# <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><br/><br/>

Monday, October 12, 2009 - 4:30pm - 6:30pm

Lind 400

**Multiscale modeling and simulation of fluid flows in**

deformable porous media

Yuliya Gorb (University of Houston)

The main focus of the current poster presentation is on fluid flows in

deformable elastic media and associated multiscale problems. Many upscaling

methods are developed for flows in rigid porous media or deformable elastic

media assuming infinitely small fluid-solid interface displacements relative

to the pore size. Much research is needed for the most general and least

studied problem of flow in deformable porous media when the fluid-solid

interface deforms considerably at the pore level. We introduce a general

framework for numerical upscaling of the deformable porous media in the

context of a multiscale finite element method. This method allows for large

interface displacements and significant changes in pore geometry and volume.

For linear elastic solids we present some analysis of the proposed method.**Human tear film dynamics on an eye-shaped domain**

Kara Maki (University of Minnesota, Twin Cities)

We present recent progress in understanding the dynamics of human tear film on an eye-shaped domain. Using lubrication theory, we model the evolution of the tear film over a blink cycle. The highly nonlinear governing equation is solved on an overset grid by a method of lines coupled with finite difference in the Overture framework. Comparisons with experimental observations show qualitative agreement.**Spherical bubble collapse in viscoelastic fluids**

Tim Phillips (Cardiff University)

The collapse of a spherical bubble in an infinite expanse of viscoelastic fluid is considered. For a range of viscoelastic models, the problem is formulated in terms of a generalized Bernoulli equation for a velocity potential, under the assumptions of incompressibility and irrotationality. The boundary element method is used to determine the velocity potential and viscoelastic effects are incorporated into the model through the normal stress balance across the surface of the bubble. In the case of the Maxwell constitutive equation, the model predicts phenomena such as the damped oscillation of the bubble radius in time, the almost elastic oscillations in the large Deborah number limit and the rebound limit at large values of the Deborah number. A rebound condition in terms of $ReDe$ is derived theoretically for the Maxwell model by solving the Rayleigh-Plesset equation. A range of other viscoelastic models such as the Jeffreys model, the Rouse model and the Doi-Edwards model are amenable to solution using the same technique. Increasing the solvent viscosity in the Jeffreys model is shown to lead to increasingly damped oscillations of the bubble radius.**Simulation of particle migration in viscoelastic fluids using the extended finite element method**

Martien Hulsen (Technische Universiteit Eindhoven)

We present an eXtended Finite Element Method (XFEM) combined with a DEVSS-G/SUPG formulation for the direct numerical simulation of the flow of viscoelastic fluids with suspended rigid particles. For the whole computational domain including both the fluid and particles, we use a regular mesh which is not boundary-fitted. Then, the fluid domain and the particle domain are fully decoupled by using XFEM enrichment procedures. For moving particle problems, we incorporate a temporary arbitrary Lagrangian-Eulerian (ALE) scheme without the need of any re-meshing. We show the motion of a freely moving particle suspended in a Giesekus fluid between two rotating cylinders. The particle migrates to a stabilized radial position near the outer cylinder regardless of its initial position. As the Deborah number increases, the stabilized radial position of the particle shifts toward the outer cylinder.**Purely-elastic instabilities in extensional flows**

Rob Poole (University of Liverpool)

Using a finite-volume numerical technique we demonstrate that viscoelastic flow in a range of symmetric geometries - with symmetric inlet flow conditions - containing a region of strong extensional flow goes through a bifurcation to a steady asymmetric state. We show that this asymmetry is purely elastic in nature and that the effect of inertia is a stabilizing one. Our results in one such geometry - the so called “cross-slot” - are in excellent qualitative agreement with recent experimental visualizations of a similar flow in a micro-fluidic apparatus [Arratia et al. Phys. Rev. Lett., 2006 96(14)]. We investigate effects of constitutive equation (UCM, Oldroyd-B, PTT and FENE-CR models), model parameters and effects due to three dimensionality.**An O(N) iterative scheme for viscoelastic flow**

simulations with DEVSS

Oliver Harlen (University of Leeds)

In largescale finite element simulations of time-dependent viscoelastic flows the major computational difficulty is the solution of the linear system derived from the momentum and continuity equations. For Newtonian fluids highly efficient iterative solvers have been developed (Elman, Silvester & Wathen Finite Elements and Fast Iterative Solvers) using block preconditioned Krylov space methods. These methods converge within a fixed number of outer iterations so that both the computational time and memory requirements are proportional to the number of unknowns. Based on these ideas we have developed an iterative scheme for viscoelastic computations discretised using the popular DEVSS (Discrete Elastic-Viscous Stress Splitting) algorithm. We show that this scheme also converges within a fixed number of outer iterations for both two and three dimensional calculations, allowing large three dimensional calculations to be performed efficiently.**A maximum entropy principle based closure method and**

hysteresis for macro-micro models of polymeric materials

YunKyong Hyon (University of Minnesota, Twin Cities)

We consider the finite extensible nonlinear elasticity (FENE) dumbbell

model in viscoelastic polymeric fluids. The maximum

entropy principle for FENE model is employed to obtain the solution which

maximizes the entropy of FENE model in stationary situations. Then

the maximum entropy solution is approximated using the second order

terms in microscopic configuration field to get an probability

density function (PDF). The approximated PDF gives a solution to

avoid the difficulties caused by the nonlinearity of FENE model. The moment-closure

system satisfies the energy dissipation law. The moment-closure system can also show the hysteresis which is a nonlinear

behavior of viscoelastic dilute polymeric fluids. The hysteresis of FENE model can be seen during a relaxation in simple

extensional flow employing the normal stress/the elongational viscosity versus the mean-square extension. The hysteretic

behaviors of viscoelastic dilute polymeric fluids with moment-closure approximation models, FENE-L, FENE-P, FENE-D, are

presented in extensional/enlongational flows.**Effective viscosity and**

dynamics of dilute bacterial suspensions: A three-dimensional model

Brian Haines (The Pennsylvania State University)

We present a PDE model for dilute suspensions of bacteria

in a three-dimensional Stokesian fluid.

This model is used to calculate the statistically-stationary bulk

deviatoric stress and effective viscosity of the suspension

from the microscopic details of the interaction of an elongated body

with the background flow.

A bacterium is modeled as a prolate spheroid with self-propulsion

provided by a point force, which shows up in the model as an

inhomogeneous delta function in the PDE.

The bacterium is also subject to a stochastic torque in order to model

tumbling (random reorientation).

Due to a bacterium's asymmetric shape, interactions with a prescribed

generic background flow, such as

pure shear or planar shear, cause the bacterium to preferentially align in

certain directions. Due to the stochastic torque, the steady-state

distribution of orientations is unique for a given

background flow. Under this distribution of orientations,

self-propulsion produces a reduction in the effective viscosity.

For sufficiently weak background flows, the effect of self-propulsion

on the effective viscosity dominates all other contributions, leading

to an effective viscosity of the suspension that is lower than the viscosity

of the ambient fluid. This is in agreement with recent experiments

on suspensions of Bacillus subtilis.**Efficient numerical computation of fluid interfaces with soluble**

surfactant: a viscous drop

Michael Siegel (New Jersey Institute of Technology)

We address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant. At large values of bulk Peclet number

for representative fluid-surfactant systems, a

transition layer forms adjacent to the

interface in which the surfactant concentration varies rapidly.

Accurate calculation of the concentration gradient at the interface

is essential to determine

bulk-interface exchange of surfactant and the drop's dynamics.

We present a fast and accurate `hybrid' numerical method that

incorporates a separate singular perturbation reduction of the

transition layer into

a full numerical solution of the interfacial free boundary problem.

Results are presented for a drop of arbitrary viscosity in the

Stokes flow limit, where the underlying flow solver for insoluble

surfactant uses a direct (primitive variable) boundary integral method.**The response of a hydrophobic superparamagnetic**

ferrofluid droplet suspended in a viscous fluid in a uniform

magnetic field: the influence of microstructure on interfacial tension

Yuriko Renardy (Virginia Polytechnic Institute and State University)

The microstructure of a ferrofluid influences its motion under

applied magnetic fields.

A ferrofluid typically consists of magnetite nanoparticles

suspended in a solvent. Here, we consider a

ferrofluid that has no solvent, with the advantage that the

particles do not migrate under externally applied

magnetic fields, and therefore the physical properties of the

ferrofluid can be more easily characterized.

The deformation of a biocompatible hydrophobic ferrofluid

drop suspended in a viscous medium is investigated numerically

and compared with experimental

data. At high magnetic fields, experimental drop shapes deviate

from numerical results when a

constant surface tension value is used. One hypothesis for the

difference is the dependence of

interfacial tension on the magnetic field in the experimental

data. This idea is investigated

with direct numerical simulations.**Microscale shear flow of focal conic defects in layered liquids**

Shelley Anna (Carnegie-Mellon University)

Intermolecular interactions in liquid crystals and concentrated surfactant solutions lead to unique microstructures including lamellae, in which parallel layers are incompressible but bend easily. In such systems, planar layers are easily destabilized via external fields and nearby surfaces to produce topological defects of the order of tens of microns in size. These microscopic defects play a leading role in the flow behavior of such materials, and therefore impact numerous industrial applications including optoelectronic devices and displays and the processing of coatings, adhesives, and biomaterials to encapsulate drugs. To examine the interaction between such microscale defects and flow, we have developed a shear cell to impose a linear Couette flow in a microscale thin gap, while allowing for real time microscopic visualization. We use the shear cell to visualize the dynamics of defect formation in initially defect-free samples of a common small-molecule thermotropic liquid crystal, 8CB. We observe that the formation of focal conic defects, a specific topological defect typically found in thermotropic smectic liquid crystals, is triggered by edge effects and occurs in a series of phases, marked by distinct changes in the birefringence intensity. The defects are seen to annihilate partially or completely on reverse shear. The effect of shear rate and strain amplitude on defect formation and annihilation is studied.**Complex motions of vesicles and red blood cells in flow**

Petia Vlahovska (Dartmouth College)

Blood flow in the microcirculation is an extensively studied problem, yet the behavior of red blood cells (RBCs) continues to surprise researchers. For example, recently it was discovered that in steady shear flow RBCs not only tank-tread or tumble, but can also swing (tank-treading accompanied by oscillations in the inclination angle) [Abkarian et al. PRL 2007]. I will present our analytical work that quantitatively explains this behavior and other features in the RBCs dynamics.

In steady shear flows, the theory shows that a closed lipid membrane (vesicle or RBC) deforms into a prolate ellipsoid, which tumbles at low shear rates, and swings at higher shear rates. The amplitude of the oscillations decreases with shear rate. The viscosity of a dilute suspension of vesicles or RBCs exhibits a minimum at the tank-treading to tumbling transition. In quadratic flows, the theory predicts a peculiar coexistence of parachute- and bullet-like vesicle shapes at the flow centerline. Vesicles and RBCs always migrate towards the flow centerline unlike drops, whose direction of migration depends on the viscosity ratio. In time-dependent flows, vesicles can exhibit chaotic dynamics.**Structural instability in sedimentation through**

viscoelastic fluids

Ronald Phillips (University of California)

A theory has been developed to describe a structural instability that is observed during the sedimentation of particulate suspensions through viscoelastic fluids. The theory is based on the assumption that the influence of hydrodynamic interactions in viscoelastic fluids, which tend to cause particles to aggregate, is in competition with hydrodynamic dispersion, which acts to maintain a homogeneous microstructure. In keeping with the experimental observations, it predicts that the suspension structure will stratify into vertical columns when a dimensionless stability parameter exceeds a critical value. The column-to-column separation, measured in particle radii, is predicted to be proportional to the square root of the ratio of the dimensionless dispersion coefficient to the product of the particle volume fraction and the Deborah number. The time for the formation of the columns is predicted to scale with the inverse of the average volume fraction. These predictions are in agreement with experimental data reported in the literature.**Numerical prediction of the dynamics of nanoparticles embedded in a liquid crystalline solvent**

Juan Hernandez-Ortiz (National University of Colombia)

A hierarchical modeling approach has been adopted to examine the structure and dynamics of nanoparticle suspensions in confined liquid crystals. A molecular model and a combination of Monte Carlo and molecular dynamics simulations are used to investigate the defects that arise around the nanoparticles, both at rest and other imposed flow fields, and to explore how such defects influence the aggregation behavior of the particles. The continuum molecular model is solved by resorting to a unsymmetric radial basis function based technique. The validity of the model and our numerical results are established by direct comparison to results of molecular simulations and to experimental mobility data in both the isotropic and nematic phases. The model is then used to examine the response of different types of confinement, surface treatment, and flow field on the aggregation pathways of nanoparticles in liquid crystals.**Hydrodynamic pattern formation in ultrathin metal films: Robust**

route to plasmonic nanomaterials

Radhakrishna Sureshkumar (Washington University)

Sustainable production, storage and transportation of renewable energy

is one of the greatest challenges of the 21st century. Harnessing Sun's

energy for powering our planet has long been a dream of scientists and

engineers. Despite the universal appeal and growing usage of solar

energy systems across the globe, notably in developing economies, the

efficiency of energy conversion has remained well below desirable levels

for commercial installations. This is especially a major concern for new

generation photovoltaics, which utilize a thin film (~ 1 micron thick)

of the photoactive material. In this case, traditional light trapping

techniques such as optical gratings (~ several microns) employed for

cells based on bulk photoconductors are not applicable. Metallic

nanocomposites offer much promise in efficient and cost-effective solar

energy harvesting especially for thin film photocells. The central idea

is to exploit the plasmonic interaction between electromagnetic waves

and the localized oscillations of the free electron gas density at the

nanoparticle-dielectric interface.

From a renewable energy perspective, plasmonics principles can be used

to tailor the spectral response of a material to fit applications such

as broadband solar absorption and photo-bioreactor design. This is

accomplished by manipulating the particle size, aspect ratio and volume

fraction as well as utilizing hybridization techniques (e.g. core-shell

materials, multi-metal composites). In this talk, a robust manufacturing

route for such materials, namely laser-induced melting, dewetting and

self-organization of ultrathin (~ nm) metal films deposited on a

suitable substrate, will be discussed [APL 91, 043105 (2007); Phys. Rev.

B, 75, 235439 (2007); Nanotechnology, 17, 4229 (2006); Phys. Rev. Lett.,

101, 017802 (2008)]. Specifically, it will be shown that the knowledge

of thin film hydrodynamic instabilities can be utilized to predict

nanoparticle size and spacing observed in such experiments. The

mechanisms of pattern formation will be illustrated using experimental

visualizations of the dewetting process.**Simulation and experiments on selective withdrawal of polymer solutions**

James Feng (University of British Columbia)

Selective withdrawal refers to the removal of stratified fluids by a suction tube placed near the interface. We view this as an interesting complex fluid flow problem since the interface is disturbed by the nearby sink flow, and the interfacial morphology depends on the bulk rheology of the fluids. The poster will show recent numerical and experimental results for the selective withdrawal of polymer solutions. The most notable result is a transition from a smooth continuous interface to one with a thin air jet emanating from the tip of the interface, reminiscent of the Taylor cone.**Validity and limitations of the statistical scaling**

hypothesis for a nematic liquid crystal flow

Arghir Zarnescu (University of Oxford)

The transition from the isotropic into the nematic state occurs, in a

thermotropic liquid crystals, through the creation of nematically ordered

islands in the overall isotropic fluid. It was argued in the physics

literature that the domain growth of the nematic state is a scaling

phenomenon: the pattern of domains at a later time looks statistically

similar to that at an earlier time, up to a time-dependent change of scale.

The statistical scaling hypothesis states that at a large enough time the

equal time scalar correlation function C(r,t) will assume a scaling form

f(r/L(t)) where L(t) is the time-dependent length scale of nematic domains.

The precise asymptotics of L(t) for large t have been the subject of a

significant debate in the physics literature.

We present a mathematically rigorous analysis of the equations that shows

under what conditions the scaling hypothesis holds and what are the correct

asymptotics of L(t) for large t.

This is joint work with Eduard Kirr (University of Illinois at

Urbana-Champaign).**A thermodynamically compatible rate type**

fluid to describe the response of asphalt

Karel Tuma (Charles University in Prague)

We consider a class of viscoelastic rate type models that in particular includes: (i) Oldroyd-B fluid model with three parameters, (ii) nonlinear fluid model derived Rajagopal and Srinivasa [2000] with three parameters, and (iii) nonlinear model with five parameters. We are interested in observing how well are these models capable to capture the experimental data for asphalt performed by J. Murali Krishnan, Indian Institute of Technology, Madras using dynamic shear rheometer. We find out that the model (i) is not able to capture the experimentally observed overshoot for the torque, while we obtain overshoots for the models (ii) and (iii).**Shape optimization of peristaltic pumping**

Shawn Walker (New York University)

We present a variational method for optimizing peristaltic pumping in a two dimensional periodic channel with moving walls to pump fluid (peristalsis is common in biology). No a priori assumption is made on the wall motion, except that the shape is static in a moving wave frame. Thus, we pose an infinite dimensional optimization problem and solve it with finite elements. L^{2}-type projections are used to compute quantities such as curvature and boundary stresses.**Planar extensional motion of an inertially-driven liquid**

sheet

Linda Smolka (Bucknell University)

We derive a time-dependent exact solution of the free surface problem for the Navier-Stokes equations that describes the planar extensional motion of a viscous sheet driven by inertia. The linear stability of the exact solution to one- and two-dimensional symmetric perturbations is examined in the inviscid and viscous limits within the framework of the long-wave or slender body approximation. Both transient growth and long-time asymptotic stability are considered. For one-dimensional perturbations in the axial direction, viscous and inviscid sheets are asymptotically marginally stable, though depending on the Reynolds and Weber numbers transient growth can have an important effect. For one-dimensional perturbations in the transverse direction, inviscid sheets are asymptotically unstable to perturbations of all wavelengths. For two-dimensional perturbations, inviscid sheets are unstable to perturbations of all wavelengths with the transient dynamics controlled by axial perturbations and the long-time dynamics controlled by transverse perturbations. The asymptotic stability of viscous sheets to one-dimensional transverse perturbations and to two-dimensional perturbations depends on the capillary number (Ca); in both cases, the sheet is unstable to longwave transverse perturbations for any finite Ca. This work is in collaboration with Thomas P. Witelski.**Teaching rheology using product design**

Christopher Macosko (University of Minnesota, Twin Cities)

The poster describes two

courses on experimental rheology offered over the past several years to

seniors and first year graduate students at our institutions (KU Leuven

Belgium and U of Minnesota). These laboratory courses use complex materials

available from the shelves of our local retailers. We have found that

measuring the rheology of face cream, shampoo, paint, chewing gum or plastic

bags provides great motivation for students to learn rheology fundamentals.