# <span class=strong>Reception and Poster Session</span><br><br/><br/><b>Poster submissions welcome from all participants</b><br><br/><br/><a<br/><br/>href=/visitor-folder/contents/workshop.html#poster><b>Instructions</b></a>

Monday, September 14, 2009 - 4:15pm - 6:00pm

Lind 400

**Viscoelastic flow in a two-dimensional collapsible channel**

Ravi Jagadeeshan (Monash University)

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).**Vertical structures in shear thickening fluids**

Robert Deegan (University of Michigan)

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.**A macroscopic closure approximation to the**

micro-macro FENE model for polymeric materials

YunKyong Hyon (University of Minnesota, Twin Cities)

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.**Application of the discrete slip-link model to bidisperse linear systems**

Jay Schieber (Illinois Institute of Technology)

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.**Stress relaxation of comb polymers**

Leslie Leal (University of California)

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.**Localized Jeffery-Hamel flows of viscoelastic fluids**

Thomas Hagen (University of Memphis)

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.**On the origin of vorticity banding**

Jan Dhont (Forschungszentrum Jülich)Pavlik Lettinga (Forschungszentrum Jülich)

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.**Flowing Complex Fluids: Rheological measurements and constitutive modeling**

James Adams (University of Surrey)

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.**Human tear film dynamics on an eye-shaped domain**

Kara Maki (University of Minnesota, Twin Cities)

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.**Self-organised criticality in sheared suspensions**

Emmanouela Filippidi (New York University)

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.**Processing, morphology and properties of graphene**

reinforced polymer nanocomposites

Hyunwoo Kim (University of Minnesota, Twin Cities)

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.**3D-Imaging of cocontinuous blends**

Carlos López Barrón (University of Minnesota, Twin Cities)

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.**Measurements of flow induced birefringence of complex**

fluids undergoing high rate deformations in microscale

geometries

Thomas Ober (Massachusetts Institute of Technology)

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.**Using time-resolved SANS to understand the flow behavior of PB-PEO wormlike**

micelles

Jan Dhont (Forschungszentrum Jülich)Pavlik Lettinga (Forschungszentrum Jülich)

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.**Dynamics and rheology of wormlike micelles emerging from particulate computer simulations**

Edo Boek (Schlumberger-Doll Research)

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).**Elastic instabilities in the flow of wormlike micelles**

Marc-Antoine Fardin (Université de Paris VII (Denis Diderot))

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.**The Brinkman model for fast, viscous, and turbulent flows in porous media**

Ross Ingram (University of Pittsburgh)

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.**Director angle anchoring conditions and the dynamic moduli of nematic liquid crystal polymers**

Eric Choate (University of North Carolina, Chapel Hill)

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.**Vorticity and velocity banding in shear thickening**

solutions of wormlike micelles

Peter Fischer (Eidgenössische TH Zürich-Zentrum)

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.**Simulations of mechanical failure in transient polymer networks**

Wim Briels (Universiteit Twente)

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.**Influence of viscosity and elasticity on the statistical properties**

of meltblown polymer fibers

Dawud Tan (University of Minnesota, Twin Cities)

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.**Kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts**

Richard Graham (University of Nottingham)Peter Olmsted

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.**Influence of viscoelasticity on drop deformation in shear**

Yuriko Renardy (Virginia Polytechnic Institute and State University)

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).**Structure and rheology of nanoparticle gels and glasses**

Aaron Eberle (University of Delaware)

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.