Monitoring spatially heterogeneous dynamics in a drying colloidal thin
  film
Monitoring spatially heterogeneous dynamics in a drying colloidal thin film
P. Zakharov(1),∗ and F. Scheffold(1,2)
(1)Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland; email: Frank.Scheffold@unifr.ch
(2)Fribourg Center for Nanomaterials, University of Fribourg, CH-1700 Fribourg, Switzerland and
(∗)present address: Solianis Monitoring AG, CH-8050 Zurich, Switzerland
(Dated: July 10, 2018)
We report on a new type of experiment that enables us to monitor spatially and temporally heterogeneous
dynamic properties in complex fluids. Our approach is based on the analysis of near-field speckles produced by
light diffusely reflected from the superficial volume of a strongly scattering medium. By periodic modulation
of an incident speckle beam we obtain pixel-wise ensemble averages of the structure function coefficient, a
measure of the dynamic activity. To illustrate the application of our approach we follow the different stages in
the drying process of a colloidal thin film. We show that we can access ensemble averaged dynamic properties
on length scales as small as ten micrometers over the full field of view.
I. INTRODUCTION
Soft materials are frequently studied with traditional scat-
tering techniques using light, neutron or X-ray radiation
[1]. These techniques provide invaluable information about
the structure and dynamics in complex systems spanning
timescales from nanoseconds to hours and length scales from
nanometer to mm. Scattering methods usually provide infor-
mation about time or ensemble averaged bulk properties. The
method therefore implicitly assumes that the dynamic prop-
erties are stationary and fluctuations are Gaussian. The sit-
uation is qualitatively different in many dense soft materials
such as gels, foams, emulsions, pastes, hard-sphere glasses
[2–12] that display ultraslow relaxation processes. A large
number of studies have addressed this problem over the last
decade. It has been found that slow relaxations are frequently
associated with sudden intermittent changes [7, 8]. Intermit-
tent events however are not revealed by recording the time
averaged intensity correlation function g2(τ) . High order cor-
relation functions still require time-averaging but do in fact
contain information about non-stationary dynamics as shown
by Lemieux and Durian [3]. The recently introduced time re-
solved correlation (TRC) approach of Cipelletti and Trappe
solves the time averaging problem by using an area detec-
tor. The method of TRC determines the correlation coeffi-
cient c(t, τ) by multiplying two far-field speckle images taken
at time t and t + τ without any need for further time averaging
[7]. It is now possible to monitor the amount of correlation
c(t, τ) as a function of correlation time τ, as it is done in a
traditional experiment 〈c(t, τ)〉t = g2(τ) − 1, or as a function
of t. The advent of this new technique has revealed that in-
termittency is intimately related to the slow glassy dynamics
observed in many dense complex systems [7, 8].
In this article we report on a new echo speckle imaging
(ESI) technique that allows to monitor both spatially and tem-
porally heterogeneous dynamic properties. This is of partic-
ular importance since in many cases the observed intermit-
tency of the relaxation process can be related to a succes-
sion of spatially localized events [9]. Experimental evidence
for this scenario is however scarce [4, 5]. Our new concept
is to study properties of the near-field speckles produced by
multiply scattered light diffusely reflected from the superficial
volume of a strongly scattering medium. We use a spinning
ground-glass disk to scramble the incident beam which allows
us to create a large number of statistically independent optical
configurations at each point in the image plane. The high res-
olution both in time and space distinguishes our ESI approach
from other recent developments [13, 14]. To illustrate the ap-
plication of ESI we follow the different stages in the drying
process of a colloidal thin film. In the course of this process
the suspended particles undergo a continuous transition from
liquid to an amorphous solid driven by the evaporation of the
solvent and compaction of the solid component[15–17]. Due
to the evaporation of water the particle dispersion concentra-
tion increases until the colloids are jammed [11] and subse-
quently the remaining water evaporates from the porous solid
film [16].
II. EXPERIMENT
The echo speckle imaging (ESI) approach provides a real-
time two-dimensional image of the sample dynamic properties
characterized by the intensity structure function (ISF) using a
standard digital camera and imaging optics (Figure 1). Using
this method we can access ensemble averaged dynamic prop-
erties on length scale as small as ten micrometers over the
full field of view 1.6×1.2 mm2. The experiment is set up as
follows: light from a HeNe laser (power 15 mW, wavelength
λ = 632.8 nm) is dispersed by a ground glass mounted on a
stepper motor. The dispersed light is collimated to create a
speckle beam for a homogeneous illumination of the sample
surface. The diffuse reflected light is monitored in the im-
age plane with a charge-coupled device (CCD) camera PCO
Pixelfly (640×480 pixels of 9.9×9.9 µm2 size, 2×2 pixels bin-
ning) at magnification 1.8 positioned at about 50 cm from the
sample. This sets the lateral resolution for a meta pixel (com-
posed of 4 binned physical pixel) to L0 = 11 micrometers
which is larger than the transport mean free path of the dif-
fusely scattered light (in the range 2-5 micrometers) and also
large compared to the typical size of the colloidal particles of
0.2-0.5 micrometers. The speckle size is set by the camera di-
aphragm to about 5-10 µm. The estimated depth-of-focus of
the imaging system is close to 0.1 mm. The camera is set to
acquire 100 images per second with an exposure time of 1 ms.
Sweeping the speckle field over the sample with the stepper
FIG. 1: Experimental set-up: A. Near field laser speckle imaging
experiment: The incident laser beam is dispersed by a ground glass
mounted on a stepper motor. A digital camera records the scattered
light (cross polarized channel) in the image plane of the drying paint
film. The sample is kept at constant humidity (65%) and a balance
is used to monitor the weight. The inset shows the main liquid-solid
configurations in the drying process. B. Light scattering experiment
in the far-field using a focused incident beam.
motor allows ensemble averaging in a single point on the scat-
tering area. The period is defined by the ground glass rotation
frequency of 5 Hz. Correlation echoes after a delay time of
τ = 0.2 seconds are calculated at each point by comparing
20 sequential images taken at each revolution of the ground
glass. Additional time averaging over one second has been
performed in order to reduce statistical noise. We note that
this last step could easily be omitted when using a faster dig-
ital camera. The sample dynamic properties are analyzed in
terms of the normalized ISF:
d2(t, τ) = 〈[I (t − τ/2) − I (t + τ/2)]
〉/〈I〉2. (1)
Here τ characterizes the time scale probed and t indicates the
time evolution of the experiment [20]. The structure function
as a direct measure of the dynamic activity has several ad-
vantages over the commonly used intensity correlation func-
tion (ICF) g2(t, τ) = 〈[I(t − τ/2)I(t + τ/2)]〉/〈I〉2. While both
quantities are directly related in the limit of perfect mea-
surement statistics d2(t, τ) = 2
g2(t, 0) − g2(t, τ)
, the ISF is
known to outperform the ICF in accuracy when the collection
time is limited and further the ISF is less sensitive to low fre-
quency noise or drifts [21]. Our approach is technically sim-
ilar to the recently introduced two cell diffusing wave spec-
troscopy (DWS) echo technique [18, 19]. However instead of
FIG. 2: Multiple scattering of light in backscattering geometry. The
incident wave kin is dispersed and scattered along a path s. The scat-
tered wave kout leaves the sample at a distance rx,y ≤ 4l∗. The prop-
agating waves reach a typical depth z of the same order. Overall the
scattered light probes a volume of roughly 3l∗ × 3l∗ × 3l∗.
recording speckle fluctuations in the far-field with a point de-
tector we use a digital camera to monitor fluctuations in the
image plane. Due to the fast motion of the ground glass and
the finite camera exposure time the experimental values of
d2(t, τ) are substantially reduced which complicates the nor-
malization of the ISF. Rather than attempting an absolute cal-
ibration of d2(t, τ) we have chosen to take the initial state of
the experiment, d2(t = 0), as a reference.
The scattering geometry in our experiment is similar to the
one used in traditional backscattering variant of DWS except
for the fact that we are studying speckle fluctuations in the
image plane [23–25]. Speckles in the image plane are often
referred to as near field speckles [26] which must not be con-
fused with the optical near field of evanescent waves probed
for example with scanning near field optical microscopy [27].
Traditional DWS on the other hand analyzes speckle fluctua-
tions in the far field and therefore does not provide any spatial
resolution. Speckle fluctuations in the near field have been
used in biomedical studies of blood flow in the brain cortex
or in the eye retina since the early 1980’s [28]. This ap-
proach is known under the name laser speckle imaging (LSI)
or laser speckle contrast analysis (LASCA) . Without the
echo-averaging scheme presented in this article the method
is however not sensitive enough in most cases to resolve the
subtle differences in the heterogeneous dynamics of soft ma-
terials. Only if the speckle dynamics vary rather slowly in
space this method can be applied to soft materials. In a recent
article Erpelding and coworkers show that the traditional laser
speckle imaging approach can be used to characterize the de-
formation of a soft solid [14].
Generally speaking the image speckle are formed by mul-
tiply scattered light diffusely reflected from the media as il-
lustrated in Figure 2. A detailed theoretical description of the
static scattering process can be found in references [14, 29–
31]. Briefly, the radial distribution of scattered light is ap-
proximately given by I(rx,y, s) ' (3/4πsl∗) exp
−3r2x,y/4sl
where l∗ is a transport mean free path. At the same time the
distribution of pathlengths decays as P(s) ' (s/l∗)−3/2[30]. As
a result most scattering paths do not extend beyond a few l∗. It
can be shown that half of the photons exit the sample at a dis-
tance rx,y ≤ 2.7l∗ [14]. Contributions from single scattering
and short paths s ≤ l∗ are suppressed by recording depolar-
ized light only [32]. Due to diffuse scattering the length scale
probed in z direction is of the same order. Thus at any given
point on the sample surface the speckle fluctuations are con-
trolled by the dynamics in a scattering volume of size roughly
(3l∗)3. In most cases of practical interest this means that the
spatial resolution is set by the transport mean free path of the
sample and not by the imaging optics.
Our sample is a uniformly dispersing white construction
paint (Krautol Rollfarbe Super 4062, Germany) with an ini-
tial solid content of 42±2 vol. % in a cell of 200 µm thickness
and volume 52 µl. The water based paint contains incom-
pressible TiO2 pigments (typical size 0.2−0.5µm) as the main
light scattering agent and a number of non-specified, polymer
based additives. The upper face of the cell was kept open and
the sample surface was levelled by removing excess paint with
a sharp glass plate. A thin polymer ring with inner diameter
of 5.5 mm was immersed in order to prevent the formation of
a lateral drying front. The scattering properties of the paint
are found homogeneous over the area of observation.
In order to achieve controlled water evaporation condi-
tions the sample is kept at constant humidity 65±1 % us-
ing a home-made computer-controlled optically transparent
humidity chamber. Careful precautions were taken in or-
der to prevent possible air flows from disturbing the mea-
surements which includes porous diffusers for the humidity
controlling fans and an optimized humidity stabilization al-
gorithm. In parallel to the light scattering measurements the
sample weight is monitored by a balance with 1 mg resolution
and 1 Hz measurement frequency. Sub-milligram resolution
has been achieved by a polynomial fit to the measured values.
III. IMAGING LOCAL DYNAMICS IN A DRYING PAINT
The process of colloidal thin film drying can be subdivided
in three stages [16]. The first is known as the constant rate pe-
riod (CRP) of drying. The water evaporates from the solvent
surface as long as the concentration of the liquid phase is high.
When the saturation level falls below the “critical liquid con-
tent”, for monodisperse hard spheres at approximately 64 %
volume fraction, the particles are dynamically arrested. In the
subsequent “first falling rate period” (FRP1) the drying rate
starts to decline. The liquid front now penetrates into the solid
bed but water still remains in a continuous (funicular) phase.
While continuously loosing mass the liquid jumps from one
configuration with minimal potential energy to another rapidly
withdrawing itself from previously occupied pores. This pro-
cess occurs as sudden retreats which are called “rheon” events
[33]. Evaporation still occurs near the surface where the liquid
is carried from the inside by fluid flow. At some point the liq-
uid phase breaks up into separate fractions (pendular phase)
and drying is said to enter the second “falling rate period”
(FRP2), completing the drying process.
In our light scattering experiments, during the CRP, we ob-
serve the continuous decay of the ISF value with no spatial
or temporal heterogeneities (Fig. 3, panels I and II). This is
the signature of the gradual compaction of the paint particles
and a corresponding increase of viscosity. The drying process
of the film enters a new stage when approaching dynamical
arrest. For a volume fraction (condensed phase) of approx-
imately 65 %, or after about 2000 seconds, the compaction
of the particle structure is stopped. At this transition to the
FRP1 the liquid front retreats into the porous system formed
by the paint particles and new solid-air inter-phase boundaries
are formed by uncovered particles. This process provides a
new source of refractive index fluctuations unrelated to the
particle motion which manifests themselves as the sudden in-
crease of mean ISF. From this moment on we directly observe
“rheon” events in the ISF maps (Fig.2, panels III-V). As the
flux of liquid to the surface slows down we enter the second
falling rate period (FRP2) and the film dries out completely
until d2 (t, τ = 0.2 sec)→ 0 (Fig. 3, panel VI)
IV. TIME RESOLVED CORRELATION
To characterize the intermittency of the signal we have to
look in more details on the properties of individual events and
its dependence on the systems size. The standard TRC signal
in the image plane can be obtained within the current scheme
by calculating the spatially averaged ISF 〈d2(t, τ)〉s, keeping
the motor at rest (or by replacing the motor with a beam ex-
pander). Without the imaging lens we can perform traditional
far-field TRC measurements (Figure 1 (b)). For these mea-
surements the ground glass is replaced by a set of lenses and
the incident laser beam is then focused onto the sample sur-
face. The camera exposure is set to 4 ms and the time delay is
τ = 0.2s.
In the following we compare the TRC signal 〈d2(t, τ)〉s both
in the image plane and in the far-field (Figure 4). In the former
case we can selectively choose the sample area monitored by
the digital camera. For the latter case we can select the detec-
tor area independent of the sample area and can thus compare
our data with previous observations of time intermittency in
soft glassy materials obtained from similar far-field measure-
ments [8]. A quantitative measure of dynamic heterogeneities
is the variance of the ISF σ2d = 〈d
2 (t, τ)〉 − 〈d2 (t, τ)〉
2 which
is the second moment of the probability density function of
d2 (t, τ). In the absence of experimental noise (N → ∞) the
variance tends to zero for a dynamically homogenous system
whereas intermittent dynamics leads to a finite residual vari-
ance. Both in the far field and in the near field the quantity
σ2d is however dominated by the presence of statistical noise
of the laser speckle. For the standard Gaussian experimental
noise it can be shown that the normalized variance is inversely
proportional to the number N of statistically independent val-
ues of d2(t, τ) recorded by the digital camera [21]:
σ2d/〈d2(t, τ)〉
= 5/N. (2)
For our experimental conditions we expect this relation to
be valid in good approximation [34]. It is thus possible to sep-
0 1000 2000 3000 4000
time, s
I II III
FIG. 3: Dynamic activity analyzed in terms of the normalized intensity structure function (ISF) d2(t, τ = 0.2s). The outer panels show ISF
maps obtained from echo speckle imaging (ESI) at different stages of the drying process. Center: Time evolution of the ISF 〈d2(t, τ = 0.2sec.)〉s
measured in the image plane and averaged over the full area of 1.6×1.2 mm2). All data has been normalized with respect to the initial state
t = 0. Solid line: volume fraction of solids in the condensed phase of the film.
arate the contribution of intermittent dynamics by analyzing
the noise as a function of N, which is proportional to the area
of the detector matrix A used for the analysis. As suggested
by Duri et al. for the far field case the presence of a finite in-
tercept in the limit 1/N → 0 can be exploited to quantify the
bare intermittent noise [35]. In Figure 5 (a) we demonstrate
the intercept in σ2d originating from intermittent dynamics in
the far-field measurement in the FRP1 stage when paint solids
occupy about 75 % of the condensed phase volume [36].
For measurements in the image plane the situation is dif-
ferent. In the image-plane the speckles are smaller than L0
and the recorded values of d2(t, τ) are statistically indepen-
dent. Thus the number N is directly given by the number of
meta-pixels of size L20. We note again that in the image plane
the number N also scales with the area under consideration.
Therefore, if the dynamical heterogeneities are localized in
space, increasing N results in an increasing number of events
observed. In this case the sample surface area again contains
a large number of events and Gaussian statistics is recovered
according to the central limit theorem.
Our experiments nicely reveal this feature as shown in Fig-
ure 5 (b). During the CRP stage the system dynamics is homo-
geneous and the varianceσ2d follows eq. (2). In the presence of
spatial heterogeneities, and for sufficiently large N, the statis-
tical signature is still Gaussian but the slope is now defined by
the number of events N′ such that σ2d/〈d2〉
2 = 5(N/N′)N−1.
We can thus determine N/N′ and extract the length scale of
the dynamic heterogeneities L = (N′/N)1/2L0. Initially L
is equal to the resolution of our experiment of L0 = 11 µm
but in the FRP1 the size grows to approximately 55 µm (Fig-
ure 5 (c)). We find this value in good agreement with the
direct observations in the imaging experiment (Fig.3, Panels
Camera
detector
Sample with
dynamical 
heterogeneities
Detector areas used for 
the statistical analysis
Imaging 
(a) Far-field geometry (b) Near-field geometry
FIG. 4: Time resolved correlation (TRC) experiment in the far-field
(left) and in the near field (right). The selected detector area A sets
the number of meta-pixels N = A/L20 available for the statistical
analysis. For the stationary case the noise of the intensity struc-
ture function scales as σ2d/〈d2(t, τ)〉
2 ' 5/N. The presence of spa-
tially heterogenous dynamics influences both experiments in a dis-
tinct manner. a) In the far-field geometry the sample surface area
under study remains unchanged when changing N. Therefore spa-
tially and temporally heterogenous dynamics leads to a finite value
of σ2d/〈d2(t, τ)〉
2 even for N → ∞ . b) In the near-field imaging
geometry the sample area increases proportionally to N and there-
fore a statistical distribution of spatial heterogeneities provides a new
source of random fluctuations of σ2d/〈d2(t, τ)〉
2 albeit with a reduced
characteristic number N′ < N.
II-V). When the size of the area under study becomes com-
parable to the size of the dynamic heterogeneity the quan-
tity σ2d/〈d2〉
2 is not well described by Gaussian statistics any
more. In the FRP1 significant deviations from the linear scal-
ing are found for N−1 > 0.001 or a sample area smaller than
N′ ∗ (L0)2 ≈ 350 × 350 µm2.
V. CONCLUSIONS
In conclusion we demonstrate that a combination of multi-
speckle illumination and time resolved echo speckle imaging
enables us to perform spatially resolved dynamic light scatter-
ing in real time. The results presented in this work give im-
portant input for a better characterization and modelling of the
drying process in general. Moreover the ESI approach can be
applied to study many other dense systems. The length scale
of 10 µm that can be probed is small enough to resolve spatial
heterogeneities in soft glassy materials. At the same time the
penetration depth, and the effective scattering volume, is large
compared to size of an individual scatterer. Our approach thus
allows to access spatially heterogeneous dynamics of soft ma-
terials with sufficient resolution and accuracy. We think this
method has the potential to bring major advances in the un-
derstanding of the slow dynamics of complex systems and the
general phenomena of dynamical arrest and the glass transi-
tion.
FIG. 5: Statistical properties of the normalized variance of the inten-
sity structure function σ2d/〈d2(t, τ)〉
2 in the far-field and in the imag-
ing TRC experiment (τ = 0.2sec). a) Measurements analyzed in the
far field for an incident Gaussian beam of size 220 µm (1/e) during
the constant rate period (CRP, t = 600 s) and during the first falling
rate period (FRP1, t = 2500 s) b) Same drying stages observed in
the image plane (expanded beam illumination) c) Size of the effec-
tive correlated area L as a function of time (for details see text). In
the absence of dynamic heterogeneities the lower bound is set by the
resolution of the experiment L0 = 11 µm (dashed line).
Acknowledgments
Financial support by the Swiss National Science Founda-
tion (project number 200020-117762/111824/109137) and the
Marie Curie network Grant No. MRTN-CT2003-504712 is
gratefully acknowledged. We would like to thank Jörn Peuser,
Sergey Skipetrov and Roberto Cerbino for interesting discus-
sions. Correspondence and request for materials should be
addressed to F.S.
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and imaging techniques (submitted), arXiv:1005.2875v1
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resolved-correlation measurements of temporally heteroge-
neous dynamics. Phys. Rev. E 72(5):051401.
[36] In the far field the speckles are larger than L0 and N has been
determined from a fit to the data in the CRP (solid squares). We
note that only for a beams spot size (1/e) well below 500 µm
we were able to observe the time intermittency shown in Figure
5 (a) in agreement with our observation in the near field (Figure
5 (b)).
http://arxiv.org/abs/cond-mat/0509637
http://arxiv.org/abs/1005.2875
	I Introduction
	II Experiment
	III Imaging local dynamics in a drying paint film
	IV Time resolved correlation
	V Conclusions
	 Acknowledgments
	 References
