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Abstracts and Talk Materials

Experiments on solutions of entangled DNA[1], and polymers of high
molecular weight dissolved in their oligomers[2] have produced some
interesting rheological results. When subjected to shear flow simple
fluids adopt a uniform shear rate. However, in these polymer solutions
experimentalists have observed the formation of a more structured
velocity distribution; regions of different shear rate on the order of
100 μ m form.

To model this behaviour we analyse the transient behaviour of the diffusive Rolie-Poly model, a modern polymer constitutive equation, and incorporate a Newtonian solvent. The model parameters are chosen so that the constitutive model is monotonic. Numerical solution of this model in 1 spatial dimension shows that for certain parameter values inhomogeneous flow can develop during the transient, which then reverts to homogeneous flow in the long time limit. To understand this behaviour a linear stability analysis of spatial perturbations in the stress field is performed by expanding about the homogeneous transient. In particular the eigenvalues from the linear stability analysis are compared with numerical solution.

[1] P. E. Boukany et al., Macromolecules 41, 2644, 2008. [2] S. Ravindranath et al. Macromolecules 41, 2663, 2008.

To model this behaviour we analyse the transient behaviour of the diffusive Rolie-Poly model, a modern polymer constitutive equation, and incorporate a Newtonian solvent. The model parameters are chosen so that the constitutive model is monotonic. Numerical solution of this model in 1 spatial dimension shows that for certain parameter values inhomogeneous flow can develop during the transient, which then reverts to homogeneous flow in the long time limit. To understand this behaviour a linear stability analysis of spatial perturbations in the stress field is performed by expanding about the homogeneous transient. In particular the eigenvalues from the linear stability analysis are compared with numerical solution.

[1] P. E. Boukany et al., Macromolecules 41, 2644, 2008. [2] S. Ravindranath et al. Macromolecules 41, 2663, 2008.

December 31, 1969

We study the large scale dynamics and rheology of semidilute wormlike micelles (WLMs) by coarse grained simulations. Specific mechanical properties of individual WLMs, such as the persistence length, diameter and elastic modulus, are determined from atomistic simulations, providing a link with the chemistry. We apply the method to a solution of erucyl bis (hydroxymethyl)methylammonium chloride (EHAC). Different scission energies lead to unentangled and entangled WLMs. We can explain the relaxation modulus of unentangled samples with a simple breakable Rouse chain theory. Increasing the shear rate leads to a decrease of the contour length and increase of the breaking rate. The stress is constant at intermediate shear rates. At high shear rate the stress is proportional to (shear rate)^(1/3), as confirmed by experiments [1].

[1] J. T. Padding, E.S Boek andW.J. Briels, J. Chem. Phys. , 074903 (2008).

[1] J. T. Padding, E.S Boek andW.J. Briels, J. Chem. Phys. , 074903 (2008).

We study dynamics from models for the human tear film in one and
two dimensional domains. The tear film is roughly a few microns thick over a domain on a centimeter scale; this separation of
scales makes lubrication models desirable. Results on one-dimensional
blinking domains are presnted for multiple blink cycles. Results
on two-dimensional domains are presented for different boundary conditions.
In all cases, the results are sensitive to the boundary conditions; this is
intuitively satisfying since the seems to control the tear film from the boundary and its motion. Quantitative comparison with in vivo measurement
will be given in some cases. Some discussion of tear film properties will
also be given, and results for non-Newtonian models will be given as available,
as well as a wish list for future data and models in this direction.

We present a simulation model to describe the rheology of associative
(telechelic) polymer networks, and solve some outstanding questions in
the study of mechanical failure in polymeric fluids. The model uses a BD
scheme, but accounts for transient forces arising from slow relaxations
of the polymeric bridges in the network. In this way we account for
structural memory occurring in our system.

September 16, 2009

The property enhancements associated with dispersion of nanoparticles
in polymers will depend not only on the state of dispersion achieved
during the synthesis or formulation of the nanocomposite, but also on
the degree and direction of particle alignment induced during
subsequent processing. Here we present data on flow-induced
orientation in two classes of nanoparticle dispersions, based on
multi-walled carbon nanotubes (MWNTs) and organically modified clay.
Particles are dispersed in viscous but Newtonian matrices (uncured
epoxy resin and oligomeric polybutene, respectively) to allow focus
on the fundamentals of flow-induced particle orientation free from
complications associated with polymer melt viscoelasticity. Small-
and wide-angle x-ray scattering under shear are used to probe
flow-induced anisotropy in the particle orientation distribution.
Both samples show particle alignment increasing with shear rate. In
dilute MWNT dispersions, flow-induced alignment is correlated with
break-down of large aggregates. In more concentrated dispersion,
unexpected rapid relaxation of flow-induced alignment suggests that
some of the observed alignment stems from elastic distortion of
entangled nanotubes within clusters. In the clay dispersions,
attempts are made to explore the relationship between particle
orientation and bulk rheological behavior. In both systems, we have
explored the relation between anisotropy measures extracted from
small- and wide-angle x-ray scattering, which probe fluid structure
at different length scales.

Non-colloidal suspensions of spheres undergoing oscillatory shearing flows demonstrate a range of unique, and even surprising, behaviors. Examples from rheological experiments include the existence of a non-monotonic dependence of the complex viscosity upon the strain amplitude and the observation of two distinct scales for the development of the rheology in time. Simulations of the oscillating suspensions predict the non-monotonic relationship between strain amplitude and the steady value of the complex viscosity while providing insights into the underlying microstructure that generates the macroscopic rheology observed in the experiments. Furthermore, the oscillatory rheology is related to the more general dynamics of suspensions within more complicated flows.

In the study of shear banding phenomena in wormlike micelles, Rheo-NMR has
proven of especial value, not only indicating the clear existence of shear
bands, but also that they are associated with fluctuations, and sometimes,
with molecular alignment. The subtlety of the correspondence (or lack of
correspondence) between birefringence effects and shear banded flow has also
been revealed. Recent measurements of shear-banded flow under Couette flow
of the micellar system cetylpyridinium chloride and sodium salicylate
(CPyCl/NaSal) indicate that shear banding fluctuations that are inconsistent
with the usual lever rule picture. We have also used Rheo-NMR to investigate
the flow and alignment properties of worm-like micelles formed by a 5% w/w
solution of the BASF difunctional block copolymer non-ionic surfactant,
Pluronic P105 in water along with 4.3% w/v 1-phenylethanol-d5. A variety of
bizarre shear-banding and alignment behaviours are observed, along with both
stable and fluctuating flows.

The glass transition in quiescent colloidal suspensions is reasonably well accounted for by a mode coupling theory which treats the collective freezing of density fluctuations but neglects activated processes. In recent years we have extended this approach, with the aid of an exact nonequilibrium Green-Kubo formula, to address the nonlinear rheology of colloidal suspensions. The theory addresses the case of interacting Brownian particles with velocities biased by that of the local fluid flow (assumed homogeneous) thereby ignoring hydrodynamic interactions. The resulting constitutive equations are complicated but can be simplified for certain flows and/or by constructing a schematic model with similar features. The latter makes rheological prediction for general nonlinear flows a realistic goal, and allows the nontrivial yield behavior in the glass phase to be studied.

December 31, 1969

Joint work with M. Gregory Forest and Lili Ju.

We break the orientational degeneracy of a nematic liquid crystal polymer system by applying strong anchoring conditions with an arbitrary director angle at the parallel plates in a shear cell. Then we apply a small amplitude oscillatory shear flow and predict the response of the storage and loss moduli with a tensor model with one-dimensional heterogeneity. We pay special attention to the role of the director angle anchoring conditions. For normal and tangential anchoring conditions, the model reduces to a form similar to the analytically solvable Leslie-Ericksen model. For oblique anchoring angles, we solve the system numerically, and we find a window of moderate frequencies where the storage modulus and viscosity are significantly larger than the corresponding Leslie-Ericksen predictions. We are able to approximate this very well with a linear superposition of the Leslie-Ericksen prediction and the corresponding monodomain prediction, and we find that for low frequencies and high frequencies the Leslie-Ericksen prediction is dominant, but for the window of moderate frequencies, the tensor order parameter contribution becomes dominant.

We break the orientational degeneracy of a nematic liquid crystal polymer system by applying strong anchoring conditions with an arbitrary director angle at the parallel plates in a shear cell. Then we apply a small amplitude oscillatory shear flow and predict the response of the storage and loss moduli with a tensor model with one-dimensional heterogeneity. We pay special attention to the role of the director angle anchoring conditions. For normal and tangential anchoring conditions, the model reduces to a form similar to the analytically solvable Leslie-Ericksen model. For oblique anchoring angles, we solve the system numerically, and we find a window of moderate frequencies where the storage modulus and viscosity are significantly larger than the corresponding Leslie-Ericksen predictions. We are able to approximate this very well with a linear superposition of the Leslie-Ericksen prediction and the corresponding monodomain prediction, and we find that for low frequencies and high frequencies the Leslie-Ericksen prediction is dominant, but for the window of moderate frequencies, the tensor order parameter contribution becomes dominant.

I will study the flow of complex fluids (emulsions , wormlike micelles solutions) in
microfluidic devices. The velocity profiles are measured using Particles Imaging Velocimetry.
Shear banded flows are evidenced in wormlike micelles solutions. The role of the confining and of the
nature of the boundaries conditions will be adressed. These experiments will be analysed in the framework of non local rheology.
Experimental data dealing with concentrated emulsion will be presented. In this case, no shear banding is evidenced eventhough some dynamical heterogeneities
are pointed out. The size of the heterogeneities is measured using confocal imaging.

The situation of yield stress fluids in physics is very original: they borrow their properties partly to solids and partly to liquids, both material types which have strikingly different structures, and it is assumed that they can undergo a simple transition from one state to the other at a critical shear stress. This also implies difficulties for the mechanical description of their behavior: in the solid regime one usually follows the stress vs deformation while in the liquid regime one follows the stress vs shear rate. The experimental difficulties for determining the yield stress are inherent to this peculiar behaviour: one needs to identify the critical stress for which a flow occurs, which implies to detect a flow of a material with a viscosity tending towards infinity; as the flow curve tends to exhibit a plateau at low shear rates the uncertainty on measurements are obviously large and this is complicated by possible slight stress heterogeneities. Local measurements, i.e. inside the materials, are thus needed to determine the effective constitutive equation of the material. From MRI data we show that a certain class of materials appears to be simple yield stress fluids, except below a critical shear rate for which we cannot get any relevant data and which seems to be the “Bermuda Triangle” of pastes. For another class of materials the transition between the solid and the liquid regime is more abrupt: it occurs at a finite viscosity, so that no flow at a shear rate below a critical value can be observed in steady state. For these materials shear-banding in steady-state flows is the rule whatever the flow geometry. In addition this behaviour is associated with time-dependent properties: the shear-banding effect is obtained as a viscosity bifurcation in time.
The behaviour of simple yield stress fluids (first class) in more complex geometries (extrusion, squeezing, object displacement, flow through a porous medium, etc) has received some attention in recent years and it is remarkable that the force vs velocity data are always well described by a model of the Herschel-Bulkley type, in analogy with their simple shear behavior.
However the behaviour of yield stress fluids along a solid interface still constitutes a challenging field although of great interest for controlling various processes such as mud adhesion or drying, cream or gel coating, fouling deposits, welding of pottery pieces, adhesion of dental cements or glues, etc. We show some first observations with model materials which illustrate the complexity of this field and some unexplained results.

Aqueous foams, like other macroscopically divided materials, display
intriguing rheological properties. The bubble-scale structure allows for
the existence of frozen stresses within the material which can not
spontaneously relax by thermal activation. Upon shearing, the system
undergoes a series of plastic events which irreversibly modify this
internal stress pattern. Reversely, the internal state of the material
controls to a large extent its mechanical response to shear.

To study this coupling, we have used a two-dimensionally confined aqueous foam along with a numerical simulation. Through image analysis of the film network, we can simultaneously probe the plastic flow and the frozen stress field dynamics under quasi-static shearing. We show that under oscillatory shear of moderate amplitude, the foam experiences a structural relaxation that leads to a decrease of the shear modulus and the emergence of normal stress differences. Upon continous shear, a shear-banding instability is observed, which coincides with the emergence of spatial heterogeneities in the internal stress field characteristics. The dynamics of the internal stress field can be interpreted using a simple statistical model.

To study this coupling, we have used a two-dimensionally confined aqueous foam along with a numerical simulation. Through image analysis of the film network, we can simultaneously probe the plastic flow and the frozen stress field dynamics under quasi-static shearing. We show that under oscillatory shear of moderate amplitude, the foam experiences a structural relaxation that leads to a decrease of the shear modulus and the emergence of normal stress differences. Upon continous shear, a shear-banding instability is observed, which coincides with the emergence of spatial heterogeneities in the internal stress field characteristics. The dynamics of the internal stress field can be interpreted using a simple statistical model.

The simplest models of matter posit a linear relationship between the stress and deformation, as for example in Hooke's law. However, many useful and important fluids (such as, shampoos, industrial slurries, geophysical fluids, polymeric melts) exhibit a nonlinear response to stress. In shear thickening fluids this nonlinear response manifests as an increase of the apparent viscosity with increasing shear rate. I will show that vibrated shear thickening fluids display a unique ability to maintain a vertically oriented free-surface despite the action of gravity. I will present my experimental results correlating this behavior with the rheological properties of the fluids, and my attempts to model the observed phenomena.

Jan Karel George Dhont

http://www.fz-juelich.de/iff/d_iwm

Pavlik Lettinga

http://www.fz-juelich.de/iff/Lettinga_P

http://www.fz-juelich.de/iff/d_iwm

Pavlik Lettinga

http://www.fz-juelich.de/iff/Lettinga_P

Joint work with K. Kang (Forschungszentrum Jülich).

We propose a possible scenario for the vorticity-banding instability on the basis of experiments on suspensions of long and thin colloidal rods (fd-virus particles). Vorticity banding of these suspensions is only observed inside the two-phase, paranematic-nematic coexistence region. Inhomogeneities that are formed due to initial paranematic-nematic phase separation are shown to drive the vorticity-banding transition, and stabilize the stationary vorticity-banded state. The kinetics of the banding transition depends on whether inhomogeneities are formed (after a shear-rate quench) due to paranematic-nematic spinodal decomposition or nucleation-and-growth. Particle-tracking experiments indicate that the vorticity bands are in weak, internal rolling motion. These and other observations indicate that normal stresses along the gradient direction are responsible for the vorticity-banding instability, and that these hoop stresses originate from the inhomogeneities. The mechanism underlying the vorticity banding transition is thus similar to the well-known elastic instability for polymers, where the role of polymers is now played by inhomogeneities that are formed due to paranematic-nematic phase separation.

We propose a possible scenario for the vorticity-banding instability on the basis of experiments on suspensions of long and thin colloidal rods (fd-virus particles). Vorticity banding of these suspensions is only observed inside the two-phase, paranematic-nematic coexistence region. Inhomogeneities that are formed due to initial paranematic-nematic phase separation are shown to drive the vorticity-banding transition, and stabilize the stationary vorticity-banded state. The kinetics of the banding transition depends on whether inhomogeneities are formed (after a shear-rate quench) due to paranematic-nematic spinodal decomposition or nucleation-and-growth. Particle-tracking experiments indicate that the vorticity bands are in weak, internal rolling motion. These and other observations indicate that normal stresses along the gradient direction are responsible for the vorticity-banding instability, and that these hoop stresses originate from the inhomogeneities. The mechanism underlying the vorticity banding transition is thus similar to the well-known elastic instability for polymers, where the role of polymers is now played by inhomogeneities that are formed due to paranematic-nematic phase separation.

Jan Karel George Dhont

http://www.fz-juelich.de/iff/d_iwm

Pavlik Lettinga

http://www.fz-juelich.de/iff/Lettinga_P

http://www.fz-juelich.de/iff/d_iwm

Pavlik Lettinga

http://www.fz-juelich.de/iff/Lettinga_P

December 31, 1969

Dispersions of giant wormlike micelles of self-assembled
Polybutadiene-poly(ethylene oxide) (2.5 kd:2.5 kd) diblock copolymers are
known to undergo a phase transition around 3 to 10 w%. The response to shear
flow around this concentration range is characterized by a considered shear
thinning behavior. The object of this study was to obtain microscopic
insight in the microscopic origin of shear thinning and the resulting
instabilities. We first localized the (non-)equilibrium Isotropic
(I)-Nematic (N) binodal, using the rheological response after shear-rate
quenches. Using laser-Doppler velocimetry we confirmed that indeed close to
I-N transition the shear thinning results in the formation of shear bands in
the gradient direction. It is assumed that shear thinning is connected to
the vicinity of the spinodal point where the rotational diffusion goes to
zero. Therefore we used time-resolved Small Angle Neutron Scattering
experiments in combination with Fourier-Transfer Rheology to probe the
response of the Kuhn-segments subjecting the sample to an oscillatory shear
field. Theory for ideal rods was used to connect the resulting stress
response to the ordering response. With this approach we found not only the
equilibrium spinodal point of this dispersion but also the microscopic
origin of the shear thinning behavior.

Colloidal suspensions gel to a soft solid state when interparticle attractions increase sufficiently to overcome Brownian and stabilizing forces. Gelation at lower concentrations results from formation of a percolated, space-filling network, whereas at high concentrations, an attractive driven glass forms. At intermediate concentrations, phase separation, gel formation, percolation, and glass formation are all possible states leading to solid-like behavior and the exact mechanism of dynamic arrest is often unclear.
In this work, we study the connection between the rheological properties and interparticle potential of a model thermoreversible gel and compare the results to the predictions of the new Krishnamurthy and Wagner model. Dynamic light scattering (DLS), fiber optic quasi-elastic light scattering (FOQELS), and small angle neutron scattering (SANS) are used to establish the single particle characteristics. Rheology, FOQELS, and SANS are used to study the interparticle potential, mechanisms of aggregation, and structure. The goal of this study is to test the ability of the new Krishnamurthy and Wagner model to predict the interparticle potential form bulk rheological measurements.

Marc-Antoine Fardin

http://www.msc.univ-paris7.fr/English/annuaire/pageperso.php?nom=marc-antoine_fardin

http://www.msc.univ-paris7.fr/English/annuaire/pageperso.php?nom=marc-antoine_fardin

Under shear, complex fluids often undergo instabilities leading to new flow patterns. The flow being usually inertialess, these instabilities are triggered by non-linear terms in the stress tensor itself. Shear-banding is such a flow-induced instability, observed in many systems of various microstructures from surfactant and polymer solutions, to emulsions, granular materials and foams. Above a critical shear-rate, a new fluid phase nucleates and the flow reorganizes into two macroscopic shear-bands of different viscosities coexisting in the velocity gradient direction. In a recent study performed in Taylor-Couette geometry, we showed that the flat interface between bands is unstable with respect to wavevectors along the vorticity direction. This interfacial instability is associated with the reorganization of the flow into Taylor-like vortices. Here, we attempt to connect this complex behaviour to the elastic instability occurring in dilute polymer solutions. In the latter case, the non-linear elastic term in the stress tensor has been shown to drive the flow instability, leading to the formation of Taylor-like vortices with patterns evolving towards turbulence when increasing shear rate. We propose a scenario where the induced fluid band undergoes an elastic instability. In the coexistence regime, the viscous phase act as a soft boundary and the instability leads to the formation of vortices mainly localized in the fluid band. For shear-rates above the coexistence regime, the boundary changes to a hard wall, increasing the threshold for the instability. The stability of the induced phase is then recovered. When the control parameter is further increased the flow becomes unstable again, leading to patterns reminiscent of elastic turbulence.

I will summarise some recent progress modelling shear banding in complex fluids, focussing particularly on the following topics: bulk and interfacial instabilities that lead to complex dynamics of the bands; vorticity banding; and 3D roll-like flows. Time permitting, I will also discuss a novel kind of shear banding that has recently been predicted in biologically active suspensions.

We study the behavior of non-colloidal suspensions under slow periodic strain. They undergo a dynamical phase transition from an active fluctuating state to an absorbing steady state. Starting from a random initial configuration, the system finds its staedy state via self-organisation. In the case of density-mismatched particles, the competing forces of sedimentation and shear-induced diffusion drive the system to its critical state. The timescales and lengthscales of active particle clusters are explored via a model and exhibit power law behavior. Future research will try to measure them the clusters in the experiment.

Joint work with Vishweshwara Herle, Joachim Kohlbrecher, and Sebastien Manneville.

An equimolar mixture of cetylpyridinium chloride and sodium salicylate exhibits pronounced shear thickening and vorticity bands (alternating transparent and turbid bands) in non-linear flow regime. Rheological, flow visualization and rheo-SALS studies indicate a stress driven mechanism for the development of shear bands. A combination of rheo-NMR and UVP shows that not only vorticity bands, but also radial bands coexist in this system. To access the microscopic structure in these bands, time-resolved SANS measurements are performed in a transparent Couette geometry. These triggered experiments show that the transparent and turbid bands are composed of different kinds of highly anisotropic structures. Analysis of the structure factor indicates that long wormlike micelles are strongly aligned in flow direction in the turbid state and this alignment is destroyed to some extent in the transparent state.

An equimolar mixture of cetylpyridinium chloride and sodium salicylate exhibits pronounced shear thickening and vorticity bands (alternating transparent and turbid bands) in non-linear flow regime. Rheological, flow visualization and rheo-SALS studies indicate a stress driven mechanism for the development of shear bands. A combination of rheo-NMR and UVP shows that not only vorticity bands, but also radial bands coexist in this system. To access the microscopic structure in these bands, time-resolved SANS measurements are performed in a transparent Couette geometry. These triggered experiments show that the transparent and turbid bands are composed of different kinds of highly anisotropic structures. Analysis of the structure factor indicates that long wormlike micelles are strongly aligned in flow direction in the turbid state and this alignment is destroyed to some extent in the transparent state.

The goal of this lecture is to inform the audience of the types of challenges that arise, and open problems that remain, in a specific class of biological fluids: mucus. Mucus is prevalent in biology and its rheology is fundamental for: locomotion (e.g., of snails); flow transport (e.g., of mucosal layers in mammalian lungs); and controlling diffusive transport of invasive particles (e.g., in the nasal cavity, lung, and reproductive organs). Mucus varies dramatically across species, across populations, across organs, and in a single organ across disease states. The lecture will address challenges faced in the Virtual Lung Project at UNC for design of experiments, for data-based inference of constitutive parameters, and for development of direct simulation tools for lung biology and medical applications.

Richard S. Graham

http://www.maths.nottingham.ac.uk/~rg/

Peter D. Olmsted

http://www.irc.leeds.ac.uk/~phy6pdo/

http://www.maths.nottingham.ac.uk/~rg/

Peter D. Olmsted

http://www.irc.leeds.ac.uk/~phy6pdo/

We derive a kinetic Monte Carlo algorithm to simulate flow-induced nucleation in polymer melts. The crystallisation kinetics are modified by both stretching and orientation of the amorphous chains under flow, which is modelled by a recent non-linear tube theory. Rotation of the crystallites under flow is modelled by a simultaneous Brownian dynamics simulation. Our kinetic Monte Carlo approach is highly efficient at simulating nucleation and is tractable even at low under-cooling. The simulations predict enhanced nucleation under both transient and steady state shear. Furthermore the model predicts the growth of shish-like elongated nuclei for sufficiently fast flows, which grow by a purely kinetic mechanism. A comparison with experimentally observed nucleation rates during steady shear flow is also presented.

Joint work with Jonathan D. Evans (University of Bath).

The steady planar sink flow through a converging channel is considered for the upper convected Maxwell (UCM) and Oldroyd-B fluids. The local asymptotic structure near the wedge apex exhibits an outer core flow region together with thin elastic boundary layers at the wedge walls. A class of similarity solutions is described for the outer core flow in which the streamlines are straight lines, giving rise to stress and velocity singularities. These solutions are matched to wall boundary layer equations which recover viscometric behavior. The local solutions as described permit a wide variety of external flows from the far-field region and generalize the classical Newtonian case of Jeffery-Hamel flow.

The steady planar sink flow through a converging channel is considered for the upper convected Maxwell (UCM) and Oldroyd-B fluids. The local asymptotic structure near the wedge apex exhibits an outer core flow region together with thin elastic boundary layers at the wedge walls. A class of similarity solutions is described for the outer core flow in which the streamlines are straight lines, giving rise to stress and velocity singularities. These solutions are matched to wall boundary layer equations which recover viscometric behavior. The local solutions as described permit a wide variety of external flows from the far-field region and generalize the classical Newtonian case of Jeffery-Hamel flow.

December 31, 1969

We present an enhanced moment-closure approximation to the finite-
extensible-nonlinear-elastic (FENE) models of polymeric fluids.
This new moment-closure method involves the perturbation of the
equilibrium probability distribution function (PDF), which takes
into account of the drastic split into two spikes and centralized behavior under the large macroscopic
flow effects. The resulting macroscopic system includes the
moment-closure equations, the momentum (force balance) equations,
as well as an auxiliary equation
representing implicitly the dynamics of the spikes for the
microscopic configurations.

We consider a finite element method for the nonlinear Brinkman equation
for modeling fast, viscous (possibly turbulent) fluid flow in porous
media. Application areas include gaseous fluid flow in pebble bed nuclear
reactors and wind sweeping across a wind farm. The Brinkman equations can
be applied in two ways. The first perspective is to apply Brinkman as a
porous media model, like Darcy’s equation, on a homogenized domain. The
second is to apply Brinkman as a penalized Navier-Stokes equation (NSE),
letting the Brinkman viscosity and inverse of the permeability tend to
zero in the solid obstacles embedded in the problem domain. We derive a
finite element formulation for non-generic constraints: non-homogeneous
Dirichlet boundary conditions and non-solenoidal velocity (allowing for
sources/sinks in a porous medium). Coupling between these two conditions
makes even existence of solutions subtle (noting the Brinkman model
contains the same nonlinearity as NSE). We provide conditions for
stability, existence and uniqueness of solutions as well as
pseudo-skew-symmetrization of the discrete, nonlinear convective term
required for analysis of discrete, non-solenoidal Brinkman problem.

The effect of viscoelasticity on flow in a two-dimensional collapsible channel has been studied numerically. This geometry has some bearing to blood flow in a compliant blood vessel. Three different viscoelastic fluid models have been considered - the Oldroyd-B, the FENE-P and Owens’ model for blood [1], along with a zero thickness membrane model with constant tension for the collapsible wall [2]. The rheological behaviour of the viscoelastic fluids is described in terms of a conformation tensor model. The mesh equation and transport equations are discretized by using the DEVSS-TG/SUPG mixed finite element method [3]. The shape of the collapsible membrane, and the pressure, stress, velocity, and conformation tensor fields predicted by the different models is compared with the predictions of a Newtonian liquid. The existence of a limiting Weissenberg number beyond which computations fail is demonstrated for each of the viscoelastic fluids, and the dependence of the limiting Weissenberg number on the various model parameters is examined. Predictions for the different viscoelastic fluids differ significantly from each other, with the key factor being the extent of shear thinning predicted by the individual models.

References:

1. R. G. Owens, J. Non-Newtonian Fluid Mech. 140, 57-70 (2006).

2. X. Y. Luo and T. J. Pedley, J. Fluids and Structures 9, 149-174 (1995).

3. M. Bajaj, J. R. Prakash and M. Pasquali, J. Non-Newtonian Fluid Mech. 145, 137-156 (2007).

References:

1. R. G. Owens, J. Non-Newtonian Fluid Mech. 140, 57-70 (2006).

2. X. Y. Luo and T. J. Pedley, J. Fluids and Structures 9, 149-174 (1995).

3. M. Bajaj, J. R. Prakash and M. Pasquali, J. Non-Newtonian Fluid Mech. 145, 137-156 (2007).

Recent developments in dilute polymer solution rheology are reviewed, and placed
within the context of the general goals of predicting the complex ﬂow of complex
ﬂuids. In particular, the interplay between the use of polymer kinetic theory and
continuum mechanics to advance the microscopic and the macroscopic description,
respectively, of dilute polymer solution rheology is delineated. The insight that
can be gained into the origins of the high Weissenberg number problem through an
analysis of the conﬁgurational changes undergone by a single molecule at various
locations in the ﬂow domain is discussed in the context of ﬂow around a cylinder
conﬁned between ﬂat plates. The signiﬁcant role played by hydrodynamic
interactions as the source of much of the richness of the observed rheological behaviour
of dilute polymer solutions is highlighted, and the methods by which this
phenomenon can be incorporated into a macroscopic description through the use of
closure approximations and multiscale simulations is discussed.

December 31, 1969

A unique combination of excellent electrical, thermal and mechanical
properties has made graphene a multi-functional reinforcement for
polymers. Exfoliated carbon sheets can be obtained from graphite oxide
(GO) via either rapid pyrolysis (functionalized graphene sheets, FGS) or
chemical modification (isocyanate treated graphite oxide, iGO).
Solvent-based blending led to better dispersion of FGS in thermoplastic
polyurethane than melt processing. Polyurethane became electrically
conductive at even less than 0.5 wt% of FGS. Up to 10 fold increase in
tensile stiffness and 90% decrease in nitrogen permeation of TPU were also
observed with only 3 wt% of iGO implying high aspect ratio of exfoliated
platelets. Dispersion of melt compounded graphite and FGS in
poly(ethylene-2,6-naphthalate) was characterized with electron microscopy,
X-ray scattering, melt rheology and solid property measurements. Unlike
graphite, dispersion of FGS quantified from different routes spreads over
a wide range due to structural irregularity and simplified assumptions for
composite property modeling. For polycarbonate, flow-induced orientation
reduced property gains by graphene dispersion, while quiescent-state
annealing restored rigidity and electrical conductivity of the composites.
Micro-structural evolution of FGS in polystyrene through annealing was
monitored using melt-state rheological and dielectric measurements.
Graphene-based polymer nanocomposites can be a new versatile soft material
with numerous benefits.

Magnetorheological (MR) fluids are suspensions of small particles
whose apparent rheological properties can be altered dramatically
by applying a magnetic field. For example, magnetic flux
densities of the order of 1 Tesla can induce a yield stress of the
order of 100 kPa in an otherwise essentially Newtonian fluid.
After a brief introduction to magnetorheology, including a few of
the more common applications, four vignettes of experimental
observations and resulting modeling challenges will be presented.
In the first vignette, transients in shear flow rheology observed
for large applied magnetic field strengths are addressed. These
transients are associated with the formation of lamellae within
the suspension, whose dynamics can be modeled at the particulate
or continuum levels. In the second vignette, unexpectedly large
yield stresses observed for suspensions with bidisperse particle
size distributions are described. Particle-level modeling reveals
the mechanism, but predicting the magnitude of the enhancement
remains a challenge. The third vignette examines effects of
friction, which only appear at large concentrations. Observations
are similar to jamming transitions observed in similar systems.
The last vignette examines a surprising enhancement caused by
replacing magnetizable particles with nonmagnetizable particles in
MR fluids.

Using concepts developed over the years by de Gennes, Doi, Edwards, Marrucci, Rubinstein, McLeish, Milner, and others, a kind of "standard model" for entangled polymer relaxation and rheology has been developed, which, like the "standard model" of high-energy physics, has a number of ad hoc assumptions and fitting parameters. The “standard model” of polymer relaxation is based on a phenomenological "tube" surrounding each polymer chain that represents the effect on that chain of non-crossability constraints imposed by surrounding chains. As a result of its confinement to the tube, the chain relaxes by reptation – or sliding along the tube, accordion-like fluctuations of the chain within the tube, and movement of, or dilation of, the tube due to motion of the surrounding chains creating the tube-like region. These ingredients have been generalized into algorithms for the prediction of linear rheology of arbitrary mixtures of linear and long-chain-branched polymers; these algorithms have a number of phenomenological parameters and ad hoc assumptions. An increasing body of experimental data on “well characterized linear and branched polymers” allows these theories to be tested in increasing detail. Here we describe the successes and failures of the “standard” model and discuss new molecular dynamics simulations and more refined experiments that might help the field transcend the limitations of the “standard model.

Joint work with Keith M. Kirkwood and Dimitris Vlassopoulos.

In this presentation, we consider stress relaxation of comb polymers in both the linear and non-linear deformation regimes. In this poster, we focus primarily on the linear viscoelastic response and on the relaxation from a step shear strain for a set of comb polymers that have short branches, ranging from two Me to smaller values less than the entanglement molecular weight.

In this presentation, we consider stress relaxation of comb polymers in both the linear and non-linear deformation regimes. In this poster, we focus primarily on the linear viscoelastic response and on the relaxation from a step shear strain for a set of comb polymers that have short branches, ranging from two Me to smaller values less than the entanglement molecular weight.

Under shear, complex fluids often undergo instabilities leading to new flow patterns. Shear-banding is such a flow-induced instability, observed in many systems of various microstructures from surfactants and polymer solutions, to liquid crystal polymers, emulsions, granular materials and foams. It results from the coupling between the flow and the mesoscopic architecture of the system. The flow changes the structure of the fluid that feeds back on the flow itself. A spectacular consequence is a reorganization of the flow into two macroscopic shear-bands of different viscosities coexisting in the velocity gradient direction. In this scenario, the flow is supposed to be purely one-dimensional.
Using flow visualizations in Couette geometry, we demonstrate, for a system of giant micelles that, in contrast with this classical picture, the banded state is unstable and evolves towards a three-dimensional flow. We show that vortices stacked along the vorticity direction develop concomitantly with interfacial undulations. These cellular structures are mainly localized in the induced band and their dynamics is fully correlated to that of the interface. As the control parameter increases, we observe a transition from a steady vortex flow to a state where pairs of vortices are continuoulsy created and destroyed. Normal stress effects are discussed as potential mechanisms driving the three-dimensional flow.

I will briefly review multiscale approach to modelling of entangled polymers, which includes molecular dynamics (MD), single chain stochastic models (slip-springs) and the tube model. After that I will concentrate on the link between many chain (MD) and single chain models. I will report results from molecular dynamics simulations on stress relaxation and show the detailed comparison with slip-spring model. In the second part of the talk I will turn to the issue of microscopic definition of entanglement in molecular dynamics. We propose to define entanglement as a long-lived contact between mean paths of the two chains. Using this definition, we present empirical evidence and statistical properties of such entanglements, and discuss the implications for the tube theory and the slip-spring model.

Geometrical parameters of the interface of a polymer blend with cocontinuous structure were obtained from differential geometry of 3D images. Fluorescently labeled polystyrene (FLPS) and styrene-acrylonitrile copolymer (SAN) were imaged with laser scanning confocal microscopy (LSCM). Images were analyzed for time evolution of interfacial area, curvature and curvature distributions. The coarsening kinetics is dominated by hydrodynamics which explain the initial linear growth of the microstructure. A slowing down of the coarsening at later times can be explained by the decrease of the interface curvature which is proportional to the coarsening driving force, i.e. the interfacial energy. The curvature distributions reveal the type of interface in the blend. For the 50/50 blends the distribution of the Gaussian curvature show mainly negative values, indicating an anticlastic surface, characteristic of bicontinuous structures. The distributions of the mean curvature are symmetrical and centered in zero at any time, indicating that the surface is evolving through the minimal energy path.

Every time we blink a thin multilayer film forms on the front of the eye essential for both health and optical quality. Explaining the dynamics of this film in healthy and unhealthy eyes is an important first step towards effectively managing syndromes such as dry eye. Using lubrication theory, we model the evolution of the tear film during relaxation (after a blink). The highly nonlinear governing equation is solved on an overset grid by a method of lines in the Overture framework. Our simulations show sensitivity in the flow around the boundary to the choice of the flux boundary condition and to gravitational effects. Furthermore, the simulations capture some experimental observations.

September 18, 2009

December 31, 1969

Surfactant solutions make up a unique class of complex fluids, offering a wide variety of rheological behavior, e.g. shear banding, which may be tailored for a particular application. Within this class of solutions, micellar solutions, being composed of amphiphilic molecular chains, are representative of many consumer products, find use in advanced oil recovery, exhibit turbulent drag reduction, and they constitute an archetypal fluid for the study of flows in small-scale biological devices and porous media.

The present understanding of the flow behavior of these micellar solutions is incomplete and to that end much experimental works is required in order to calibrate and improve current constitutive models of their rheological behavior. Of particular interest is the study of these fluids under high rate deformations (10^{4}-10^{5} s^{-1}) (Pipe et al. 2008), representative of flows in ink jet printers and lab on a chip experiments. Such high rates can be unattainable with conventional rheometers, but they are readily achievable in microscale geometries.

Here, we present measurements of flow-induced birefringence (FIB) with micro particle image velocimetry (µ-PIV) measurements of micellar solutions undergoing both extensional and shear deformations at the microscale. We describe a novel birefringence microscopy system, which is capable of making time-resolved full-field measurements of the local extinction angle and retardance in a microfluidic device, providing for high-resolution tracking of the local microstructural evolution in a micellar solution undergoing strong deformation.

The present understanding of the flow behavior of these micellar solutions is incomplete and to that end much experimental works is required in order to calibrate and improve current constitutive models of their rheological behavior. Of particular interest is the study of these fluids under high rate deformations (10

Here, we present measurements of flow-induced birefringence (FIB) with micro particle image velocimetry (µ-PIV) measurements of micellar solutions undergoing both extensional and shear deformations at the microscale. We describe a novel birefringence microscopy system, which is capable of making time-resolved full-field measurements of the local extinction angle and retardance in a microfluidic device, providing for high-resolution tracking of the local microstructural evolution in a micellar solution undergoing strong deformation.

In 1975 Doi and Edwards predicted that entangled polymer melts and
solutions can have a constitutive instability, signified by a
decreasing stress for shear rates greater than the inverse of the
reptation time. Early experiments did not support this, and more
sophisticated theories were developed that incorporated Marrucci's idea (1996) of
removing constraints by advection; this produced a monotonically
increasing stress and thus stable constitutive behavior. Recent
experiments have suggested that entangled polymer solutions may
possess a constitutive instability after all, and have led some
workers to question the validity of existing constitutive models.
Based on this intense interest we have revisited some of the phenemology present in state of the art tube models for entangled polymers, and performed calculations that take into account the stress inhomogeneity inherent in rotating rheometers (cone and plate and cylindrical Couette). Using the Rolie-Poly model with an added solvent viscosity, we show that (1) instability and shear banding is
captured within this simple class of models; (2) shear banding
phenomena is observable for weakly stable fluids in flow
geometries that impose a sufficiently inhomogeneous total shear
stress; (3) transient phenomena can possess inhomogeneities that
resemble shear banding, even for weakly stable fluids. Many of these
results are model-independent.

In this talk results of pressure gradient vs. volume flow rate calculations over a wide range of oscillatory frequencies for oscillatory tube flow of healthy human blood are performed using the non-homogeneous hemorheological model of Moyers-Gonzalez et al. [M.A. Moyers-Gonzalez, R.G. Owens, J. Fang, A non-homogeneous constitutive model for human blood. Part I. Model derivation and steady flow, J. Fluid Mech. 617 (2008) 327–354]. Results at low (2 Hz) oscillatory frequencies are shown to be in close conformity to the experimental data of Thurston [G.B. Thurston, The effects of frequency of oscillatory flow on the impedance of rigid, blood-filled tubes, Biorheology 13 (1976) 191-199] and the behaviour may be interpreted using a linear viscoelastic model. As the oscillatory frequencies increase a resonant frequency at which flow rate amplitude enhancement occurs is encountered. For frequencies greater than the resonant frequency the pressure gradient amplitude required to maintain a constant volume flow rate amplitude increases with the oscillatory frequency.

For very high frequency oscillations we use a multiple time scales technique in conjunction with our non-homogeneous hemorheological model to solve for the leading order flow variables. It is found that the leading order expressions for the cell number density, average aggregate size and rr-component of elastic stress (i.e. that due to the red blood cells) are functions only of the radial coordinate r. The O(1) elastic shear stress is shown to be zero, so that, for sufficiently large values of the oscillatory frequency, the red cell contribution to the total shear stress tends to zero. Using our multiple time scales method it is also shown that the model behaves in the very high frequency regime like a generalized linear viscoelastic fluid, having a radially dependent complex viscosity. This allows us to explain the computed results using asymptotic expressions for the in phase and quadrature components of the pressure gradient in a linear viscoelastic fluid. In particular, we may predict the apparent complex viscosity of human blood in very high frequency oscillatory tube flow.

For very high frequency oscillations we use a multiple time scales technique in conjunction with our non-homogeneous hemorheological model to solve for the leading order flow variables. It is found that the leading order expressions for the cell number density, average aggregate size and rr-component of elastic stress (i.e. that due to the red blood cells) are functions only of the radial coordinate r. The O(1) elastic shear stress is shown to be zero, so that, for sufficiently large values of the oscillatory frequency, the red cell contribution to the total shear stress tends to zero. Using our multiple time scales method it is also shown that the model behaves in the very high frequency regime like a generalized linear viscoelastic fluid, having a radially dependent complex viscosity. This allows us to explain the computed results using asymptotic expressions for the in phase and quadrature components of the pressure gradient in a linear viscoelastic fluid. In particular, we may predict the apparent complex viscosity of human blood in very high frequency oscillatory tube flow.

I will review the methodology of imaging the flow of concentrated
suspensions at single-particle and nearly-real-time resolution, and then
discuss a number of surprising recent findings indicating that traditional
constitutive equations applied to rheometric geometries may not tell the
whole story about these supposedly well understood systems.

Biologically active fluids, such as bacterial suspensions or
cytoskeletal extracts with molecular motors and ATP, are a source of
intriguing problems in the physics of complex fluids. They are composed
of particles that with internal machinery that take up energy from their
surroundings and actively move the surrounding medium. My talk will
review recent results on thin fluid films and drops of active fluids,
and possibly the dynamics of a single stiff filament in an active film.

Numerical simulations and experimental data are compared for the investigation of the influence of viscoelasticity on drop deformation in shear. A viscoelastic drop suspended in a Newtonian liquid, or a Newtonian drop suspended in a viscoelastic liquid, is sheared and investigated for transients, relaxation after cessation of shear flow, and step-up in shear rate. The Oldroyd-B and Giesekus constitutive models are implemented. Experimental data and numerical results are detailed in Verhulst et al., J. Non-Newtonian Fluid Mech. 156, 44-57 (2009).

The discrete slip-link model (DSM) predicts that the
contribution of chain
sliding dynamics (SD) to the relaxation modulus has a shape
significantly
different from the contribution by constraint dynamics (CD) for
monodisperse
linear chains. These contributions are also different from
what is predicted by
tube models. However, the product of these two contributions
are
nearly identical for the two models, so no real difference is
observable, at
least for monodisperse systems. On the other hand, this
observation suggests
that tube models and slip-link models might yield different
predictions for
the observable relaxation modulus of bidisperse blends. Tube
models essentially
predict double reptation for blends. However, better agreement
with data is
obtained by using a phenomenological exponent of 2.2, which was
proposed by
Marrucci and also recommended by Rubinstein et al. and by
Ruymbeke et al.
The exponent is hypothesized to be an effect either of
non-binary
entanglements or tube dilation. We find that the DSM with
binary
entanglements predicts data at least as well as double
reptation
with the phenomenological exponent of 2.2. We conclude that the
assumption of binary events for entanglements is sufficient.

Part 2: Margination of micro- and nano- particles in the flow through microchannels

September 14, 2009

Part 1: In this part of the talk we will discuss the coil-stretch hysteresis in dilute polymer solutions for extension dominated flows, including three-dimensional mixed flows. We will then turn to entangled systems and discuss the role of slip-link simulations in elucidating the extensional behavior in concentrated solutions and melts.

Part 2: Platelets are 7 times more likely to be at the periphery of the flow through microtubules than red blood cells above 35% hematocrit. The transport mechanism by which this occurs can be elucidated through dynamic simulation. In particular we will look at the effect of hematocrit and shear rate on these dynamics

Part 2: Platelets are 7 times more likely to be at the periphery of the flow through microtubules than red blood cells above 35% hematocrit. The transport mechanism by which this occurs can be elucidated through dynamic simulation. In particular we will look at the effect of hematocrit and shear rate on these dynamics

We discuss bacterial biofilms and the scope for describing their viscoelastic mechanical properties as a consequence of their underlying polymeric and multiphase morphology. Biofilms are the most prevalent phenotype of bacteria in nature. Biofilms form under conditions common in industry and in the body. They are structurally heterogeneous on multiple scales. We argue that the resolution of microscale mechanical properties is essential to fundamental understanding of the fate of biofilms in situations of flow, including the human circulatory system. Because of this need for microscale characterization, we developed the flexible microfluidic rheometer to characterize the elastic modulus and relaxation time of bacterial biofilms. The biofilms studied here are bacterial communities of Staphylococcus epidermidis and Klebsiella pneumoniae. The microfluidic device exploits the response of a flexible, deforming membrane to characterize the viscoelasticity of the test material. Attributes of the device are its simple fabrication and operation as well as its ability to accept biofilms grown at biologically relevant shear rates in the microfluidic environment. We find that the static and temporal responses of the valve membrane, as quantified by confocal microscopy, agree well with the viscoelastic properties of a model gellan gum as modeled by finite element simulation. Measurement of steady-state deformation yields both the linear and non-linear elastic response of the biofilms. We also report the transient response of the PDMS membrane coupled to the biofilm when the system is subjected to a stress relaxation experiment. We track the membrane deformation with the aim of extracting the viscoelastic relaxation time of the soft biological solid.

We study experimentally complex shaped partially wet particles on liquid-air interfaces. The interface deforms to satisfy the contact angle boundary conditions at the particle-liquid-air contact line. The deformations create excess liquid-air interface. When deformation fields between neighboring particles overlap, the excess area decreases as the particles approach each other. This creates a capillary attraction between the particles. Particle geometry influences the deformation field, creating preferred modes for particle assembly. Preliminary studies on the role of surfactants in altering these interactions will also be discussed.

December 31, 1969

Melt blowing is a commercialized processing technique that produces a
significant portion of nonwoven fiber products. It utilizes two
streams of hot air to stretch an extruded polymer strand into a fiber,
typically 2 μm in diameter. Our group has demonstrated the capability
of producing defect-free fibers with an average diameter of roughly
400 nm using a lab-scale melt blowing device designed after a typical
commercial instrument[1]. A systematic study of melt blowing of
bidisperse polymeric blends with different rheological properties,
obtained by mixing low and a high molecular weight polymer, will be
presented. This work demonstrates the impact of melt viscosity and
elasticity on the distribution of melt blown fiber diameters.

[1] Ellison, C.J. et al. Polymer 2007, 48, 3306-3316.

[1] Ellison, C.J. et al. Polymer 2007, 48, 3306-3316.

September 15, 2009

Measurements of the microstructure commensurate with the viscosity and normal stress differences in shearing colloidal suspensions provides an understanding of how to control the viscosity, shear thinning, and shear thickening rheological behavior typical of concentrated dispersions. In this presentation, I will review some of the experimental methods and key results concerning the micromechanics of colloidal suspension rheology. In particular, colloidal and nanoparticle dispersions can exhibit shear thickening, which is an active area of research with consequences in the materials and chemical industries, as well as an opportunity to engineer novel energy adsorbing materials. A fundamental understanding of shear thickening has been achieved through a combination of model system synthesis, rheological, rheo-optical and rheo-small angle neutron scattering (SANS) measurements, as well as simulation and theory. In particular, the shear-induced self-organization of “hydroclusters” (transient colloid concentration fluctuations) as predicted by Stokesian Dynamics simulations are measured and connected to the suspension rheology. The onset of shear thickening is demonstrated to be understood as a balance of convective, colloidal and hydrodynamic forces and their associated timescales. The limits of shear thickening behavior are also explored at extreme shear rates and stresses, where particle material properties come into play.

Although many applications of concentrated suspensions are hindered by shear thickening behavior, novel materials have been developed around shear thickening fluids (STFs). Ballistic, stab and impact resistant flexible composite materials are synthesized from colloidal & nanoparticle shear thickening fluids for applications as protective materials. The rheological investigations and micromechanical modeling serve as a framework for the rational design of STF-based materials to meet specific performance requirements not easily achieved with more conventional materials, as will be discussed.

Although many applications of concentrated suspensions are hindered by shear thickening behavior, novel materials have been developed around shear thickening fluids (STFs). Ballistic, stab and impact resistant flexible composite materials are synthesized from colloidal & nanoparticle shear thickening fluids for applications as protective materials. The rheological investigations and micromechanical modeling serve as a framework for the rational design of STF-based materials to meet specific performance requirements not easily achieved with more conventional materials, as will be discussed.