert Albania"s sovereignty. However, because it symbolized the "modernization" and "europeanization" of the country for secularist intellectuals and civil servants, the ban was also a sign given to these groups and to the rest of society that the state building process was progressing. So they had to be faithful to the country and the government. More generally, the problem of the relationship between religion and state was crucial.

State and religion

Throughout these debates and measures, the relationship between state and religion appeared repeatedly. In 1923, when the ban on the veil was discussed in parliament along with the prohibition of polygamy, some deputies reacted saying that such decisions could not be taken by the Assembly and that the government had no right to intervene in religious affairs. Time and education would resolve the problem. Others believed in duty of parliament and the state to take care of the cultural and social development of the nation and thus to solve this kind of question. Using a juridical approach, Mehdi Frashëri sided with the former (claiming that parliament had no authority in religious matters), but explained that other questions, such as the equality between women and men before the court, and inheritance and divorce, could be debated by the Assembly. 52 In the following years, the Albanian government did in fact adopt the latter position and often interfered in religious affairs, by directing, controlling or using the religious scene, as illustrated by the question of the veil. That is why we can say that the Albanian state was multi-denominational rather a-denominational. There was no separation of state and church as, at least theoretically, in France. But, as in Turkey, only the government could combine religion with politics. 53 The difference with Turkey was that, despite Albania"s Muslim majority in demographic terms, the state did not give the nation a Muslim character, which means that there arose the question of the plurality of confessional groups.

The problem of building a nation out of several denominational groups appears clearly in the arguments put forward by Mehdi Frashëri in his famous article of 1928 on the reforms of Islam. For him, Albania"s fate was linked to the progress of the Muslim community, since it formed the majority of the population.

In order to achieve a true and non superficial union of the different parts of the nation, which was a question of survival for a small nation like Albania, the Muslim majority had to be liberal. At the same time Mehdi Frashëri thought that abandoning Shari"a-based jurisprudence was necessary not only because this was an "old-fashioned" legislation and because religion concerned the consciousness and legislation of the state, but also because the Albanian people was made up of non-Muslims as well as Muslims. 54 Like Mehdi Frashëri himself, people who were not Sunni Muslims (e.g. Bektashis or Christians) had of course a specific position towards the former dominant religion. They wanted it to loose its hegemonic status, and demanded for more rights for other denominational groups. 55 In the course of the debate, the question of the secularization of public space also arose, since the veil was generally considered as a mark of the Islamic religion. Secularist intellectuals, as well as a lot of officials and political leaders, seem to have been extremely sensitive to this, also because for them "secularization" was synonymous with "de-ottomanization" and "modernization".

All marks of Ottoman domination, often mistaken for marks of Islam, were to be banned, leading to a certain depreciation of Islam. Public space was partially deislamized, especially in schools and in the administration, but also in urban space, even if the state itself contributed to the building of some mosques during the interwar period. Consequently, the context was not that of the re-islamization of the public sphere and "disillusioned secularization" that characterize Western Europe today. 56 Another difference with the current situation in some European countries is that the school was not the main theatre of the public sphere involved in the debate on the veil. In Albania at that time, the percentage of girls attending school was rather low ; veiled girls were simply not sent to school. 57 However, apart from the veil, the separation of religion and education, which was an important facet of state politics, notably through the question of religious teachings, became a subject of polemics. Hafiz Abdullah Zëmblaku, for instance, saw the state, and particularly the Ministry of Education, as enemies of religion and promoters of unbelief. He considered them as "Young Turks" and "Free-Masons." He himself had a lot of trouble with the authorities which banned him from teaching the 54 See reference in footnote 34. Here the difference between the Albanian and the Turkish case has to be stressed. In Albania, the non-Muslim minorities were larger (approximately 30% of the population), and most of the non-Muslims were also ethnic Albanians. 55 In 1923, as well as in 1929, the question of relations between the Islamic Community and the Bektashis was at the heart of the question of religion and state. 56 The expression is from Jocelyne Césari and Jean Baubérot ("Laïcité, communautarisme et foulard : vrais et faux débats," http://lmsi.net).

57 Musaj, op.cit., p. 142. seen. 61 In the same way, in 1935, Hafiz Abdullah Zëmblaku explained that, since the Kingdom had no official religion, religion was free and nobody had the right to meddle with religious matters, except the religious scholars. Thus, he urged the journalists to speak about the economy rather than religion. 62 The secularist intellectuals were really challenging the religious authority because of their direct access to the Qur"an through translations 63 and their constant attacks on Islam, but also because of widespread ignorance among Muslim clerics. This led some Muslims to react by proposing a plan to train clerics capable of guiding people with an Eastern as well as a Western culture, and more generally to launch reforms based on ijtihad. 64 Furthermore, the question of the veil reveals that the authority of the leaders of the Islamic Community was not only challenged by secularist intellectuals but also by some religious entrepreneurs. The new religious hierarchy had difficulty gaining recognition from all the country"s Muslims. Some "ulama were unwilling to accept the reforms which the Community had agreed to implement in close collaboration with the civil authorities, or to accept the new hierarchy and the centralization of the religious authorities. Hafiz Abdullah Zëmblaku, for example, had refused a position of mufti. A lot of "ulama in Shkodër went on teaching in a traditional way, without any contact with the new Tirana Madrasa. Most of them considered the introduction of the Civil Code and the ban on the veil as being in conflict with the Shari"a. 65 Europe as reference or towards a "European Islam"

Despite the opposition, if we analyze the content of the whole debate, it is striking to see "Europe" appearing as a common reference for all the actors, 61 Later on, in July 1938, Mehdi Frashëri gathered Muslim intellectuals in the Albanian capital, in order to help the cultural development of the "Muslim element" (Zani i naltë, n°8, August 1938, p. 255). 62 Bilbili besëtar, Korçë, 28 September 1935, pp. 51-52. 63 A first partial translation of the Qur"an had been made by a Christian Albanian (1st fascicle, Bucarest, 1921 ; 2d fascicle, Korçë, 1928). In addition, an English translation and commentary by Muhammad Ali, from the Ahmadiyya, was circulating in the country. 64 "Persri mbi fonksionarët t"onë fetarë," in Zani i naltë, August-September 1930, pp. 1121-1126. 65 See, for example, the great debate about the required reforms which started in 1927, whose echoes are to be found in the journal of the Islamic Community (Zani i naltë). After this period, the only criticism expressed towards the leaders of the Islamic Community through printed matter was that of Hafiz Abdullah Zëmblaku, but it certainly points to a broader opposition.

whatever their position concerning the veil. 66 In fact, the relationship between Islam and Europe was at the heart of the debate. The Islam shaped by all the actors was not only an Islam in Europe. In the Paris mosque, in 1930, Ilyas Vrioni, the Albanian Ambassador, presented his country as "a fortress of the Islamic traditions in Europe". 67 But it was also a "European Islam." For the secularists, as we have seen, the reform of Islam had to be carried out precisely because the country was situated in Europe. On the other side, Hafiz Ismet Dibra, one of the leading "ulama of the official Community, agreed with Mehdi Frashëri that Muslims, although a majority in Albania, would not be able to live and to retain their faith, without accepting the principles of "modern" and "European" life. In particular, in order to live in the middle of Europe it was necessary for them to make their own all kind of sciences that were the product of progress.

Consequently the reform of Islam was essential. 68 Nevertheless, it seems that the position of the various actors was not exactly the same vis-à-vis this reference. For the secularist intellectuals or state representatives, the reference was always positive, whereas for the "ulama, it could be positive or negative. The "ulama used it when they wanted something from the government, when they answered the secularists or when they wanted to convince Muslims about the need for reforms. Thus, they often mentioned that European states had realized again the importance of religion, had strengthen the teaching of religion at school or hosted religious Congresses. They pointed to the fact that even developed countries did not prevent their people from being "fervent believers". Even Abdullah Zëmblaku, when he was criticized for using too many Arabic words, argued that, in Europe too, Arabic words had been incorporated into the language. 69 In this way they were highlighting out European realities that the secularists and Westernists did not refer to. However, when the "ulama tried to revalorize Islam, they could oppose "Europe" to "Islam" in a negative way for the former and a positive way for the latter. In this case, Europe became « materialist », the seat of unbelief, of women"s dishonour, of luxury and frivolity. 70 The official Islamic hierarchy, through its journal, denounced the "new 66 Here, of course, I cannot take into account the adversaries of the ban on the veil who did not take part in the debate through printed matter. 67 AQSh, F. 882, V. 1930, D. 114. 68 See reference in footnote 60. There was never a debate about darülharb and darülislam. 69 See, for example, "Veprimet e Këshillit të Naltë të Sheriatit dhe nevojat e trupit musliman," in Zani i naltë, II/3, Maj 1925, pp. 459-464 ;"Bisedimet e Kongresit Muslyman," in Zani i naltë, II/4-5, June-July 1925, p. 502 ;Hafiz Ali Kraja, op.cit. ;H.A. Sëmlaku, Trëndafil i 1, Korçë, 1932, p. 154. 70 See, for example, "Zbulimi u Grues Muslimane," in Zani i naltë, XI/5, May 1936, pp. 142-149. trends with a European influence", the "Oksidentalofilë" (those who loved the West). 71 Another important reference in the debate was Turkey, as was the case throughout the Muslim world at that time. 72 The reforms of Mustafa Kemal were quoted as an example by the secularists and the state representatives. 73 On one hand, the leaders of the Islamic Community, probably with the aim of convincing the political authorities, explained that Mustafa Kemal was not against Islam. 74 But someone like Hafiz Abdullah Zëmblaku could criticized the "Young Turks" and the "masons" of Turkey, as bad examples for the Muslim world, while criticizing the state representatives as well as the leaders of the Islamic Community. 75 On the other hand, references to the Arab World (or to India) posed problems, and arguments based on such a reference were violently rejected by secularist intellectuals. 76 Even the Arabic script and the Arabic language were stigmatized by the secularists as well as by the state representatives. The political authorities tried to ban prayers (dua) in Arabic from the public sphere, arguing that it could make a bad impression on foreigners ; that the people had to understand what they were hearing ; and finally, that it was contrary to the independence of the Albanian Islamic Community. 77 This last point shows that the authorities, as in France today, were faced with the problem of "domestication in a global religious field". 78 Albanian Islam and external networks 71 Ibid. 72 See Catherine Mayeur-Jaouen and Anne-Laure Dupont (eds.), Débats intellectuels au Moyen-Orient dans l"entre-deux-guerres, REMMM, n°95-96-97-98, 2002. 73 In the religious field, the Turkish model could even be followed very concretely. Thus, in 1928, the Albanian ambassador in Ankara sent a collection of khutbas for translation into Albanian because, "it fitted with the religious principles and to the need of the time". The book was translated as Këshillet e së premtes (Shkodër, 1928). 74 See, for example, "Vepra e Gazi Qemal Ataturkut," in Zani i naltë, X/3, March 1935, pp. 81-84 ; "Përsëri Mustafa Kemali flet mbi maltësinë e Islamizmës…," in Zani i naltë, X/9-10, September-October 1935, pp. 319-320. 75 Trëndafil i 1, Korçë, 1932, p. 120. 76 See, for example, the article "Zani I naltë kundra Qytetnimit," published in Bota e re (n°20, 30/1/ 1937), where the author, Selim Shpuza, criticized the journal of the Islamic Community for having quoted the discourse of an Arab shaykh of Al-Azhar (Selim Shpuza, Vitet "20-"30, Tiranë, 1999, pp. 146-151). 77 AQSh, F. 882, v. 1926, D. 90, fl. 1-2. foreign individuals or institutions; correspondence with religious centres situated abroad had to be authorized. 84 Thus the progressive ban on the veil which occurred in Albania in the interwar years reveals different phenomena. In order to build and to gain recognition for their state in the "middle of Europe," and despiteor because ofthe Muslim majority in the country, Albanian political authorities and secularist intellectuals wanted to built a "modern" and "European" Islam. Their action was also dictated by a wish for secularization in order to set up a multi-denominational nation, but also by the devalorization of Islam among the elites. Some leaders of the Islamic Community were also convinced of the need to build a "European Islam", but not exactly in the same way, and not at the expense of a loss of power.

The most significant result of their action was the appearance of a new religious elite promoting an Islam of the Qur"an and of progress, such as that presented by the Lahori Ahmadiyya working at that time in the middle of Europe for the promotion of Islam. However, the process of banning the veil shows the complexity of building a European Islam "à l"albanaise", i.e. a specific approach to secularization, a submission of the upper levels of the Islamic official hierarchy to the political authorities, a difficulty for this hierarchy to impose itself on all Muslims in the country and a limited impact of the reforms within Albanian society. 84 See the text of 1923 on the status of the religious Community (AQSh, F. 152, V. 1923, D. 855, fl. 15), and Roberto Morozzo della Rocca, Nazione e religione in Albania (1920-1944), Bologna 1990, p. 32.

  occupied a specific place. Deputy, civil servant, minister, president of the Council of State and intellectual, he was one of the main officials responsible for the autonomy of the Bektashi Community, which he represented in 1943-1944 on the Regency Council, being himself a Bektashi Muslim. He was also one of the main architects of the Civil Code introduced in 1928-1929 in Albania. 32

  The most significant work in this respect was that of Hafiz Ali Korça (Bolshevizma. Çkatërimi i njerëzimit [Bolshevism. The destruction of humanity], Tirana 1925). From 1933-34 on, atheism was one of the main targets of the Islamic Community in its journal. See also the booklet of Hafiz Ali Kraja (A duhet feja. A e pengon bashkimin kombëtar [Is Religion necessary. Does it prevent the national union], Shkodër 1934).

11

Thus, in 1929, all the provincial madrasas were closed down and a new General Madrasa 8 AQSH, F. 882,

V. 1922, D. 10, fl. 26 ; V. 1931, D. 106, fl. 3-4 ; V. 1936, D. 53, fl.

1 ; Zani i naltë (Tiranë), XII/2, February 1937, p. 34. In 1937, measures were taken by the political authorities against Communist groups (cf. Michael Schmidt-Neke, Entstehung und Ausbau der Königsdiktatur in

Albanien (1912-1939)

, Munich: Oldenbourg 1987, p. 262). 9 10 Nathalie Clayer, L"Albanie, pays des derviches, Berlin : Otto Harrassowitz 1990. About the reactions of the Muslim religious leaders, see for example AQSh,

Albania was first recognized by the European powers as an independent principality in 1913, but it was occupied by different countries during the First World War.

The expression is from Xavier Bougarel.

See my forthcoming book Aux origines du nationalisme albanais. La naissance d"une nation majoritairement musulmane en Europe.

Approximately 20% of the population were Orthodox Christians, mainly in the South of the country, and 10% Catholic Christians, mainly in the Northern part.

Arkivi Qendror i Shtetit (AQSh), Tirana, Fondi 152 (Ministri e puneve të Brendshme),Viti 1923, Dosja 31, fl. 1-3.

See for exampleAQSh F. 152, V. 1925, D. 623 ; F. 882 (Komuniteti Mysliman), V. 1929, D. 3 ; Statuti i Komunitetit Mysliman Shqipëtar, Tiranë, 1929. In this text, "Community" with a capital letter refers to an institution and not to a group of people.

AQSh, F.

882, V. 1926, D. 90, fl. 17-26.

See Alexandre Popovic, L"islam balkanique, Berlin: Otto Harrassowitz 1986, pp. 27 ss.

Here the discussion will be on the veil (perçe in Albanian), covering the face, and not on the headscarf. At that time, in Albania, the veil was worn by urban women, whereas in the countryside it was quite rare.

In 1923, following a proposition of Ali Këlcyra, a deputy from Southern Albania, the President of the Albanian Parliament proposed a vote concerning a recommendation to the government to make propaganda through the Islamic Congress in order to improve the social life of women, taking Turkey as an example. But the proposition was not never put to the vote (Bisedimet e këshillitKombtar, viti III, n°4, Tiranë, 1923, pp. 49-57).

Fatmira Musaj, Gruaja në Shqipëri [The woman in Albania] (1912-1939), Tiranë:Akademia e Shkencave 2002, pp. 306-307.

Ibid.,

Ibid., p. 311.

Ibid.

F. Musaj, op.cit., p. 302.

On the political level too, religious diversity was marked. Members of parliament represented proportionally the denominational composition of the population.

140-143). Among the most important texts I used are also texts published in the newspaper Zëri i popullit, from Korçë inMarch 1923 (n°28) and in March-April 1924 (29/3 and 6/4), articles published in Shqipëria e re, in Rumania, in April 1925 ; various articles from Namik Delvina published in his newspaper Ora in 1932 (see n°541,544, 561) ; articles written by Mehdi Frashëri quoted below, as well as some of his texts published in the journals Illyria in 1934 and Minerva in 1935 ; two articles published in Arbënia (n°209 et n°256 of 1936) ; and the article of Selim Shpuza published in 1936 in the journal Bota e re, under the title « Modernism and çarçaf » (n°7).30 In 1934, the journal Illyria (n°38, 11/1/1936, p. 1), explained that it was necessary to form a front against Eastern influences, and to assimilate the Western mentality, not by importing it, but by creating an Albanian culture.31 Bisedimet e këshillitKombtar, viti III, n°3, Tiranë 1923, p. 48.

It was particularly the case when the jurisdiction of Shari"a judges were limited in 1919 and when the Civil Code was introduced in 1928-1929.

AQSH, F. 882, V. 1926, D. 71, fl. 1-2. This member was Salih Vuçitërn, a figure who belonged both to the religious and to political field.

In 1924, the mufti of Shkodër criticized the idea put forward in Catholic newspaper to ban the veil (see footnote 28), because it undermined Islam, and stated that if the Catholics committed a second offence, there would be a quarrel between the two "elements" (Zani i naltë, I/11, August 1924, p. 348). Reacting to the same affair, the Muslim editors of the newspaper Dajti in Tiranë explained that the veil was one of the fundamental means of preserving a woman"s honour(Dajti, n°45, 17/9/1924, p. 3). As we will see below, in 1928, the answer of Hafiz Ismet Dibra to Mehdi Frashëri mainly concerned the question of religious authority.

H.A. Sëmlaku, Kanar I ri dhe bilbili faqe bardhë,Korçë, 1938, p. 5.

So it is unclear whether he considered that the face had to be covered or not(H.A. Sëmlaku, Trëndafil i 1, Korçë, 1932, pp. 169-170.

See below.

Bisedimet e këshillitKombtar, viti III, n°4, Tiranë 1923, pp. 49-57.

See H. Bozarslan, "Islam, laïcité et la question d"autorité de l"Empire ottoman à la Turquie kémaliste," in Archives de sciences sociales des religions, n°125,January-March 2004, pp. 99-112.

Albanian language, because he taught it together with religion. 58 Here we can perceive of course the problem of the loss of legitimacy for clerics in the educational sphere, mentioned above. As a result, the journal of the Islamic Community strongly denounced the role of teachers in propagating atheism and bolshevism. 59 But, for Hafiz Abdullah Zëmblaku, even the head of the Islamic Community, who sided with the political authorities, was an enemy of religion and a promoter of unbelief. The religious authority in itself was thus also questioned.

Religious authority

The question of religious authority came up in the debate on the veil firstly because the ban on the veil was considered as one of the key reforms of Islam to be implemented and because some of the actors raised the following questions : who is able to debate about Islam ? who can decide on reforms ?, and who can lead them ? I already pointed out that the leaders of the Islamic Community very often used the argument of religious authority to answer opponents of the veil. In 1928, when one of the leaders of the Islamic Community, Hafiz Ismet Dibra, had to answer the long article by Mehdi Frashëri, he answered not directly to him, but to "the Muslims who wonder after reading Mehdi"s Frashëri on the reforms of Islam." Moreover, instead of criticizing the point of view of his adversary, H.I.

Dibra first denied his authority in the field of religion, pointing out all his "mistakes" as proof of his incompetence. In particular, Mehdi Frashëri"s tendency to imagine an ijtihad (rational interpretation) out of context of the Shari"a, as well as his failure to show signs of respect towards the Prophet, were considered unacceptable. 60 Such an answer, in fact, followed the same line as that of Mehdi Frashëri, since the latter had advocated returning to the sources without the intermediary of an authority, proposing to establish Islamic councils composed of laymen and to train new muftis using modern educational methods, as we have 58 See, for example, H.A. Sëmlaku, Bibil i Fesë. Sheri-ati Muhamedija, Korçë, 1930, pp. 77-79 and Trëndafil i 1, Korçë, 1932, pp. 83 During the inter-war period, many Albanian entrepreneurs were in contact with the outside Muslim world : with Turkey, Egypt, India and with Muslims in the Balkans and in the rest of Europe. 79 These contacts were used in the local field in different ways and for different purposes : to train students, to obtain Islamic literature, to benefit from various debates, etc. Apart from their relations with Egypt, the leaders of the Islamic Community, in particular, made extensive use of their relations with the Lahori-Ahmadi network based in India, as well as in Berlin, Vienna or London. From 1927 onwards, they sent students to Lahore and ordered the translation of many articles and booklets developing the idea of the compatibility between Islam and modernity in order to reply to the arguments of those who devalorized Islam and to underline the compatibility of Islam and Europe embodied by the activities of the Lahori missions in England or Germany. 80 Hafiz Abdullah Zëmblaku, although opposed to the Community, also justified his "missionary action" in putting forward the work of the Lahori-Ahmadi in the Western World and his own contacts with them. He also used their networks to disseminate his method of transcription of Arabic. 81 However, it seems that an official networking was not possible, because of the principle of nationalization imposed by the state. As early as 1923, the decision to break with the Caliphate had been of specific political importance with the aim of setting up an independent Islamic Community. Eight years later, when the leaders of the Albanian Islamic Community received an invitation to attend the Jerusalem Congress, they declined it on the pretext that their Treasury did not have sufficient funds to send a representative. 82 There was also no delegate from Albania at the Geneva Congress of European Muslims held in 1935. 83 We have to point out that, according to the law, religious communities in Albania could not be financed from abroad and could only have spiritual and cultural relations with 78 John R. Bowen, "Does French Islam Have Borders ? Dilemmas of Domestication in a Global Religious Field," in American Anthropologist, 106(1), 2004, pp. 43-55. 79 A lot of them corresponded with different persons from abroad, the hajj was performed, and students were sent to Egypt (some to University and some to Al-Azhar) or even to Lahore. 80 Nathalie Clayer, "La Ahmadiyya Lahori et la réforme de l"islam albanais dans l"entre-deuxguerres," in De l"Arabie à l"Himalaya. Chemins croisés en hommage à Marc Gaborieau, Véronique Bouillier and Catherine Servan-Schreiber (eds.), Paris, 2004, pp. 211-228. 81 See footnote 48. 82 AQSh, F. 882, V. 1931, D. 116. 83 The Albanian participants to these congresses came from Macedonia, i.e. from Yugoslavia.


Michel Bellet

Implementation of surface tension with wall adhesion effects in a three dimensional finite element model for fluid flow

Keywords: surface tension, finite element method, average curvature, consistent normal vectors, wall adhesion

This paper addresses the finite element modelling of surface tension. The external stress vectors associated with surface tension are assumed proportional to the average curvature and oriented along the normal vector to the fluid surface. The issue of estimating the average curvature of a discretized surface is then discussed. It is proposed to use the surface divergence of a field of nodal normal vectors. A special attention is devoted to the calculation so called consistent normal vectors. In the case of a surface composed of linear triangular facets, it is demonstrated that these normals are given at each node by the average of the normals of the surrounding facets, weighted by their surface. In order to account for wall adhesion effects, the method which consists in modifying the normal vectors at nodes in contact is discussed and extended to the three dimensional case. In order to validate the approach, the three dimensional finite element resolution of the equilibrium a drop of liquid on a plane is treated.

At the surface of a liquid, surrounded by a gas, some forces develop, due to out of balance molecular forces of attraction acting on the molecules close to the surface [START_REF] Nelleon | Mechanics and properties of matter[END_REF]. Such molecules are submitted to a resulting force that tends to attract them towards the interior of the fluid, inducing a state of tension in the liquid surface. Such phenomena play an important role in fluid dynamics, as they are able to affect significantly liquid flow through thin tubes or between planes, when surface effects are important. Surface tension effects are also encountered along the surface separating two immiscible fluids.

We consider here a fluid surrounded by an inviscid fluid of pressure . From a macroscopic point of view, surface tension effects reduce to an additional normal stress applied to the fluid surface. Locally, the normal stress vector T will have the following expression, according to the Laplace formula [START_REF] Landau | Fluid Mechanics[END_REF]:

n n σn T κ γ - - = = ( 1
)
where σ is the Cauchy stress tensor, n the outward unit normal vector, γ the surface tension coefficient (in units of force per unit length) and κ the local average curvature of the surface (assumed positive when the surface is locally convex).

The implementation of such forces in a finite element model depends on the formulation. In the framework of Eulerian formulations, in which the fluid surface is tracked through a fixed mesh (volume of fluid -VOF -or other methods), this raises two problems. First the accuracy to which the free surface is determined is most of the time insufficient for a correct determination of local normal vectors. Second, the determination of the applied surface loading is difficult. To overcome these difficulties, Brackbill et al. [START_REF] Brackbill | A continuum method for modeling surface tension[END_REF] propose to represent the vicinity of the fluid surface as a transition region of finite thickness. In this region, the volume of fluid function varies continuously from 1 to 0. The normal vector can then be approached by:

∇ ∇ - = 1 n (2)
The authors demonstrate that surface tension forces can then be reduced to volume forces, eliminating the need of surface reconstruction. They have applied this method to two dimensional fluid flow computations.

In order to eliminate any imprecision issued from free surface and associated normal determination, Navti et al. [START_REF] Navti | Finite element modelling of surface tension effects using a Lagrangian Eulerian kinematic description[END_REF] have preferred an arbitrary Lagrangian Eulerian (ALE) formulation in which only the fluid domain is enmeshed, yielding an explicit description of the free surfaces. In this case, the stress vector issued from (1) is directly entered as an external stress vector in the weak form of the momentum equation. This method has been applied by the authors to different two dimensional cases.

In the present paper, we will present the implementation of surface tension in a three dimensional finite element model for fluid flow, using an ALE formulation. In a first section, the numerical model will be presented. Then the implementation of surface tension will be detailed in section 2. Two methods will be presented for the computation of the average curvature of faceted three dimensional surfaces. Then, in part 3, wall adhesion effects will be discussed. Finally, in section 4, a validation of the method will be presented through an application to the three dimensional resolution of the static equilibrium of a drop of liquid.

Before discussing the implementation of surface tensions, it is necessary to present briefly the finite element model which has been used.

Governing equations

The equations governing the motion of an incompressible Newtonian fluid are the following momentum and incompressibility equations :

     = ∇ = ∇ + ∇ - 0 . 2 v g v v ρ µ ρ (3)
where v denotes the fluid velocity, ρ the specific mass, µ the dynamic viscosity, the pressure, g the gravity vector.

Boundary conditions

Ω denotes the domain occupied by the fluid at a current time (boundary ∂Ω). The boundary conditions are the following.

• Free surface boundary, Ω ∂

A given normal stress vector is applied:

T σn = (4)
This vector T , colinear to the outward unit vector n, results from the pressure of the surrounding fluid (default pressure is the atmospheric pressure) and from surface tension, according to [START_REF] Nelleon | Mechanics and properties of matter[END_REF].

• Solid wall boundary, Ω ∂

A sticking contact condition can be considered ( v v =

). In practice, the near wall region is often affected by steep velocity gradients and the sticking contact condition can require a very fine mesh near walls. An alternative consists in using a wall friction law of Newtonian type in which tangential sliding is permitted, the tangential stress vector T depending on the tangential velocity of the fluid v , according to the relation, α being a friction coefficient:

v T αµ - = (5)
In addition the non penetration condition has to be fulfilled:

0 ). ( = - n v v (6)

Velocity pressure formulation

The weak form of previous equations is given hereunder, where velocity and pressure are the primitive variables for which the problem has to be solved

       = ∇ ∀ = + - - ∇ - ∇ + ∇ ∀ ∫ ∫ ∫ ∫ ∫ ∫ Ω Ω Ω Ω ∂ Ω Ω 0 . 0 . . . . : ) ( * * * * * * * * v v v v g v T v d v v v ρ ρ µ (7)
where * and v * are any virtual velocity and pressure fields, d * being the strain rate tensor associated with v * .

Time discretization

Given the configuration occupied by the fluid at time , the equations to be solved for (v, ) , velocity and pressure field at time , can be expressed in the following way:

       = ∇ ∀ = ∆ - + - - ∇ - ∇ + ∇ ∀ ∫ ∫ ∫ ∫ ∫ ∫ Ω Ω ∆ - Ω Ω ∂ Ω Ω 0 . 0 . . . . : ) ( * * * * * * * * v v v v v g v T v d v v v ρ ρ µ (8)
The time derivative of the velocity is approached by a Euler backward finite difference scheme:

) ( 1 ∆ - - ∆ = v v v (9)
where v and v ∆ are the velocity of the same fluid particle respectively at time and ∆ . The latter is obtained by an advective transport procedure described later. After resolution, the configuration updating is defined by: [START_REF] Gray | An efficient finite element scheme for two dimensional surface water computation[END_REF] This unconditionally stable Newmark scheme is second order accurate and is also called Adams Bashforth scheme (AB2). It is equivalent to assume a constant acceleration over each time step [START_REF] Gaston | An Arbitrary Lagrangian Eulerian Finite Element Approach to Non Steady State Turbulent Fluid Flow with Application to Mould Filling in Casting[END_REF].

      - ∆ + = ∆ + ∆ + = ∆ - ∆ + v v x v v x x 2 1 2 3 2 2
Regarding the non penetration condition along solid walls, it is enforced by a penalty technique. The normal stress vector is defined by:

n n v v v T ∆ -       - - - = ∆ - δ χ . 2 1 2 3 ( 11
)
where χ is the penalty constant, δ is the algebraic distance to the wall at time . The expression between brackets is taken equal to zero when negative (loss of contact).

Finite element discretization and resolution

Equations ( 8) are discretized with tetrahedral P1+/P1 elements [START_REF] Bellet | Finite element approach of thermomechanics of solidification processes[END_REF]. The velocity field is linear continuous, including additional degrees of freedom at the centre of the element (bubble formulation), and the pressure field is linear continuous. After elimination of the internal degrees of freedom, the set of discretized equations can be solved for the nodal velocities and pressures.

Arbitrary Lagrangian Eulerian formulation (ALE)

The basic principle of the ALE method is to separate clearly the mesh velocity field v from the material velocity field v. Hence the ALE method is between the Lagrangian method (v = v) and the Eulerian one (v = 0).

The computation of v consists in regularizing the position of nodes in order to minimize the deformation of the mesh. This is achieved by an iterative procedure which aims at positioning each node at the centre of gravity of the set of its neighbours. This is done under the constraint of conservation of material flux through the domain surface:

n v n v . . = ( 12
)
where n is the outward unit normal. The nodal normal n is taken equal to the consistent normal, as proposed by Gray [START_REF] Gray | An efficient finite element scheme for two dimensional surface water computation[END_REF] and Engelman et al. [START_REF] Engelman | The implementation of normal and/or tangential boundary conditions in finite element code for incompressible fluid flow[END_REF]. Its expression is detailed in appendix. The constraint ( 12) is enforced by a penalty technique. The condition being written here incrementally, the variable v includes the second order acceleration terms of the updating scheme ( 10):

∆ - - = v v v 2 1 2 3 ( 13
)
The velocity field v determines the incremental updating of the configuration, according to the following scheme:

v x x ∆ + = ∆ + (14)
Knowing the mesh velocity, it is necessary to proceed to the updating of nodal fields. Denoting such a field by , ( can be the temperature in the case of a thermo mechanical coupled computation), this is done by writing

∆ + = ∆ + (15)
where the derivative of with respect to the grid can be expressed as follows:

∇ - - = ). ( v v (16)
Once the evolution equation of has been solved on the time increment, the total derivative of is known at each node. After computation of v and v , the updating of can be obtained by writing (15 16) at each node and only requires the nodal gradient of . Using an upwind technique, this nodal gradient is computed in the upstream element, which is found according to the advection velocity vv [START_REF] Bellet | Finite element approach of thermomechanics of solidification processes[END_REF].

In order to express the acceleration terms in the momentum equation, a transport of the material velocity field is necessary. In [START_REF] Temperley | Liquids and their properties. A molecular and macroscopic treatise with application[END_REF], the velocity v ∆ is the material velocity of the particle at the previous time level. Hence, after configuration updating, this requires a pure advective transport of the velocity field. This is achieved by a similar scheme as (15 16), but in which the material derivative is taken equal to zero:

∆ - ∇ - = ∆ + ) ) ( )( ) ( ( ) ( ) ( v x v x v x v x v (17)
In the above numerical model, the free surface is explicitly described, as a part of the boundary of the finite element mesh. It is then composed of linear triangular facets. The problem is then to compute the local average curvature of such a discretized three dimensional surface in order to evaluate the second term of (1).

We describe hereunder two methods for this computation. The first one consists in computing the edge curvature for each edge joining two nodes of the surface triangulation, and in cumulating the associated forces at nodes. The second one consists in computing an average normal vector at each node, and then in expressing the curvature at each integration point of the facets by taking the divergence of the field of normal vectors.

Method 1: average curvature based on edge curvature

Let us consider an edge between two nodes and (fig. 1). The elements being linear, one of the principal curvature radius can be considered infinite (zero curvature). The average curvature κ reduces then to the curvature in the plane orthogonal to the edge direction. An approximate formula is given by [START_REF] Jaouen | Calcul de surfaces minimales discrètes par minimisation de l'intégrale d'énergie (Calculation of discrete minimal surfaces by minimization of energy integral)[END_REF]:

+ = = δ κ 1 ( 18
)
in which denotes the average curvature radius, the edge length, δ the angle between the two adjacent triangles, and their respective surface. This expression derives from the following analysis. It is to be noticed that the ratios / and / are proportional to the characteristic lengths and of the facets in the normal direction to the edge, as we have: This yields:

) ( 2 1 + = + (20)
and denoting the average of and , we can see that (18) is nothing but:

δ = (21)
This relation can be derived naturally by considering the discretization in linear segments of length of an arc of circle of radius (fig. 2). In the triangle OAB, we have:

2 sin 2 δ = (22)
In the case of a small desorientation of the facets ( low curvature), the angle δ is small and ( 21) is effectively obtained. The increasing difference between formula (21) and ( 22) with increasing δ is given by table 1. When the curvature increases, we can see that the approximate formula (21) provides underestimated values of , and consequently overestimated curvature and associated surface tension terms. However, the maximum difference for curvature is "only" 37%, for extremely sharp edges. Taking into account that this computation is based on an averaged mesh size around the edge, (21) and consequently (18) appear to be valid.

The contribution of surface tension terms in the principle of virtual power ( 7) is:

∫ Ω ∂ - * .v T (23)
In a discretized form, on an edge of the surface, we have from ( 1) and ( 18):

n T + = δ γ (24)
where n is the average normal vector on the edge:

) ( 1 n n n n n + + = (25)
The elementary force exerted on the edge can then be expressed as:

n T T f δ γ = + = = ) ( (26)
Half of this force is applied to each of the nodes of the edge. The discretization of (23) then leads to:

∑ ∑ Ω ∂ ∈ - around edge * . 2 1 V n δ γ (27)
and the contribution to the residual attached to the degree of freedom ( ,!) -spatial component ! of node -is given by:

∑ - = ! ! around edge _ 2 1 n δ γ (28)
The coefficient ½ applies when the node is surrounded by facets belonging to the free surface Ω ∂ . It is modified when the node belongs to a symmetry plane. It is then necessary to distinguish between the contribution of edges which have images by symmetry with respect to the plane and of edges which belong to the symmetry plane.

Method 2: average curvature computed as the divergence of nodal normal vectors

As demonstrated by Brackbill et al. [START_REF] Brackbill | A continuum method for modeling surface tension[END_REF], the average curvature is given by the surface divergence operator:

n . ∇ = κ (29)
in which the spatial partial derivatives are taken in the local tangential plane to the surface. From this relation, an alternative method has been developed to express surface tension forces applied to a faceted three dimensional surface. This method is composed of the following steps:

• nodal averaging of normal vectors

• computation of the surface divergence of the field of normal vectors, inside each triangle of the surface • expression of the surface tension terms in the mechanical equilibrium equation These steps are detailed hereunder.

" # #

Each node of the discretized three dimensional surface belongs to one or several linear triangles. On each plane facet, the normal is unique. Hence, there are essentially two methods of nodal averaging.

The first one is a simple averaging and can be expressed as:

∑ ∑ ∈ ∈ = ) ( ) ( 1 τ τ n n n ( 30
)
where τ( ) denotes the set of triangular facets surrounding node and n the normal vector to facet . When the average normal to the free surface is looked for, the set of facets τ( ) is restricted to the facets of the free surface surrounding the node If the node belongs to one or two symmetry planes, the average normal vector n must be projected onto those planes in order that the final averaged vector belong to those planes.

A second method consists in taking n as the consistent normal vector already defined in the appendix. The normal is then a weighted average of the normal vectors of the facets surrounding the node. The weighting coefficients are simply the surfaces of the facets (see appendix):

∑ ∑ ∈ ∈ = ) ( ) ( 1 τ τ n n n (31)
In the sequel, the consistent normal vectors will be used for the estimation of curvature.

# #

Let us consider now a linear triangular facet. The three nodes ( , , ) have averaged normal vectors n , n and n . In the plane of the facet, a local coordinate system ($,%) is defined, where the unit vector e $ is tangential to the edge joining the two first nodes of the facet, and e % is orthogonal to e $ (fig. 3). Denoting (ξ,η) the coordinates in the reference triangular element, we have:

% $ % $ % $ % " % " $ " $ " % " $ " % $         ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ +         ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ = ∂ ∂ + ∂ ∂ = ∂ ∂ + ∂ ∂ = ∇ η η ξ ξ η η ξ ξ n . ( 32
)
in which " denotes the interpolation function attached to node . The summation on nodes ( = , , ) is implicit, using the convention of summation of repeated indices. The derivatives of interpolation functions are constant in the element, whereas the derivatives of the local coordinates (ξ,η) with respect to ($,%) are obtained by expressing the Jacobian matrix ] / [ ξ X ∂ ∂ and its inverse, which are also constant in the element. Finally, the divergence of n is obtained by the following formula:

( ) ( ) ( ) [ ] % % % % $ $ $ $ % - + - - - = ∇ 2 1 .n (33)
denotes the surface of the facet. The facets being linear, n . ∇ is constant on each of them. It can be easily computed after calculating the coordinates of the nodal normals in the local coordinate system ($,%) attached to each facet. In each point of the facet of local coordinates (ξ,η), the expression of the surface tension resulting force is then:

) , ( ) . ( ) , ( η ξ γ η ξ n n T ∇ - = (34) When n . ∇
is positive (respectively negative), the surface is locally convex (resp. concave) and the associated surface tension effort is compressive (resp. tensile).

Surface tension terms in the mechanical equilibrium equation

It is now possible to give a detailed expression of the discrete form of (23). Given a tetrahedral element having at least one its faces on the boundary , the contribution of to the residual attached to the degree of freedom ( ,!) can be written in the following way.

∫ ∫ Ω ∂ Ω ∂ ∇ = - = " " " ! ! ! . ) . ( . _ n T γ (35)
Wall adhesion is the term used to describe the forces acting on the fluid interface along the line of contact with a solid wall (contour of the free surface). In this region are exerted very complex microscopic phenomena, that result in an equilibrium angle θ which is function of the different surface free energies which are characteristic of the different interfaces: γ & (solid liquid interface), γ &' (liquid gas interface) and γ ' (solid gas interface) (fig. 4). The angle θ characterizes the wetting of the wall by the fluid: wetting for θ < 90°, no wetting for θ > 90°.

Hence, this angle is not an intrinsic parameter of the fluid, but depends on the contact system. It can be measured experimentally when the fluid is at rest. As mentioned by Temperley and Trevena [START_REF] Temperley | Liquids and their properties. A molecular and macroscopic treatise with application[END_REF] or Kothe and Mjolsness [START_REF] Kothe | RIPPLE: a new model for incompressible flows with free surfaces[END_REF], it is to be noted that this equilibrium angle depends also on the fluid velocity (modulus and orientation with respect to the interface). In the present work, only the static equilibrium angle will be considered.

Following the approach of Brackbill et al. [START_REF] Brackbill | A continuum method for modeling surface tension[END_REF], the system of forces applied to the free surface contours is not modelled. It is preferred to account for the establishment of the equilibrium angle along those contours. This is achieved by introducing additional forces which apply to this region when the actual contact angle θ is different from the static equilibrium one θ . In other words, the average curvature is calculated in a specific way in the neighbourhood of the contour of the free surface, in order to generate adequate forces. We shall detail this point.

At this stage, it can be noticed that the introduction of such forces appears to be impossible when using the formulation based on edge curvature. The reason is that, as already said, the edge curvature only provides curvature in the orthogonal direction to the edge. If we consider the contour of the free surface of a three dimensional fluid domain, it is difficult to imagine how to implement a consistent set of nodal forces issued from edge curvature: around each node in contact with the wall, the edges belonging to the free surface can have very different directions with respect to the contour line. This is the reason why we have extended to 3D the approach suggested by Brackbill in 2D. If the average curvature is computed by the surface divergence of the averaged normal, and if we apply the vectors resulting from (34), it should be possible to account for wall adhesion through a simple modification of the averaged normal vector at nodes in contact.

If we refer to fig. 5, the normal vector n which is used to compute the surface tension forces is modified at each node belonging to the free surface contour, according to the following relation:

t n n θ θ sin cos ˆ+ = (36)
In this relation, n is the outward unit vector to the wall surface. Vector t is tangent to the wall surface, and given by the projection onto the plane of the initial average normal vector to the free surface n. This initial n vector is obtained by (31). For the other nodes of the free surfacethose which are not in contact -we take n ˆ equal to n, and in each facet of the free surface, the contribution of the surface tension to the applied external stress vector is computed as:

" n n T ) , ( ) . ( ) , ( η ξ γ η ξ ∇ - = (37)
Figure 6 schematically explains, in 2D, the effect of this local change of vector n when the actual contact angle θ is different from θ . By changing locally the value of n . ∇

, the system of surface tension forces is modified, providing additional forces that will make the interface evolve towards the equilibrium state.

The evolution of a liquid drop, initially of cubic shape, in contact with a plane wall is modelled. Starting from an initial cubic configuration, the liquid flow is computed until the drop shape stabilizes. The liquid is submitted to gravity, viscosity, inertia, surface tension including wall adhesion as explained in the previous sections. The contact with the wall is frictionless. The dynamic viscosity of the fluid is µ = 50 Pa.s and its specific mass is ρ = 1000 kg.m 3 . The surface tension coefficient is γ = 2 N.m 1 and three values of the contact angle θ have been considered: 60, 90 and 120 degrees. The initial cube is 5 x 5 x 5 mm. The initial mesh is composed of 1331 nodes, 5000 tetraheadral elements, with 1200 triangular facets on the boundary. The time step is 0.01 s. The evolution of the cube is presented in fig. 7. We can see that the fluid domain configuration converges towards a stable shape, which is reached after 0.5 s approximatively. Knowing θ , it is possible to calculate analytically the diameter of the circular contact area and the height of the stable configuration. Such a result provides a good reference solution to evaluate the finite element solution. First, the volume of a truncated sphere, of radius and making a contact angle θ with the truncation plane, is given by:

      + - = θ θ π 3 3 cos 3 1 cos 3 2 (38)
The volume conservation ensures = 0 , the given initial volume, which yields , the curvature radius of the equilibrium configuration. From , we can deduce the height of the drop and φ the diameter of the circular contact area:

θ φ θ sin 2 ) cos 1 ( = - = (39)
The comparison between the exact values of and φ and those obtained with the finite element model is given in table 2. The differences are very low. Moreover, it is to be noted that the errors indicated in the table include errors of determination, as the dimensions issued from the finite element model are raw results obtained from position of nodes (no interpolation). Another contribution to the error is the slight change in volume that is observed in the finite element computation (a relative loss of volume of 1.2, 0.3 and 0.3 % in the three cases respectively). The treatment of contact by penalty also contributes to the error, since the fluid is allowed to penetrate the wall very slightly (about 10 5 m).

Hence, these results validate the implementation of surface tension and wall adhesion.

Let us make a last comment about the evaluation of the average curvature. If we consider a node of the free surface far enough from the contact line, the value obtained by averaging the edge curvature of all the edges converging to this node compare well with the value of obtained by (38), the error being in the range of the errors indicated in table 2. The same remark can be done for the value of n . ∇ in the facets of the free surface. This validates the two different ways to compute the average curvature of a surface discretized in linear triangles.

!

The implementation of surface tension phenomena in a three dimensional finite element model has been detailed. Regarding the estimation of the average curvature, two different methods have been presented and discussed. In order to take into account wall adhesion effects, the curvature deduced from the surface divergence of normal vectors has been preferred. The method which consist of a local perturbation of these normal vectors has been presented. It has been tested successfully in the case of the static contact of a drop of liquid on a plane.

% &

The objective of this appendix is to define a set of proper nodal normal vectors, starting from the discretized form of the incompressibility condition. We use then the same reasoning as Gray [START_REF] Gray | An efficient finite element scheme for two dimensional surface water computation[END_REF] and Engelman et al. [START_REF] Engelman | The implementation of normal and/or tangential boundary conditions in finite element code for incompressible fluid flow[END_REF], but extended in 3D. In the case of linear spatial interpolation, this will allow us to give a precise expression of consistent nodal normal vectors.

Given Ω = Ω the finite element discretization of a computational domain, we have, from the incompressibility equation (3b):

0 . = ∇ ∫ Ω v (A1)
Equation ( A1) is a global form of the incompressibility equation. It corresponds to (7b) in which the particular case 1 * = is considered (the interpolation space for pressure must contain the constant functions). The injection of the spatial interpolation of the velocity field v in (A1) yields:

0 =  ⌡ ⌠ ∂ ∂ =  ⌡ ⌠ ∂ ∂ Ω Ω ( " ( " (A2)
where " denotes the interpolation function attached to node , and is the component of the nodal velocity at node ( = 1, 3). Using the gradient theorem, we obtain:

∫ 0 = Ω ∂ " (A3)
The summation in (A3) is then restricted to the nodes belonging to the boundary Ω ∂ of Ω .The integrals of (A2) and (A3) are in fact computed by summation of integrals on the elements Ω the node belongs to. Then (A3) can be cast under the form:

0 m nodes boundary = ∑ A V (A4)
Following the reasoning of Engelman et al., the consistent normal vectors should be such that any tangential nodal velocity ( . . a velocity which is orthogonal to the consistent normal vector) should not contribute to the external flux (A1). Therefore, we should have: for any boundary node , 0

= A V (A5)
where V is the tangential velocity vector at node . This means that for each boundary node , the consistent nodal normal vector n ~ should be colinear to A . Its expression is then given by:

Fig. 1 :

 1 Fig. 1: Notations used in the definition of the curvature along an edge joining two nodes and and separating two triangles and .

Fig. 2 :

 2 Fig. 2: Arc of circle discretized in linear segments.

Fig. 3 :Fig. 4 :Fig. 5 :

 345 Fig. 3: Local system of coordinates used to compute n . ∇ in each triangular facet.

Fig. 7 :

 7 Fig.7: Finite element computation of the evolution of a volume of liquid, initially cubic, towards its equilibrium state, for three different contact angles. In each case, profile view on the first line and perspective on the second line.

In the specific case of a linear discretization, (A7) reduces to:

where τ( ) denotes the set of triangular facets surrounding node , n is the normal vector to facet and 1/3 is the value of the interpolation function attached to the node at the centre of each surrounding facet. Finally, the consistent normal vector at node is the average of the normals of the surrounding facets weighted by their surface: