The present study aims to analyse the clinical presentation, treatment and prognosis of a group of patients with orbital cavernous venous malformation (OCVM) with an insidious onset.The clinical data of 35 patients with OCVM treated at our centre between 2003 and 2020 were retrospectively analysed. The OCVMs were classified as one of six types (I–VI) according to the orbital position of the tumour. The clinical characteristics, treatment methods and follow-up results were recorded.A total of 35 patients with OCVM under the optic nerve sheath in the orbital apex area or the common tendon ring (Types I and II) were included in the present study. In 20 cases (57.1%), patients were misdiagnosed with optic neuritis, and in 20 cases (57.1%), the tumour was not identified based on imaging. The presentation was acute or subacute in 23 cases (65.7%). All patients underwent surgery: transnasal surgery in 22 cases (62.9%) and craniotomy in 13 cases (37.1%). A total of 9 patients (25.7%) experienced postoperative complications, and 17 patients (48.6%) experienced vision improvement. The average patient age at first diagnosis was 43.3 ± 10.3 years, and the median follow-up period was 64.5 months. Overall, 14 patients (40%) experienced postoperative complications: postoperative blindness in 6 cases, postoperative vision loss in 8 cases and orbital apex syndrome in 7 cases.Patients with Type I and Type II OCVMs are the most complex cases. They have an insidious onset and are associated with a high rate of misdiagnosis and missed diagnosis. Acute and subacute decreases in visual acuity are mainly caused by OCVM haemorrhage. The difficulty of surgical treatment and the poor prognosis of postoperative vision are characteristics of this tumour. Transnasal surgery and craniotomy can be used to remove OCVMs located in the common tendon ring or optic canal as well as those involving the intracranial area through the supraorbital fissure. Meanwhile, the orbital approach (orbitotomy) has proven to be an effective method of treating OCVMs not involving the deep orbital apex and intracranial area. Orbital cavernous venous malformation (OCVM) is a common benign tumour of the orbit occurring in adults and accounting for 13–22% of all orbital tumours . It is tOnce found, orbital cavernous haemangioma (OCH) is usually surgically resected. The tumour has a complete capsule, and a tumour located in or outside the orbital muscle cone has no evident adhesion to the orbital contents. Its clinical manifestations are primarily protrusive eyes, and it can generally be completely resected with few surgical complications.However, there is an OCH type that does not present as protrusive eyes; it is characterized by a hidden onset, difficult detection and treatment, rapid disease progression and poor clinical prognosis.An OCVM can occur in any part of the orbit; those situated in the deepest part of the orbit, namely the common tendon ring and the optic canal of the orbital apex, are the most difficult to treat. Deep OCVMs generally occur at the common tendon ring in the extraocular muscle cone or the optic nerve sheath; the tumours are deep and adjacent to vital structures, such as the optic nerve, extraocular muscles and intra-orbital blood vessels. Consequently, surgery in this area is challenging and risky.In addition, tumours located in the deep part of the orbit are usually small in size, and therefore do not exert a space-occupying effect. As a result, they are not easy to find in the early stages, and the rate of clinical misdiagnosis and missed diagnosis is therefore extremely high.Bleeding of the tumour can result in an acute decline in vision, leading to late diagnosis in the clinical course . The oveOCVMs have a potential risk of rupture and haemorrhage, which can cause irreversible blindness. Therefore, the authors of this study believe that early diagnosis and strict follow-up should be conducted for OCVMs located in the deep orbital apex or near the optic canal (Types I and II). Because these kinds of OCVMs are small and deep, the operation is difficult, and the complication rate is high. The surgical indications are questionable ; howeverIn the present study, 35 cases of OCVM with imaging appearance, histopathology and surgical approaches were researched; the clinical features and prognosis were then compared according to tumour position type.The clinical data of 35 patients with OCVM treated at our centre between January 2003 and October 2020 were collected and retrospectively analysed. The study met the requirements of the World Medical Association’s Declaration of Helsinki and was approved by the ethics committee of our centre. The patients or their family members provided informed consent.The clinical characteristics of this series of patients with insidious onset OCVM were analysed. Each OCVM was then classified as one of six types (I–VI) based on the orbital position of the tumour and its positional relationship to the bony orbit, eyeball, optic nerve canal within the orbit and communication area inside and outside the orbit.The classification criteria were mainly based on the characteristics of all our retrospective clinical cases. Six main types of OCVM were broadly outlined based on the tumours’ different anatomical locations in the cranio-orbital region , and hand-drawn diagrams were provided.Moreover, it was also on the basis of the prognosis of the different clinical disease subtypes brought about by these different anatomical OCVM features that a part of the quite distinctive clinical case features was synthesized.All patients were treated surgically with either a transnasal endoscopic approach or a transfronto-orbital approach. The appropriate surgical approach was conducted according to the different anatomical tumour locations in the orbit; an effort was then made to adopt the most suitable method for tumour removal, i.e., avoiding damage to the optic nerve and extraocular muscles was required while removing the tumour.Transnasal endoscopic approach: With the combined neuronavigation and endoscopic operation, a single nostril approach to the lateral middle turbinate was conducted; after incising the septal vesicle, the pterygoid sinus was entered and the optic canal exposed.via orbital periosteum incision.According to the different anatomical locations of the tumour, the bone of the orbital wall in the orbital apical region and the bone of the wall in the optic canal were removed by pneumatic drilling. The superior, medial and inferior walls of the optic canal were also removed by 270° grinding. The tumour was finally exposed and removed Transfronto-orbital approach: A frontotemporal arcuate incision was made, the frontotemporal bone flap on one side and the brow arch bone flap on the other side were removed by milling, and the supraorbital wall and the optic nerve canal wall were abraded. The bony structure of the supraorbital fissure was then fully opened, and the tissue structure inside the supraorbital fissure was completely exposed. Next, the intra-orbital tumour was exposed under the microscope, with the full protection of the optic nerve, the extraocular muscle and the neuromuscular structure inside the general tendon ring. Finally, the tumour was completely removed.Transnasal surgery was used to remove tumours located on the medial or inner-lower side of the optic nerve at the orbital apex. A craniotomy microscope is often used to cut the total tendon ring and remove tumours located on the upper side of the optic nerve at the orbital apex. When a tumour is located on the temporal side of the optic nerve at the orbital apex, a transorbital approach or a craniotomy can be used to remove the tumour with the aid of a microscope. The general principle is to minimize the surgical approach of the most important orbital structure in order to remove the tumour.The researchers in the present study recorded the patient clinical characteristics, surgical approaches, computed tomography (CT) and magnetic resonance imaging (MRI) results, pathology specimens and follow-up outcomes.The study included 35 patients with OCVM; of these, 10 (28.6%) were male and 25 (71.4%) were female. The average age at first diagnosis was 43.3 ± 10.3 years, and the median follow-up period was 64.5 months. In 20 cases (57.1%), the patients were misdiagnosed with optic neuritis, and in 20 cases (57.1%), the tumour was not identified based on imaging. The presentation was acute or subacute in 23 cases (65.7%). All patients underwent surgery: transnasal surgery in 22 cases (62.9%) and craniotomy in 13 cases (37.1%). Postoperative complications were present in 9 cases (25.7%), and vision improvement was present in 17 cases (48.6%).All OCVMs were Type I or Type II; a total of 9 were located under the optic nerve sheath in the orbital apex area, and 26 were found in the common tendon ring region. On T1-weighted images, all OCVMs appeared to be homogeneous and isointense. On the T2-weighted images, the tumour appeared hyperintense, homogeneous and heterogeneous; hyperintensity was characteristic. The most common enhancement mode was multiple patchy starting points distributed throughout the tumour, finally becoming homogeneous or heterogeneous in the later stage.In 20 patients, no tumour was identified in the brain MRI, and the diagnosis was confirmed using either optic nerve or orbital MRI.All patients had an orbital or optic canal CT confirming the absence of bone hyperplasia, absorption, or destruction caused by the OCVM and showing no obvious OCVM calcification.All 35 patients included in the study underwent surgical tumour removal, and all samples obtained during the operation were confirmed as originating from an OCVM. Surgical specimens were collected for histological and immunohistochemical analyses. Immunohistochemical studies for CD34, CD31, CD99, SMA, Vimentin, P53 and Ki-67 were tested in partial samples. The Ki-67 index of the surgical samples was <2%. However, partial OCVMs have been shown to exhibit positivity with CD99, CD34 and Vimentin.All 35 patients completed the follow-up, which had a median period of 64.5 months. There were 35 operations: transnasal endoscopic approach in 22 cases (62.9%) and transfronto-orbital approach in 13 cases (37.1%). No patients experienced recurrence, and a total of 9 patients (25.7%) experienced postoperative complications. Vision improved postoperatively in 17 cases (48.6%), and there were no apparent visual changes after surgery in 9 cases (25.7%).The surgical prognosis and clinical characteristics of Type I and Type II OCVMs are shown in The typical OCVM locations were identified according to the optic nerve MRI and following intraoperative confirmation Figure 1Type I: The OCVM is located under the optic nerve sheath of the orbital apex. The tumour has a complete envelope and generally does not penetrate the optic nerve sheath. The tumour is less than 0.77 ± 0.17 cm in diameter and compresses the optic nerve. It is easy to miss the diagnosis in MRI and CT of the brain.The OCVMs in cases 1, 2 and 3 5 were aType II: The OCVM is located in the area of the common tendon ring of the orbital apex and has a complete capsule. The tumour body is less than 1.02 ± 0.24 cm in diameter. The tumour is generally located in the muscle cone and does not extend through the common tendon ring and orbital periosteum. The total tendon ring contains extraocular muscles; the optic, oculomotor, trochlear, and abducent nerves; and other structures. The space in the entire tendon ring is narrow, and the tumour is small; it is therefore easy to miss the diagnosis in MRI and CT of the brain. However, once bleeding occurs, there will be acute or subacute visual loss and even the occurrence of orbital apex syndrome.Missed diagnosis, misdiagnosis, insidious onset, and acute and subacute visual loss are characteristics of Type II OCVM. Due to the location of the OCVM in the common tendon ring, the extent of the operative field for transnasal endoscopic surgery is limited, and microscopic craniotomy is preferred. Case 4 Figure 6The histopathological examination of specimens in cases 1–4 showed proliferated and expanded spongy blood vessels, and the cut surface was porous. In Case 3, it proliferated and expanded cavernous vessels accompanied by previous bleeding. The OCVM pathology does not have any rare manifestations; all have the characteristics of OCVMs, and the previous bleeding in the pathological pictures can better explain the acute change in the disease Figure 7via brain CT and MRI.Type III: The OCVM is located inside the muscle cone of the orbit and has a complete capsule. The OCVM is generally large and exerts a space-occupying effect; consequently, patients often have exophthalmos. As the tumour is commonly located in the muscular cone in a deep location, the operative field is narrow. Due to the relatively large size of the tumour and the clinical presentation of exophthalmos, the tumour is usually diagnosed via brain CT and MRI due to its relatively large size and the clinical presentation of exophthalmos.Type IV: The OCVM is located outside the muscle cone of the orbit. The tumour has a complete envelope and generally does not extend into the orbital periosteum. The OCVM is generally large and exerts a space-occupying effect; consequently, patients often have exophthalmos. The tumour is commonly located in a shallow position outside the muscle cone and rarely compresses the optic nerve; thus, vision is typically not affected. Due to the location of the tumour, more surgical approaches are available. The tumour is usually diagnosed Type V: The OCVM involves both the inside and outside communication region of the muscle cone. The tumour has a complete envelope and generally does not extend through the orbital periosteum. The OCVM is usually large and exerts a space-occupying effect; consequently, patients often have exophthalmos. The base of the tumour is commonly located deep in the muscular cone and often compresses the optic nerve, resulting in very poor vision.Type VI: The OCVM involves both the inside and outside communication region of the orbit, and there is a slight chance of breaking through the orbital periosteum. The tumour body breaks through the orbital periosteum to the surrounding space. The entire tumour body can extend into the sphenoid sinus, ethmoid sinus, pterygopalatine fossa and even the cavernous sinus. Type III–VI OCVMs are generally large and exert a space-occupying effect; consequently, patients often have exophthalmos. Surgery requires a multidisciplinary approach involving various specialties.OCVM is a benign vascular disease; it is a vascular malformation characterized by abnormal changes in the vascular cavity. In the past, some authors have classified it as a type of benign tumour. As the OCVM often occurs in the muscle cone behind the eyeball, it can cause axial exophthalmos and slowly grow to compress the optic nerve or eyeball, resulting in loss of vision. Therefore, early diagnosis and treatment of patients with OCVM are recommended as technology permits in order to avoid irreversible damage to visual function caused by advanced tumours. The current description of this orbital tumour’s location involves using the muscular cone as an anatomical boundary (divided into the inner and outer muscular cones) or using the optic nerve as a reference point to describe the relative position of the tumour .However, there is no consensus on how to describe the different depths of the tumour within the orbit. Some authors provide an anatomical basis for the clinical, surgical approach, dividing the bony orbit into peripheral, posterior and orbital apexes: (1) the orbital apex is marked by the posterior ethmoid sinus; (2) the posterior part of the eyeball is marked by the anterior ethmoid sinus; and (3) the peripheral is the part of the orbit before the posterior part of the eyeball.This method is based only on the anatomy of the bony orbit. However, during surgery, the surgeon needs to consider the bony anatomical landmarks of the orbit and the soft tissue landmarks, such as the eyeball and the extraocular muscles. If only the bony orbit is used as a partition, the specific relationship between each partition and the eyeball cannot be accurately represented. Therefore, each OCVM was classified as one of six types based on the orbital position of the tumour and its positional relationship to the bony orbit, the eyeball, the optic nerve canal within the orbit and the communication area inside and outside the orbit.There have been many reports on the different surgical approaches for orbital tumours: the conjunctival approach to the orbital opening, the skin approach to the orbital opening, the lateral orbital opening, combined internal and external orbital openings and transnasal endoscopic approaches –16.via nasal endoscopy is becoming increasingly accepted and promoted by the majority of doctors. Transnasal endoscopic surgery induces minimal trauma and leads to a faster patient recovery and limited surgical damage. However, for many OCVMs, limitations remain  the tumours were small and deep. Surgery was technically challenging, often requiring neuronavigation techniques for successful tumour removal; and (6) transnasal endoscopy and craniotomy could be used for surgical removal. However, the probability of postoperative recovery of vision was small, the probability of complications and further visual loss was high, and the risk of orbital apex syndrome after surgery was high.The authors of this study believe that the clinical history and surgical prognosis of Type I and Type II patients have some commonalities: (1) in the majority of cases, the average tumour diameter was <1.0 cm ; (2) as the tumour was small, it was often missed by ordinary cranial MRI and CT. The average missed diagnosis rate is 57.1% ; (3) the patients showed no clinical signs of exophthalmos, with only visual loss in a single eye as a manifestation. All of the patients were first diagnosed with decreased vision (100%); (4) the majority of patients presented with optic disc atrophy  and optic disc edema  and were initially treated based on a diagnosis of optic neuritis , although the effect of treatment was limited. After a sudden drop in visual acuity, tumours were identified The authors of this study propose that this kind of OCVM often occurs in the optic nerve sheath at the orbital apex or is confined to the muscle cone of the common tendon ring. Space is limited at the anatomical location of these tumours, restricting tumour growth, and the average diameter of the tumour at this location is <1.0 cm.Although the space-occupying effect of the OCVM is not great, tumours at this location usually involve the optic nerve. In most patients, visual acuity decreases slowly and is accompanied by optic disc edema, potentially contributing to a misdiagnosis of optic neuritis in the outpatient setting. However, when an OCVM in this location bleeds due to the limited space in the tumour’s location, the clinical symptoms and signs will change dramatically, resulting in severe damage to the optic nerve and marked visual loss for the patient.When this acute change in visual acuity occurs, the outpatient doctor may carry out an orbital or optic nerve MRI resulting in the correct diagnosis. The history of OCVM is not accurately reported in the relevant literature. Still, it is known that bleeding is the major complication of this type of tumour, and the probability of rebleeding is high.Ren Jian  reportedDepending on the location of the OCVMs, craniotomy and transnasal endoscopic surgery are performed in patients with Type I and Type II OCVMs. When the tumour is located on the medial or inferior side of the optic nerve, the medial side of the common tendon ring and close to the orbital periosteum, a transnasal endoscopic surgical approach is adopted. Under the endoscope, only the optic nerve canal and the bones of the orbital apex need to be removed.It is evident that blue staining occurs in the dura of the optic nerve sheath. After cutting the sheath at the tumour, the optic nerve is protected while the tumour is carefully separated.When the tumour is located in the superior or lateral side of the optic nerve, or the depth of the common tendon ring is in position, craniotomy with the transfrontal orbital approach can open the optic nerve sheath or the common tendon ring to remove the tumour. Craniotomy completely exposes the superior orbital fissure and optic nerve, removes the bones of the optic canal and superior orbital fissure and completely exposes the structures of the orbital apex area. It is imperative to cut the common tendon ring structure. The orbital periosteum of the orbital apex is often cut using a lateral incision at the superior fissure.Note that the trochlear nerve usually crosses over the ring of the tendon. To avoid postoperative orbital apex syndrome, the orbital apex structures  must be protected during surgery.Most cases of missed diagnosis or misdiagnosis occur in the ophthalmology or neurology departments of the primary hospital; thus, the question of how to effectively screen at first presentation is worth considering. In the incidence of a decrease in monocular vision, combined with a lack of response to hormonal therapy for presumed optic neuritis in the clinical setting, optic nerve MRI is an effective investigation for identifying diseases such as OCVM. Once OCVM haemorrhage has occurred, visual acuity will be irreversibly damaged.In the pathological pictures of some typical cases, there will be characteristic manifestations of tumour haemorrhage. OCVM is a type of venous malformation in the strictest sense, although it is a vascular malformation associated with low flow. Despite our experience in OCVM surgery, it remains unclear why Type I OCVM has a higher bleeding rate than Type II OCVM or even other OCVM types.The medical history of OCVM has not been adequately studied, and tumour characteristics at each site are not the same. In addition, the overall sample in the present study is relatively small.Ren Jian  reportedPatients with Type I and Type II OCVMs, which have an insidious onset, are the most complex cases. They are associated with a high rate of misdiagnosis and missed diagnosis.Acute and subacute reduction in visual acuity are usually caused by tumour haemorrhage. The difficulty of the operation and poor prognosis of postoperative vision are the characteristics of this tumour. Based on the present study, transnasal surgery can be used to remove OCVMs. Nevertheless, treatment complications of missed diagnosis and misdiagnosis are hard to avoid, and the incidence of surgical complications remains high.The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.The studies involving human participants were reviewed and approved by Tongren Hospital of China Capital Medical University. The patients/participants provided their written informed consent to participate in this study.PY have made substantial contributions to the conception or design of the work. H-CL and YL acquisition, analysis, or interpretation of data for the work. PY, J-LZ, and JR have been involved in drafting the work or revising it critically for important intellectual content. L-BJ and H-GL have given final approval of the version to be published. EQ and JK agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy of integrity of any part of the work are appropriately investigated and resolved. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.The handling Editor, JZ, has declared a shared parent affiliation with the authors at the time of review.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Solitary fibrous tumours (SFTs) in the female genital tract are uncommon. Resection of these tumours is controversial because it can cause life-threatening haemorrhage. We report a case of vulvar SFT that was excised in a combined abdominal-sacral approach after preoperative embolisation.At another hospital, an inoperable intrapelvic tumour was diagnosed in a 34-year-old woman. Computed tomography and magnetic resonance imaging showed that the uterus, urinary bladder and rectum were compressed laterally by a pelvic tumour with a maximum diameter of 11 cm. This mass was hypervascular and had a well-defined border. Transperineal biopsy was performed, and immunostaining revealed that the mass was an SFT. The tumour was supplied by feeding vessels from the right iliac arteries. First, we embolised the feeding vessels. Second, we performed surgical resection in a combined abdominal-sacral approach; no blood transfusion was necessary, and no perioperative complications occurred. The final pathological diagnosis was SFT that was positive for CD34 and signal transducer and activator of transcription 6 according to immunohistochemical staining.During a year of follow-up, the disease did not recur. Treatment of pelvic SFT should aim at complete resection through various approaches after careful measures are taken to prevent haemorrhage. Solitary fibrous tumours (SFTs) were first described by Klemperer and Rabin in 1931 as mesenchymal tumours of the pleura , 3. Of tWe succeeded in complete en bloc resection of vulvar SFT, without morbidity or the need for blood transfusion, by a combined abdominal-sacral approach after embolisation of the vessels supplying blood to the tumour.A 34-year-old woman was referred to our hospital to evaluate an asymptomatic pelvic mass detected with transvaginal ultrasonography in a private clinic, which she had visited for treatment of infertility. Computed tomography (CT) revealed a 112 × 62 × 58 mm hypervascular mass with a well-defined border. This mass compressed the bladder, uterus and rectum in the peritoneum (Fig. Before surgery, we performed embolisation of the feeder vessels with an absorbent gelatin sponge to reduce intraoperative blood loss because this SFT was hypervascular, supplied primarily by the right obturator artery and the internal pudendal artery, according to angiography Fig. d. The nePostoperative pathological study showed that the tumour was encapsulated and elastic but hard, and the cut surface was greyish-white Fig. . MicroscIn this case, a solitary fibrous tumour invading the retroperitoneum from the vulva was treated successfully by a combined abdominal-sacral approach after embolisation, without a need of blood transfusion. To our knowledge, this is the first case report of the resection of a vulvar SFT through a combined abdominal-sacral approach.SFTs are rare soft tissue tumours that commonly arise in the pleura . Such tuSFTs are soft tissue tumours with spindle-shaped cells of mesenchymal origin. From among CD34 immunostaining positive soft tissue tumours, we need to differentiate between SFT and dedifferentiated liposarcoma. Immunohistochemistry for STAT6 protein is useful for diagnosing SFT . Strong anal dysfunction [Because the tumour extended from the vulva into the pelvis, we performed the surgery through a combined abdominal-sacral approach out of concern about the difficulty in establishing an appropriate surgical field deep inside the pelvis by laparotomy. For that reason, we first separated the tumour from the right side of the rectum and uterus through a transabdominal approach and then successfully resected the tumour through a transsacral approach. Most patients with pelvic SFTs have undergone laparotomy, but some patients suffer heavy bleeding, which is difficult to control , 13. In function  (Table 1function . Thus, aWe embolised feeder vessels to the tumour before surgery to reduce intraoperative bleeding. Preoperative percutaneous arterial embolisation allows for safe and complete resection in cervical, thoracic and lumbar locations in the spinal cord , 21. EmbIn summary, we completely resected a vulvar SFT without blood transfusion. This tumour is very rare, nonmetastatic and characterised by abundant blood vessels. The main treatment for SFTs is surgical resection. However, pelvic SFTs carries the risk of massive bleeding and organ damage, and inadequate tumour resection can lead to local recurrence. Preoperative embolisation of feeder arteries reduced intraoperative bleeding in our patient. In addition, use of the abdominal-sacral approach can reduce perioperative complications. This combination thus has potential in the treatment of pelvic SFTs.


This article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as  These models are simple but each model has its own limitations. For example, the behavior of fluids with shear dangling viscosity is well supported by the power-law model, the elastic behavior does not include in the power-law model. Similarly, second and third grade show the inverse effects, they show the elasticity but viscosity for shear doesn’t depend on such models. Furthermore, these fluid models don’t convey the stress-relaxation period.Non-Newtonian fluids have much more applications in science and technology than Newtonian fluids. Non-Newtonian fluids are still used in manufacturing of variety of extremely concentrated products, including fabrics, carbon, glass, and paints. Many non-Newtonian fluids are found in foods such as jams, chocolate, mayonnaise, and other condiments. Toothpaste also contains certain non-Newtonian fluids. The certain models that explain the non-Newtonian behavior of fluids are Oldroyd-B, Maxwell, Jeffry, second and third-grade, Casson6 is the first who introduced the principle of nano-fluid in 1995. Such fluids are suspensions of nano-sized particles in a base fluid, such as metals, carbides, and oxides. The nano-fluids model produces very useful applications. Nanofluids contain a suspension of nanomaterials and show many interesting properties. Some of the applications involve enhanced heat transfer in electronic appliances, heavy-duty engines, industrial cooling, nuclear system cooling, heating building and reducing pollution, cooling of space defense equipment, vehicular brake fluids. In this article we are interested in Bio-magnetic fluid, because Bio-magnetic fluid dynamic (BFD) is a relatively new area in fluid mechanics investigating the fluid dynamics of biological fluids in the presence of magnetic field. The application of magnetic field on the flow of biological fluids is addressed for bioengineering and medical applications like drug targeting, cell separation, or reduction of blood flow during surgeries. The most characteristics bio-magnetic fluid is blood. Here blood is taken as a base fluid and gold nano-particles introduced in it. Das et al.7 pioneered the comprehensive discussion, relevance, and potential scope of nanofluids. Nano fluids had slightly higher thermal conductivity than base fluids, according to Wong and Kurma8. In fluid dynamics, fractional derivatives models have been discussed for viscoelastic materials, like glassy state and polymers. Recently, real life problems have been analyzed via fractional time derivative operator, like Caputo9, Caputo-Fabrizio10, and Atangana-Baleanu11. Fractional calculus is an emerging field which is based on various types of kernels. The main application of kernels is to provide a better description of the dynamics among complex systems, for example, collecting the memory at whole and partial domain of certain processes. The non-locality of the new kernel investigated the memory structure with alternate scales. Asifa et al.12 investigated the generalized MHD transport of rate-type fluid under Newtonian heating and non-uniform velocity conditions near an unbounded upright plate. Free convection flow of various MHD fluid models using fractional-order derivative having local and non-local kernel was analyzed by20. Saqib et al.21 deliberated the blood-gold nanofluid in a permeable medium with ramped conditions. They took Oldroyd-B fluid as a base fluid (Blood). In this they utilized the Laplace transform to acquire the solutions for temperature and velocity profiles of the model. Generalized magnetic blood flow with dust particles in cylindrical shape was studied by Saqib et al.22. Misra et al.23 investigated the bio-magnetic fluid over an extended sheet numerically using FDM. Apparent viscosity of blood in the presence of magnetic effect was addressed by Haik et al.24. Papadopoulos et al.25 was examined blood as bio-magnetic fluid in rectangular duct numerically. Hussain et al.26 researched the peristaltic transport of gold nanoparticles using blood as base fluid. In this, they obtained analytical solutions by the homotopy analysis method (HAM). The influence of nanosolid particle shapes, permeability material, viscous dissipative flow, Cattaneo-Christov heat flux and radiate flux are studied by Jamshed. et al.27. The predominant flow equations are systemized in form of PDEs. Keller-box's computational method was employed to identify the self-similar solution for transformed principles into ODEs by appropriate transformations. Saqib et al.28 considered the ferro-nanofluid with Brinkman type fractional model for the first time using ramped heating. LT was used to obtain the solution of the fractional CF model. The base fluid is considered as Casson fluid (blood) and CNT’s nanoparticles present inside it was illustrated by Khalid et al.29. They used LT to acquire the exact solution of the ordinary model. Aman et al.30 explained the hybrid nanoparticles in the well-known model of MHD Casson nanofluid in a permeable medium. Waqas et al.31 studied the magnetohydrodynamic flow of Burgers nanofluid with the interaction of nonlinear thermal radiation, activation energy, and motile micro-organisms across a stretching cylinder. The developed PDEs are transformed into a system of ODEs with the help of similarity transformations. The extracted problem is rectified numerically by using the bvp4c program in computational software MATLAB. Recently, Arshad et al.32 investigated bio-convective hybrid nanoparticles on a stirring needle in the presence of micro-organisms considered chemical reaction and viscous dissipation. HAM was used to acquire the analytical solution. MHD natural convection flow of nanofluid and CNT’s Oldroyd- B nanofluid in the presence of ramped conditions was illustrated by34. Entropy optimization of a system is important step of modeling36. The solution to the constructed problem is achieved by using the innovative CVFEM approach. Shah. et al.37 investigated the thermal effect for a mixed convection flow of Maxwell nanofluid spinning motion produced by rotating and bidirectional stretching cylinder. The modeled equations are converted to set of ODEs through group of similar variables and are then solved by using semi analytical technique HAM. Jamshed et al.38 studied the entropy generation in a magnetohydrodynamic flow of a Maxwell nanofluid over an infinite horizontal surface. Similarity solutions are obtained by transformation of governing PDEs to ODEs using similarity variables. Keller box method is then adopted to find the approximate solutions of reduced ODEs. The natural convection flow of different hybrid nanofluid over a radiative vertical plate and extended surfaces is discussed by41. Moured et al.42 studied the heat transfer and steady magneto-hydrodynamic natural convection in a fined cold wavy-walled porous enclosure with a hot elliptic inner cylinder occupied by hybrid Fe3O4-MWCNT /water nanofluid. The enclosure is also placed in a uniform magnetic field. The governing equations are verified by using the Galerkin Finite Element Method (GFEM). A single-phase mathematical model of Casson and second-grade nanofluid past over a stretching surface was analyzed by44. The Cattaneo-Christov based and unsteady Casson nanofluid over a stretching surface is investigated by46. The well-known nonlinear ODEs are solved via Keller-Box method.Nano-fluids are also non-Newtonian fluids, and this research focuses on nano-fluids. Choi et al.47 studied the ramped wall temperature and velocity of MHD Oldroyd-B fluid of convective flow. For inverse LT, Stehfest’s algorithms are utilized. Anwar et al.48 extended the work of47, in this, they added 49 illustrated the concept of heat and mass transfer of MHD Oldroyd-B fluid in a permeable medium using ramped conditions. They saw the comparison between three various types of non-integer order derivatives. Mehmood et al.50 studied the non-Fourier heat flux model of MHD Oldroyd-B fluid of oblique stagnation flow numerically. Runge–Kutta-Fehlberg quadrature and shooting method was utilized to acquire the solution. In52, authors studied the MHD Oldroyd-B nanofluid heat and mass transmission OHAM. Electro-osmotic slip flow of generalized Oldroyd-B fluid was researched in54. Soret and Hall effects of radiating chemically MHD fluid past on a vertical plate in a rotating system with ramped temperature also concentration in a permeable medium was discussed by Seth et al.56. Narahari et al.57 investigated the natural convection current impact of heat and mass transmission with ramped temperature. The parabolic trough solar collector (PTSC) is widely installed in concentrated solar power technology with a temperature range of 325–700 K, deliberated by61. The Keller box numerical scheme was used to find the solution of the resulting nonlinear ODEs.The influence of a chemical reaction is determined by whether it is homogeneous or heterogeneous. The inclusion of pure water and air is impossible in nature. It's possible that any outer matter is naturally there, or that it's mixed with air or water. When an outer mass is present in air or liquids, it induces a chemical reaction. Many chemical technologies, such as the manufacture of glassware or ceramics, the production of polymers, and food processing, benefit from the study of related chemical reactions. Mazhar et al.62, Stehfest’s63 are utilized to acquire the solution of temperature, concentration, and velocity. Finally, show the impacts of physical parameters on temperature and velocity fields that are present in the problem graphically as well as theoretically.The basic purpose of this investigation is to study the bio-magnetic Oldroyd-B nanofluid with ramped conditions. However, ramped velocity and ramped temperature have attracted a little attention of the researchers examining such flows. The simultaneous use of ramped wall temperature and velocity conditions are physically important, but mathematically relations are extremely intricate and handling them analytically is sometimes troublesome. Operating ramped wall temperature and ramped wall velocity is highly significant in various subdivisions in present-day technology and science. For instance, ramped velocity is useful in evaluating the functioning of heart and blood vessels. Diagnoses of cardiovascular deceases, determining treatment and establishing prognosis involve treadmill testing and Ergometry, which operate on the basis of ramped velocity. To see the behavior of fluid flow, fractional order model is good to explain the dynamics and memory effect with respect to classical model. Three types of non-integers definitions of Caputo, Caputo-Fabrizio, and Atangana-Baleanu are used to develop the given nano-fluid model. LT and numerical Laplace inverse algorithms including Zakian’s49. However, in the work of Saqib et al.21, the term Consider the unsteady flow of Oldroyd-B nano-fluid with heat and mass transmission. The vertical plate is infinite and the medium is considered to be porous. The fluid is assumed to be electrically conducting, as a result, the external magnetic force is applied parallel to the flow direction. Both the fluid and the plate are initially at rest. After some time at mentclass2pt{minim55 and accepting the small temperature variations among the temperature Using Rosseland approximations55The appropriate ICs and BCs are as follow21The thermophysical properties of nano-fluid are given asConsider the following dimensionless parametersIncorporating Eqs. , from EqThe kernel of Caputo fractional derivative is singular if Similarly, the definition of AB fractional derivative and their LT without singularity and locality are followingNow, these three definitions of fractional derivative are being utilized to find the expressions of temperature, concentration and velocity profiles.The solution of the problem is sought via the following methodology chart in Fig. 2Think time derivative in Eq.  as the CThink time derivative in Eq.  as the CThink time derivative in Eq.  as the A21 and if 55.In the absence of Think time derivative in Eq.  as the CThink time derivative in Eq.  as the CThink time derivative in Eq.  as the ANow, for velocity profile first we change the time derivative in Eq.  with fraThink time derivative in Eq.  as the CThink time derivative in Eq.  as the CThink time derivative in Eq.  as the A9. We discuss some results as a special case, like if If  in Eqs. –29, it iIn this article we investigated the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken as porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu are used to develop the resulting fractional nano-fluid model. The graphs for related parameters are plotted via MATLAB. Laplace transform technique is utilized for the solution of temperature, concentration, and velocity distributions, and for inversion purposes numerical algorithms for the inversion of Laplace numerically, like of Zakian’s and Stehfest’s are utilized. Their comparison is also presented in tabular form. The range of plots for various parameters is taken from 0 to 10.Figure mentclasspt{minimaFigure mentclasspt{minima21. Similarly, if 55. Tables Figure entclass1pt{minimaThe temperature profile of nanofluid increases with incrementing the value of The velocity of nanofluid de-escalates with the increase of volume concentration Concentration and velocity profiles get reduced while accelerating the Schmidt number The fluid’s velocity boosts with various parameters like For the growing value of The velocity of nanofluid rises near the plate with increasing This aims to study the heat and mass transfer of Oldroyd-B bio-magnetic nanofluid with ramped conditions in the permeable medium. Some unitless parameters are used to make the dimensional governing equations into non-dimensional form. To develop the resulting Oldroyd-B nanofluid model three type definitions of fractional operators are introduced. LT technique is used for the solutions of the flow problem. For comparison and authenticity of our solutions, Zakian’s and Stehfest’s algorithms are used. Following key points are concluded from this investigation;


Drilling issues such as shale hydration, high-temperature tolerance, torque and drag are often resolved by applying an appropriate drilling fluid formulation. Oil-based drilling fluid (OBDF) formulations are usually composed of emulsifiers, lime, brine, viscosifier, fluid loss controller and weighting agent. These additives sometimes outperform in extended exposure to high pressure high temperature (HPHT) conditions encountered in deep wells, resulting in weighting material segregation, high fluid loss, poor rheology and poor emulsion stability. In this study, two additives, oil wetter and rheology modifier were incorporated into the OBDF and their performance was investigated by conducting rheology, fluid loss, zeta potential and emulsion stability tests before and after hot rolling at 16 h and 32 h. Extending the hot rolling period beyond what is commonly used in this type of experiment is necessary to ensure the fluid’s stability. It was found that HPHT hot rolling affected the properties of drilling fluids by decreasing the rheology parameters and emulsion stability with the increase in the hot rolling time to 32 h. Also, the fluid loss additive’s performance degraded as rolling temperature and time increased. Adding oil wetter and rheology modifier additives resulted in a slight loss of rheological profile after 32 h and maintained flat rheology profile. The emulsion stability was slightly decreased and stayed close to the recommended value (400 V). The fluid loss was controlled by optimizing the concentration of fluid loss additive and oil wetter. The presence of oil wetter improved the carrying capacity of drilling fluids and prevented the barite sag problem. The zeta potential test confirmed that the oil wetter converted the surface of barite from water to oil and improved its dispersion in the oil. Drilling fluids are essential for a variety of reasons, including carrying drilled cuttings to the surface, cleaning, cooling and lubricating the drilling bit, reducing friction and maintaining borehole integrity ,2,3,4,5.The required properties for drilling fluids are described in the API I3B-2 procedures of standard practice for testing oil-based drilling fluids . In OBDFAdditionally, accumulated solid particles and drilled cuttings increase the likelihood of pipe sticking and reduce penetration rate . Barite Drilling fluids generally behave as non-Newtonian fluids and their behavior varies depending on the temperature and pressure. The temperature shows a prominent effect on the rheology of the drilling fluids. Additionally, the rheology of drilling fluid varies significantly with pressure and temperature, which creates complications when drilling deep wells. The viscosity of the drilling fluids can increase severalfold when the temperature of the fluid is reduced from ambient to seabed conditions (4 °C in the Gulf of Mexico). Similarly, it can plummet severalfold because of increasing the temperature of the bottomhole from ambient conditions. Such a change in viscosity can have significant consequences on the equivalent circulating density (ECD), the stability of the wellbore, and the suspension properties . The effDardir et al. evaluated the rheological characteristics of a formulated ester-based drilling fluid and original field ester-based drilling fluid at temperatures ranging from 25 °C (77 °F) to 100 °C (212 °F), as well as under aging conditions of 16 h at 177 °C (350 °F) temperature. The rheological characteristics of the formulated ester and field ester-based drilling fluids decreased as the temperature increased from 25 °C (77 °F) to 100 °C (212 °F). Further, the rheological properties of the drilling fluids degraded as the aging time increased from 0 to 16 h at high temperature of 177 °C (350 °F) .Drilling complications are expected to occur during difficult drilling conditions, such as drilling through shale layers or rock layers with different hardnesses. These drilling complications could result in a stuck pipe, shale swelling or wellbore instability ,34,35,36Over the years, surfactants are being used for several applications in drilling fluids. In OBDF, the most common applications of surfactants are as emulsifiers and wetting agents . As bariThis study’s objective is to test the performance of different oil-based drilling fluids (OBDFs) under high pressure high temperatures. Four different formulations of OBDFs  were tested in this study. The objective is to investigate how the different formulations of the OBDF will behave in terms of their density, rheology and stability. Ultimately, this work investigated the drilling fluid’s capability to provide flat rheology properties under high temperature and pressure conditions. Furthermore, the effects of hot rolling the drilling fluids for different extended periods (16 h and 32 h) were investigated too. The original formulation of the drilling fluid (DF-1) is a barite-free OBDF. Barite was used as a weighting material in the other two formulations (DF-2 and DF-3). Rheology modifier and oil wetter are both included in DF-3 and DF-4. DF-4 formulation was slightly changed from DF-3. To test the stability of the DF-2, DF-3 and DF-4 formulations, they were hot-rolled for 16 to 32 h. Several experiments were conducted to assess the performance of drilling fluids, including density, rheology, fluid loss and electrical stability.The OBDF was prepared as per API standard procedure (API-RP-13I) . A HamilTo test the stability of the DF-2 and DF-3 formulations, they were both hot-rolled (aging) at 177 °C (350 °F) temperature using a roller oven for 16 h (DF-2-16h and DF-3-16h) and for 32 h along with DF-4 . All the tests in this work were conducted on the three different formulations of OBDF drilling fluids  and conducted on the hot-rolled DF-2-16h, DF-3-16h, DF-2-32h and DF-3-32h drilling fluids as they are compared with the OBDF formulations before hot rolling. Furthermore, DF-4 formulation was tested after hot rolling for 32 h at high temperature conditions.The term “flat rheology” refers to drilling fluids, a concept born out of the desire to eliminate drilling mud loss during casing and liner operations in deepwater wells. It was believed that if a drilling fluid had a “near” constant yield point at low temperature and high pressure and increased temperature and high pressure, accuracy in predicting pressure response behavior during pipe tripping would improve, thereby eliminating or minimizing downhole losses. This is a concept worth developing further. As a result, drilling fluid manufacturers focused their efforts on the flat system. However, the ability to control a flat rheology profile is influenced by several non-controllable mechanisms, including temperature and pressure variations, rheological modifiers and drill solids, changing shear rates in the annulus and variations in the annulus alkalinity and changes in rheological modifier concentration. The superior performance is achieved by combining the appropriate emulsifiers, wetting agents, rheology modifiers and supplementary viscosifiers. A simplified and improved flat rheology system enhances emulsion stability as well as thermal and fluid lubricity.In this study, OBDFs were prepared by combining various emulsifiers, viscosifiers, wetting agents, rheology modifiers, fluid loss controllers and weighting agents to achieve the desired properties such as flat rheology and high temperature tolerance at extended hot rolling time. The primary emulsifier used is a fatty acid amide and the secondary emulsifier used is a fatty acid polyamide. These emulsifiers are a hydrocarbon-based, non-ionic wetting, demulsified surfactant, which acts on oil-water interface to prevent emulsions and generates a stable micro emulsion in water. They are designed for general use in the removal of hydrocarbons and oil-based products. Besides, they are used to clean metal surfaces. They are compatible with all cementation and stimulation additives. The viscosifier is a treated organoclay which is a gelling agent used to obtain high viscosity values. The effect of these additives in the rheology profile is tested after hot rolling for at least 16 h to observe its effect in obtaining a flat rheology profile. The fluid loss controller used is a quaternary Amine treated organophilic lignite. The rheology modifier used is a polymerized urea- formaldehyde compound with α-cellulose filler. The oil wetter additive used is an alcohol alkoxylate high-performance polymeric additive, specifically developed to control fluid loss and as a result it outperforms traditional additives. The product works well at temperatures up to 150 °C.Drilling fluid density affects the application of hydrostatic pressure and the prevention of formation’s fluid incursion into the wellbore. In this study, density was measured at atmospheric conditions using pressurized mud balance from OFITE. The retort test was conducted to measure the oil/water contents, which is a method used to calculate the percentages of oil, water and solids. The test was conducted using 10 mL retort kit provided by FANN.Drilling fluid serves a variety of purposes, including maintaining hydrostatic pressure, transporting and suspending drill cuttings. Drilling fluid rheology is one of these features. It is a branch of physics concerned with the flow and deformation of materials. It can assist us in comprehending and explaining fluid behavior under a variety of variables, such as temperature, pressure and external forces. Plastic viscosity, yield point and gel strength are all rheological properties of drilling fluids. The ability to track mud rheological parameters under downhole circumstances is a critical aspect in determining the success of any wellbore drilling operation.In this study, rheology test was conducted at 49 °C (120 °F) temperature and atmospheric pressure conditions using a digital viscometer from OFITE (Model 900). Plastic viscosity (PV) and yield point (YP) were calculated using Equations (1) and (2):The gel strength was determined as per the procedure reported in our previous publication .Filtration tests are a method for evaluating a drilling fluid’s filtration behavior and wall cake-building features. They inform how much drilling fluid filtrate has infiltrated a porous and permeable formation. Further, it indicates the change in the degree of wettability alteration in the near-wellbore zone due to filtrate invasion. It shows the potential for the tight hole or differential sticking problem.The loss of liquid (filtrate) from a drilling fluid due to filtration is controlled by the filter cake formed of the solid constituents in the drilling fluid. The test in the laboratory consists of measuring the volume of liquid forced through the filter paper for a 30-min period under given pressure and temperature using an HPHT fluid loss cell. The drilling fluids’ fluid loss and wall building potential were determined by applying the API standard procedure (API-RP-13B) . The fluAn electrical stability test is performed to evaluate the drilling fluids’ emulsion stability and oil-wetting qualities . The tesZeta potential (ζ) is defined as the difference between the potential of the dispersion medium and the stationary layer of liquid adhering to the particles. It is a vital particles physical property that determines the coagulation and dispersion of the particles in the dispersion medium. Further, the colloidal stability and surface modifications are studied using zeta potential measurements . The wetThe drilling fluid formulation DF-1 had a density of 63 PCF, whereas DF-2 and DF-3 had densities of 95 PCF mainly caused by the added barite. The formulations’ densities were steady at 95 PCF even after hot rolling as shown in A retort test was conducted to determine the oil-water contents in the drilling fluids. The oil water content in DF-2 and DF-3 differed slightly from DF-1 because barite increased the percentage of solids and decreased the percentage of liquids. For DF-1, the oil content is 81% and water content is 19%. The oil-water content of DF-2 and DF-3 were nearly the same (82% oil content and 18% water content). After hot rolling, no noticeable changes in the oil water contents were observed. DF-4 had a slight change in oil-water contents from DF-3. In DF-4, water volume was slightly reduced and the solid percentage was slightly increased compared to DF-3 by adding more fluid loss control additive.Rheological properties such as yield point, plastic viscosity and gel strength were measured. The resistance of a fluid to flow is referred to as plastic viscosity. It is used to determine the size, shape, distribution and number of solids, as well as the liquid phase’s viscosity. It is undesirable to have a fluid with a high plastic viscosity as high viscosity increases the equivalent circulating density (ECD) and energy required to run the pumps. The plastic viscosity of DF-1 was 18 cP, while the addition of barite increased the plastic viscosity of DF-2 by 106.1% to 37.1 cP. For DF-3, the addition of rheology modifier and oil wetter increased the PV by 10.8% to 41.1 cP. Furthermore, the PV was affected by hot rolling at the high temperature similar to the behaviour observed by previous studies . Althoug2 while the yield point of DF-2 formulation having barite was 39.5 lb/100 ft2, which is 60.56% higher than DF-1. Further incorporation of rheology modifier and oil wetter increased the yield point by 11.16% to 43.91 lb/100 ft2. After hot rolling DF-2 for 16 h, the yield point was slightly decreased and it was found to be 38.1 lb/100 ft2. Therefore, DF-2 relatively maintained yield point after 16 h of hot rolling. After hot rolling for 32 h, the yield point of the formulation DF-2 decreased by 44.55% —when compared to prior to hot rolling—to 21.9 lb/100 ft2. This shows that DF-2 lost rheology after 32 h of hot rolling. For DF-3, similar behaviour of DF-2 was observed but with lighter impact on yield point after 32 h of hot rolling. The yield point of DF-3 decreased by 31.38% from 43.91 to 30.13 lb/100 ft2 after 32 h of hot rolling. For DF-4, the yield point was decreased to 28.18 lb/100 ft2 after 32 h of hot rolling. It was observed that prolonged high temperature aging affected the rheology of drilling fluids. The yield point is the stress required to initiate fluid movement and represents the resistance to beginning flow. If the applied stress is less than the yield stress, the fluid will regain its strain when the applied stress is removed. Electrical charges on or near the surface of the particles cause this resistance. Higher yield points result in higher frictional pressure losses and an increase in ECD. For the yield point, DF-1 showed a yield point of 24.6 lb/100 ftThe ratios of yield point to plastic viscosity (YP/PV) is used to investigate the cutting suspension of drilling fluids. The drilling fluids having a ratio in the range of (0.75–1.5) shows good suspension capacity. This ratio was highest for DF-1 was 1.37 while the YP/PV ratio for DF-2 formulation was 1.06. For DF-2, after hot rolling for 16 h and 32 h, the YP/PV ratio was 1.14 and 0.77, respectively. Therefore, after 16 h of hot rolling, the YP/PV ratio slightly increased by 7.55% and resulted in better suspension capacity of the drilling fluid. On the other hand, drilling fluid formulation DF-2 lost cuttings suspension capacity after 32 h of hot rolling as the YP/PV ratio decreased to 0.77. For DF-3, the YP/PV ratio was affected by hot rolling and it was decreased with high temperature exposure. A very slight change observed after 16 h hot rolling while after 32 h, the YP/PV ratio reduced to 0.81. Therefore, DF-3 showed better carrying capacity after 32 h of hot rolling when compared to DF-2. Furthermore, DF-4 after 32 h of exposure did not bring major change in its ratio when compared to DF-3-32h. The ratios of yield point to plastic viscosity (YP/PV) for the tested drilling fluids are shown in 2, respectively. For DF-2, the gel strength for 10 s and 10 min were the same at 20 lb/100 ft2. After hot rolling DF-2 formulation for 16 h, the gel strength for 10 s and 10 min were 20 lb/100 ft2 and 23 lb/100 ft2, respectively. It showed that DF-2 maintained gel strengths after 16 h of hot rolling but after 32 h of hot rolling, DF-2 gel strengths for 10 s and 10 min were decreased significantly to 10 lb/100 ft2 and 12 lb/100 ft2,, respectively. The addition of rheology modifier and oil wetter did not bring much change in gel strength before hot rolling as noticed in DF-3. After hot rolling for 16 h, 10-s and 10 min gel strengths for DF-3 increased to 20 and 30 lb/100 ft2 from 17 and 19 lb/100 ft2 respectively. After 32 h of hot rolling, slight reduction in gel strengths was noticed compared with gel strength after 16 h, but the values are still high compared to gel strength before hot rolling.Gel strength describes the drilling fluid’s ability to suspend drill cuttings at static condition. The shear stress of a drilling fluid is measured with a viscometer at a low share rate (3 RPM) after being static for a length of time [10 s and 10 min in the API standard]. For the gel strength, 10 s and 10 min gel strengths were measured for all formulations. The 10-s and 10-min gel strengths for DF-1 formulation were 10 and 11 lb/100 ftSimilarly, a reduction in gel strength is observed in DF-4 after 32 h hot rolling. For DF-4, the values of 10-s and 10 min gel strengths were less when compared to DF-3 after 32 h of hot rolling. Marinating the gel strength even after 32 h of hot rolling was mainly due to the rheology modifier and the oil wetter. The gel strength results of the different drilling fluid formulations are given in From the rheology results, it can be inferred that DF-2 and DF-3 maintained their rheology profile after 16 h of hot rolling (less than 10% decrease for DF-2 and DF-3 in both PV and YP). Therefore, the flat rheology profile was obtained after 16 h of hot rolling. However, when hot rolled for 32 h, the rheological properties of DF-2 drastically changed (23.18% decrease in PV and 44.55% decrease in YP). Therefore, DF-2 lost its flat rheology profile. On other hand, DF-3 was affected less (less than 10% decrease in PV and 31.38% decrease in YP) when compared DF-2. Therefore, DF-3 only slightly lost its rheological profile after 32 h hot rolling when compared DF-2.Furthermore, DF-4 reduced rheological parameters after 32 h hot rolling and maintained results close to DF-3-32h. This showcases the impact of the rheology modifier and oil wetter additives in obtaining flat rheology of drilling fluids. The PV was maintained in DF-3 and DF-4 due mainly to the addition of the oil wetter. It is apparent that the oil wetter made the calcite and barite particles more oil-wet and therefore enhanced the stability and suspension of calcite and barite in oil .For the HPHT fluid loss tests, DF-1 formulation had less filtration loss than the DF-2 and DF-3 formulations, but with minor difference. The fluid loss was directly affected by the weighed material. However, after hot rolling DF-2 and DF-3 for 16 and 32 h, the fluid loss dramatically increased. After hot rolling for 16 and 32 h, fluid loss of DF-2 increased by 106% and 446%, respectively. Similarly, for DF-3, fluid loss increased after hot rolling for 16 and 32 h by 144% and 450%, respectively. After 16 h of high temperature aging, the emulsion stability improved, but the fluid loss volume increased. It showed that the emulsifiers retained their properties after 16 h high-temperature aging, while the fluid loss controller lost it. The most likely reason of increased fluid loss volume is the performance and quantity of fluid loss control additive. DF-4 was mixed with some changes to specific additives to keep the qualities of DF-3 at high temperatures. The amount of fluid loss control additive in DF-4 was raised among the adjusted additives. After 32 h of hot rolling, the increase in fluid loss control additive quantity had a favorable effect on fluid loss and sustained fluid loss at 2.5 mL. From the fluid loss experiments on the different drilling fluids, it was observed that the formulation of additives used in DF-4 has prevented the sag of the solids  after extended period of hot rolling and in turn reduced the filtration (fluid loss is 2.5 mL only). This formulation with the additives used, such as the oil wetter, greatly reduces the sag issues in oil-based mud.The filter cake thickness was measured for all the drilling fluid formulations and it was observed to increase in direct relation to fluid loss. A thin filter cake was obtained from formulation DF-1 (1.6 mm) and a thick filter cake was obtained from DF-2 and DF-3 after 32 h of hot rolling . After an extended period of hot rolling, DF-4 still resulted in thin filter cake with respect to its fluid loss at high temperature conditions. Having a thin impermeable filter cake will help maintain the hole and allow subsequent operations to run smoothly. Using the OBDF formulation with the additives used in DF-4 achieved this thin impermeable filter cake even after going through an extended period of hot rolling. To investigate the emulsion stability of the drilling fluids, electrical stability (ES) test was carried out at a temperature of 49 °C (120 °F). The higher electrical stability voltage the better is the emulsion stability. Before hot rolling, formulation DF-3 had the highest electrical stability (609 V) compared to formulation DF-1 (288 V) and DF-2 (560 V). It demonstrated the combined effect of barite, rheology modifier and oil wetter in improving the drilling fluid’s emulsion stability. Later, DF-2 and DF-3 were hot-rolled for 16 h and 32 h. After each hot rolling, emulsion stability was measured. It was observed that after hot rolling for 16 h, the voltage value increased by 19.28% to 668 V from 560 V for DF-2. For DF-3, it increased by 10.50% to 673 V from 609 V. This increase in voltage shows a higher emulsion stability of the DF-2 and DF-3 after 16 h of hot rolling. However, increasing the hot rolling period to 32 h resulted in lower voltages and reduced emulsion stability. This is similar the behaviors observed in previous relative studies ,48. AfteGiven that the recommended electrical stability is to be more than 400 V, DF-3 maintained an electrical stability above 400 V even after 32 h of hot rolling. DF-4 showed lower than 400 V (385 V) electrical stability—after 32 h of hot rolling, which is not that far off from the recommended value especially when compared with the effect of extended period of hot rolling in DF-2. The zeta potential test was conducted on two different samples. In the first sample, barite was mixed in water. In the second sample, the oil wetter was added in the first sample and investigated the change in wettability by measuring the zeta potential. It was observed that barite particles in distilled water resulted in negative zeta potential (−12.156 mV) at a pH of 7.4. The negative value of zeta potential depicts a water wet surface ,51. The OBDFs are, in general, considered toxic to the environment, specifically to the marine environment. Nonetheless, certain circumstances require the use of OBDFs due to their inherent advantages—for example, drilling in shale formations, high-temperature stability, extended-reach or horizontal wells, high penetration rates, lubricity, low mud weight, prevention of hydrate formation, reduced waste generation and wellbore stability. Additionally, the high cost of OBDFs can be offset by enhanced drilling performance. OBDFs have the potential to reduce the environmental impacts through rapid drilling operations and low air emissions from rig machinery. The primary source of concern in OBDFs is the base oil, which is frequently diesel. Diesel oil is discouraged and is being phased out in favor of mineral oil or other synthetic oil to mitigate the environmental impact of OBDFs. The study’s primary objective is to demonstrate the value of oil wetter in drilling fluids, which is a surfactant with minimal environmental impact. Other chemicals used in the drilling fluids’ formulations are widely used as drilling additives worldwide.(1)The rheology of the drilling fluids was changed by hot rolling at HPHT conditions. After 16 h of hot rolling, the rheology profiles of DF-2 and DF-3 were flat. After 32 h of hot rolling, the formulations lost their rheological character, having a greater impact on DF-2 than DF-3 and DF-4. The oil wetter and rheology modifier positively impacted drilling fluid performance and provided flat rheology of drilling fluids.(2)The fluid loss increased with the hot rolling duration, indicating that the fluid loss additive’s performance was compromised at high temperatures. Nevertheless, an increase in the concentration of the fluid loss controller assisted in maintaining the fluid loss as observed with DF-4 performance after 32 h of hot rolling.(3)The formulation of additives used in DF-4 prevented the sag of the solids  after an extended period of hot rolling and reduced the filtration (fluid loss is 2.5 mL only).(4)The filter cake thickness was increased with respect to fluid loss volume. After an extended period of hot rolling, DF-4 still resulted in thin filter cake with respect to its fluid loss at high temperature conditions. Having a thin impermeable filter cake will help maintain the hole and allow subsequent operations to run smoothly.(5)The oil wetter changed the barite particles’ wettability from hydrophilic to hydrophobic by interacting and adsorbing on barite particles which played a significant role in their suspension in OBDFs preventing the common barite sag problem.Several experiments were conducted to assess the performance of four OBDF formulations , including density, rheology, fluid loss, zeta potential and electrical stability studies. DF-1 is the original barite-free drilling fluid formulation. For DF-2, barite has been added as a weighting material. For DF-3, along with the addition of barite, rheology modifier and oil wetter were mixed too. DF-4 was mixed based on the performance of the DF-3 and was slightly modified from DF-3. DF-4 contained high concentrations of fluid loss controller and oil wetter. The water content was also reduced in DF-4. The rheology of the drilling fluids was changed by hot rolling at HPHT conditions. After 16 h of hot rolling, the rheology profiles of DF-2 and DF-3 were flat. While after 32 h of hot rolling, these formulations lost their rheological character, having a greater impact on DF-2 than DF-3 and DF-4. Clearly, the highest fluid loss gained was in drilling fluid that has been hot rolled for 32 h. Although, DF-4 has been hot rolled for 32 h, the increase in fluid loss control additive quantity had a favorable effect on fluid loss and sustained fluid loss at 2.5 mL. On the basis of experimental investigations, the following conclusions have been reached:


D and M, are also discussed as they relate to velocity and temperature distributions. We observed that the velocity profiles decreased with increasing values of In this work, we studied the impacts of transmitting light, nonlinear thermal, and micropolar fluid mechanics on a wire surface coating utilizing non-Newtonian viscoelastic flow. Models with temperature-dependent variable viscosity were used. The boundary layer equations governing the flow and heat transport processes were solved using the Runge–Kutta fourth order method. A distinguished constituent of this study was the use of a porous matrix that acted as an insulator to reduce heat loss. In this paper we discuss the effects of numerous development parameters, including  Many of the fluids that engineers and scientists interact with are Newtonian fluids . However, in many circumstances, the foundation of Newtonian behavior is non-rational and complex, necessitating the development of non-Newtonian responses. Non-Newtonian fluid behavior can be found in a variety of fluid materials, such as glue, custard, paint, blood, and ketchup. Many studies have emphasized the importance of non-Newtonian fluids because of their wide variety of engineering and industrial applications ,5,6,7,8.Magnetohydrodynamics deals with highly conductive flow characteristics in the applied magnetic field. Many scholars have dedicated a significant amount of time to the study of magnetohydrodynamic flow problems ,28,29,30Researchers are interested in fluid flow through porous media because of the wide range of engineering applications. Porous media include carbonated pebbles, wood, metal foams, and other well-known materials. They have many industrial and residential uses, including as filters, printing papers, fuel cells, and batteries, which now use a very thin porous layer. Porous media have received a great deal of attention in several studies ,32,33.The heat exchange of non-Newtonian flow fields has gained popularity due to its potential applications in a wide range of industries. Rehman et al.  investigNobody has yet examined the coating process for wire using a magnetohydrodynamic Eyring–Powell fluid. The goal of this work was to use Reynolds’ and Vogel’s models to describe the wire-coating process as it relates to heat production, porous materials, and variable viscosity.The proper formulas for fluid velocity, stress tensor, and temperature field in the above-mentioned circumstances are as follows ,18,19,20For viscoelastic Eyring–Powell fluid, the Cauchy stress tensor is written as ,18,19,20Equation (4) can be simplified as follows:For the sake of this discussion, the appropriate boundary conditions are as follows ,20:(6)wJEquation (7) is satisfied automatically when (1–3) are used, and non-zero terms are as follows:However, due to the pressure gradient, Equation (14) displays the flow. When departing the die, the only event occurring is wire drag. As a result, pressure gradient has no effect and Equation (14) becomes:Energy Equation (9) becomes:Dimensionless parameters are defined as ,18,19,20We derive the following form by introducing the above new variables in Equations (6), (15) and (16):Reynolds’ model is utilized to explain temperature-dependent viscosity in this case. For Reynolds’ model, viscosity in dimensionless form is :(22)μ≈1−It is used to calculate temperature-dependent viscosity variation, with m as the viscosity parameter. We introduce the following non-dimensional parameters ,18,19,20In view of Equation (23), Equations (18)–(21), after deleing the asterisks, become:For Vogel’s model :(28)μ=μ0After expanding Equation (28), we have:D and B are viscosity parameters and Here, Equations (30)–(33), which regulate the system, are reduced to first ODE.The RK4 approach is used to solve them numerically ,18:(34)dWe introduce the following new variables:The boundary conditions become:Similarly, for Reynolds’ and Vogel’s models, we transform the higher ODE into a first-order ODE as:For Reynolds’ model:For Vogel’s model:ɛ on the velocity distribution. With increasing ɛ, the velocity profile shows an increasing tendency. The influence of M increases. The impact of Br) is a dimensionless parameter used during melt processing to describe the conduction of heat from a barrier to a moving viscous fluid. With increasing β0 = 0.2, M = 0.6, Br = 0.1, Q = 0.1, and m = 0.3, Kp increased, the velocity inside the die decreased. It is self-evident that the existence of a porous material generates greater fluid dynamic restriction, causing the flow to decline. As a result, as the impermeability factor increases, the barrier to flow velocity increases, and therefore velocity falls. N on the velocity profile for the Reynolds model. The growing action caused by a rise in N is eliminated by the velocity curve. Br, with M = 0.1, Kp = 0.6, and Q = 0.6. In Vogel’s model, the velocity curve in D. Q increases in the case of Vogel’s model, with D = 0.3, M = 0.1, and Br = 0.5. When M = 0.5, Kp = 0.6, and N = 0.02 in the case of constant viscosity, ɛ. With increasing ɛ, the velocity profile shifted downward. The influence of the Brinkman number (Br) on the temperature curve with constant viscosity is shown in Br is increased in Q on the temperature profile. With increasing Q, the fluid velocity shows an increasing tendency. ɛ increases, in the case of the Reynolds model. In M increases, the temperature profile increases as well. For the Reynolds model, the temperature profiles show an increasing behavior as M increases. By applying a perpendicular magnetic field to an electrical conductor fluid, a Lorentz force is created. The resulting Lorentz force has the capacity to eliminate fluid velocity in a confined geometry while also causing a temperature increase. As a result, increasing the value of the magnetic field parameter causes the thickness of the thermal boundary layer to develop, but the speed in the flow direction drops. With increasing Q, the temperature curve shows a decreasing behavior in D = 0.5, Kp = 0.2, and Q = 0.6, M. Ω led to a declining temperature trajectory in Vogel’s model with N = 0.3, β0 = 1.2, Kp = 0.2, and D = 0.5. The influence on the streamlines of various values of Br with uniform velocity is shown in Br in the case of the Reynolds model. Br in Vogel’s model.An EP (Eyring–Powell) fluid was examined for wire surface coating in this study. In a porous medium, wire coating usually happens inside a die with persistent magnetic and heat emission effects. We examined the effects of numerous development parameters, including A HAM approach was used for confirmation of the results. As demonstrated in ɛ, M, Br, N, and D caused the fluid velocity to increase, whereas increases in the values of Kp, Q, and D caused fluid velocity to decrease. For the Reynolds model, the temperature profiles depicted increasing behavior as M increased. By applying a perpendicular magnetic field to an electrical conductor fluid, the Lorentz force is created. The resulting Lorentz force has the capacity to eliminate fluid velocity in a confined geometry while also causing a rise in temperature. As a result, raising the magnetic field parameter causes the thickness of the thermal boundary layer to develop, but the speed in the flow direction to drop. When increasing Br, the temperature profiles decreased. This is because the fluid flow transports relatively less energy nearer to the borders in comparison to the core area, which may be the result of greater temperatures near the wall area. The temperature profile indicated an increasing tendency in the values of ɛ and M, as well as a declining behavior in the values of Br and Q. In addition, the present study was also validated with HAM and compared with published literature, and the results were in good agreement.We calculated the influence of an MHD fluid as well as heat transmission on the coating of wire utilizing a viscoelastic fluid in the presence of a porous medium. The impact of temperature-dependent viscosity and Joule heating were also discussed. The wire was coated with an Eyring–Powell fluid in a pressure-type die. Because a porous matrix was employed as an insulator, the heat and mass flexibility process reduced heat loss, thus improving the melting capacity. The numerical approach was utilized to obtain a numerical solution to the given model. Regarding velocity and temperature profiles, the outcomes of the involved parameters were shown. Increases in the values of


By combining the discrete element method (DEM) with computational fluid dynamics (CFD), this study proposes a three-dimensional CFD–DEM fluid–solid coupling microscopic computational model for analyzing the micromechanisms of instability and failure in a coal-bearing soil slope during rainfall. The CFD–DEM fluid–solid coupling model indicated that the main failure mode of the coal-bearing soil slopes was rainwater washing, and the slope sliding surface was predicted as an approximately linear segment. The adaptability of this numerical method was verified by comparing its results with those of rain-washed slopes in an outdoor model test. Rainfall changed the microscopic parameters such as the force chain, coordination number, and porosity of the slope soil particles. The porosity of the slope’s top particles increased from 0.35 in the initial state to 0.80 in the unstable state. This change was directly related to the macroscopic mechanics of the slope soil. By analyzing the changes in the microscopic parameters of the particles, the failure evolution law of the coal-bearing soil slopes during rainfall was explored from a microscopic perspective. This study not only provides a theoretical basis for the protection design and construction of coal-bearing soil slopes in the region but can also analyze macroscopic mechanical laws of discrete media from a micro–macro perspective in geotechnical engineering. Rainwater infiltrates the soil pores on sloped ground. When the soil pores are completely filled with rainwater, the soil becomes saturated, and its shear strength and stability are reduced. Traditionally, saturated soils are modeled by continuous coupling models, which are usually based on homogenizing mixture theories such as Biot theory or the micromechanical equations of motion , 2. ThesThe Euler–Lagrange method usually treats the rock and soil masses as discrete particles with specific sizes and shapes, and the continuous fluid is divided into several grid units. The average characteristics of the fluid in a grid unit are considered to characterize the entire unit. Averaging avoids the computational inefficiency of calculating the microscopic pore water movements between the soil particles. In such methods, the discrete media and fluids are usually modeled with the discrete element method (DEM) and computational fluid dynamics (CFD), respectively. In the early days, CFD–DEM fluid–solid coupling methods were mainly applied in the industrial field. For example, Tsuji et al.  coupled 2D. They numerically simulated single-particle free settling in the water, a one-sided drainage one-bit consolidation test, and a biaxial undrained compression test, reporting ideal results. Wang et al. [However, the geotechnical engineering community has been slow to adopt the CFD–DEM fluid–solid coupled model. Shamy and Zeghal  applied g et al.  simulateIn this study, the research target was a coal-bearing soil slope from the Wanzai–Yichun Expressway Project in Jiangxi Province, China. On the basis of CFD–DEM coupling methods, a 3D CFD–DEM fluid–solid microaction calculation model was established for the soil slope. The failure mechanism of the coal-bearing soil slope during rainfall was analyzed, and the calculation results well agreed with the model test results. The results are expected to provide a theoretical basis for the protection design and construction of coal-bearing soil slopes in this region.m is the particle mass, I is the moment of inertia, and M is the force moment acting on the particles.Fluid–solid coupling theory (CFD–DEM) investigates the effect of fluid on soil particles . In thisε is the porosity of the unit in which the fluid is located, and χ is an empirical coefficient that renders the drag force applied to both high and low local porosity.Assuming that the force exerted by the fluid on the particles always acts on the centroid (ignoring the bending moment), the drag force is given byρf is the fluid density, r is the particle radius, μf is the dynamic viscosity coefficient of the fluid. Cd is the drag force coefficient, which is expressed as follows:χ in Rep is the Reynolds number of particles, defined asV is the volume of a fluid unit, ∇p is the fluid gradient, and the sum object on the molecule is the particles superposed by the fluid unit.The drag force of a single particle in The interaction force of the fluid on the particles is then expressed as follows:Continuum equation. The average Navier–Stokes equation is useful for meso analyses and quantitative descriptions of pore fluid characteristics. The flow control equation derived from the law of conservation of mass  defines the net mass flux through the volume element per unit time. As this quantity equals the change of mass in the volume element, we can writeMomentum equation. The momentum equation of fluids is a variant of Newton’s second law of motion. It describes the increment of momentum per unit volume per unit time and is contributed mainly by the momentum carried by the surface inflow mass and the momenta caused by various forces . Averaging the external forces in the volume element, Anderson and Jackson [p is the fluid pressure and the minus sign denotes a positive force acting on the particles. Jackson  deduced ith particle, the interaction force is given byith particle is given byith particle, respectively, and Mij is the moment of inertia of the ith particle when impacted by the jth particle.The particle motions satisfy Newton’s second law. The fluid–particle interaction force 3D, which enables data exchange between PFC3D and its embedded CFD solver and hence the coupling calculations of fluid and solid. The fluid control Eqs (The program was composed in the fish language of the business software PFCtrol Eqs  and 11)3D, whichVerifying the fluid–solid coupling program of CFD–DEM. According to Stokes’ law, a small ball immersed in water will eventually settle under the action of gravity. This fundamental principle is exploited in the densitometer method, which measures the gradation of fine-grained soil in geotechnical tests. In this subsection, the feasibility of the above fluid–solid coupling program is tested on the free-falling motion of a single particle under the action of gravity in water.ρp and ρf are the particle and fluid densities, respectively; r is the particle radius; Cd is the drag coefficient.The particles fell freely in the liquid, and their velocity became stable after a certain time. The solid particles in the fluid were affected by gravity, buoyancy, and drag forces. The motion equation of falling spherical particles is expressed as follows:Rep is very small, the drag coefficient Cd simplifies toPa · s, and the particle and fluid densities were 2400 and 1000 kg/m3, respectively. Substituting the above parameters into At the (constant) settling velocity of the particles, After opening the CFD–DEM coupling program module on the PFC software platform, the grid data were imported and the above fluid parameters were specified. Particles of the same size and mass were generated in the fluid at the same time. As they sank under the action of gravity, the 1.5- and 2.0-mm-radius particles tended to final velocities of −6.89 and −12 mm/s, respectively, close to the theoretical results see . Substit3 (length × width × height). The test soil samples were taken from remolded soil exposed during excavations on a coal-bearing soil slope at K30 + 120 in section A5 of the Wanzai–Yichun Expressway Project in Jiangxi Province, China. The slope model was filled with a soil layer at 40 cm intervals at a slope ratio of 1:1.5. The simulated rainfall intensity was set to 9.84 × 10−7 m/s, the average intensity of the maximum rainfall in Yichun, Jiangxi Province, during July and August of the most recent decade. The tests were conducted on November 19, 2018, from 8:00 am to 6:00 pm. Field observations  mrvations  showed tSoil displacement monitoring of model slope. During the test, 29 side tracer points in four rows were buried in the slope soil . As shown in On the basis of the fluid characteristics of the model slope and the artificial rainfall intensity, the fluid parameters in the saturated zone of the slope were set to the values in To observe the movement of soil particles at different locations on the wetted slope, the slope soil was examined in several areas. The saturated zone formed by rainwater infiltration was divided into four subzones, whereas the unsaturated zone was divided into three subzones . Under cTo better observe the movements of the tracer points in the slope model during rainfall, As shown in As evidenced in X, Y, and Z directions were simulated and processed in Surfer software to generate a cloud atlas. Figs To identify the internal stress changes in the slope soil during rainfall infiltration and to analyze the soil failure mechanisms, 17 measuring circles were constructed in the simulated soil. After the fluid application, the monitored stress changes of the slope soil in the Z direction was 0.16 MPa. The stresses were small on the top and bottom of the slope and large inside the slope  the walls at the top of the slope were not removed by rainfall. The interparticle contact force was high and the maximum soil stress in the he slope . (b) Afthe slope . Under the slope . (d) Afthe slope . This reAs shown in the cloud atlas of Coal-bearing soil slopes are easily weathered, softened, and disintegrated by water; accordingly, they can be treated as discontinuous media in DEM calculations and analyses. Comparing the DEM-simulated results with those of the outdoor rainfall test, we found that rainfall-induced erosion was crucially involved in the failure of coal-bearing soil slopes. Moreover, the slope–slip surface was an approximately linear segment. Finally, the erosion range of the model slope closely matched the slip surface predicted by the CFD–DEM coupling model. This study demonstrated that the CFD–DEM fluid–solid coupling method could rationally simulate the rainfall-induced failure of coal-bearing soil slopes. It also simulates Newton’s law of motion of discrete media in geotechnical engineering analyses .The macroscopic mechanical properties of soil reflect the particle movement and positions, soil thickness, and density of the force chain, and intuitively represent the forces and movement changes of particles. During the rainfall, the force chain significantly stretched along the slope. As the slope gradient reduced, the force chains at the top and on the slope surface became sparse, implying instability and massive movement of the particles in the saturated zone. Under the combined action of fluid and particles in the upper slope, the force chain in the lower slope became dense and thick, indicating that large contact forces developed between the particles in the slope, jeopardizing the stability of the zone. The simulated force–chain changes revealed the failure evolution process of the slope under the influence of rainfall, providing a deep understanding of the failure mechanism of coal-bearing soil slopes.The stability of slopes in discrete media can be analyzed in the CFD–DEM fluid–solid coupling model. Besides providing a theoretical basis for the protection design and construction of coal-bearing soil slopes in the study area, the results are expected to encourage analyses of macroscopic mechanical laws in discrete media from a micro–macro perspective in geotechnical engineering.In an outdoor rainfall test, erosion ditches were formed at different depths on the slope surface by rainwater washing, which is the main failure mode of slope soil. The ditches reached a maximum depth of 0.36 m in the mid-upper slope. The failure modes of coal-bearing soil slope were simulated in a CFD–DEM fluid–solid coupling model. The results were consistent with those of the outdoor rainfall test. The predicted slope–slip surface was approximately linear. The feasibility of applying the CFD–DEM fluid–solid coupling model to stability analyses of coal-bearing soil slopes was validated by the similarity between the simulated and actual model slope in the studied range of rainwater erosions.During the rainfall, the changes in the microscopic parameters of the slope soil particles, such as the force chain, coordination number, and porosity, were directly related to the macroscopic mechanics of the slope soil. Thus, by analyzing the changes in the particle microparameters, we elucidated the failure evolution rules of coal-bearing soil slopes under the influence of rainwater. We also analyzed the failure mechanism of coal-bearing soil slopes (a type of discontinuous medium) from a micro–macro perspective.The results verified that the stability of a discrete medium slope could be estimated by combining the DEM and the CFD method. The results not only provide a theoretical basis for the protection design and construction of coal-bearing soil slopes in this area but also provide new analyses of the macro mechanical laws of discrete media from the microperspective, which should advance the geotechnical engineering field.S1 File(PDF)Click here for additional data file.