Day 3: Tuesday morning, September 5, 2006

Session 4 Complex fluid deformation and rheology: Theories and thermodynamic relationships
Chair: M. Grmela

08:00  Dynamic van der Waals theory
A. Onuki
Physics Department, Kyoto University, Japan
We present a dynamic van der Waals theory including gradient entropy and energy. We introduce the temperature as a functional of the number density and the energy density. Our model is useful to study phase separation when the temperature varies in space. As an example, we show that if heat flow is applied to liquid suspending as droplet at zero gravity, a convective flow occurs such that the temperature gradient within the droplet nearly vanishes. As the heat flux is increased, the droplet becomes attached to the heated boundary that is wetted by liquid in equilibrium. In one case corresponding to partial wetting by gas, an apparent contact angle can be defined. In the other case with larger heat flux, the droplet completely wets the heated boundary expelling liquid. As another example, we study wetting dynamics with evaporation and condensation.

[1] A. Onuki, Phys. Rev. Lett. 94 (2005), 054501.

08:50  Thermodynamic relationships for shearing viscoelastic fluids
P.J. Daivis
Applied Physics, School of Applied Sciences, RMIT University, Melbourne, Australia
It is shown that the work done in taking a viscoelastic fluid from equilibrium into a shearing steady state can be separated into viscous and elastic parts. This separation is completely phenomenological and therefore does not require any special assumptions about the substance being studied. It is also expected to be valid for non-linear viscoelastic materials. In the limit of zero shear rate, it is possible to use the standard machinery of thermodynamics to derive a Maxwell relation between the shear rate dependence of the pressure and the reversible part of the work required to establish a shearing steady state. This leads to a useful relationship between the stored energy in a shearing linear viscoelastic fluid and the limiting zero shear rate value of the first normal stress coefficient. This relationship explicitly confirms the expectation that the first normal stress coefficient of a linear viscoelastic fluid is associated with elasticity.

09:15  Relationship between heterogeneous dynamics and internal stress
M.T. Downton, M.P. Kennett
Simon Fraser University, USA
The low temperature breakdown of the linear relationship between viscosity and translational diffusion is commonly attributed to the appearance of heterogeneous dynamics that occurs when a liquid is cooled. While diffusion is predominantly due to mobile particles (fast relaxation), viscosity is related to the stress autocorrelation function (slow relaxation), this difference in averages, coupled with the broadened distribution of relaxation timescales leads to the breakdown. In this work we consider the relaxation and spatial variance of the local stress tensor and its relationship to the particle mobility and force network using simulations of cooled binary mixtures. We make direct comparisons of our off-lattice results with recent work on dynamic facilitation.

09:40  Dynamics of an interface or membrane between two fluids
B.U. Felderhof
RWTH Aachen, Aachen, Germany
The dynamics of a flat interface or membrane between two viscous fluids is studied on the basis of the linearized Navier-Stokes equations. The dispersion equation for interfacial waves involves surface tension and elasticity moduli of the interface, besides gravitational acceleration. It is shown that in a symmetric case, where the two fluids have equal viscosity and equal mass density, there is a decoupling of the capillary-gravity wave and the longitudinal elastic wave. The displacement of the interface due to a force density applied at the interface is characterized by a susceptibility tensor. Wave excitation due to a monochromatic plane wave source or a monochromatic line source located at some distance from the interface are discussed.

10:05  Coffee break

10:20  Polymer rheology and nonlinear transient elasticity
O. Müller¹, M. Liu¹, H. Pleiner², H.R. Brand^3
1 Theoretical Physics, University of Tübingen, Germany
² Max Planck Institute for Polymer Research, Mainz, Germany
³ Theoretical Physics III, University of Bayreuth, Germany
We simplify our previously derived general macroscopic equations incorporating transient elasticity by assuming incompressibility as well as linear response for the dissipation. We take into account terms up to quartic order in the elasticity (3 independent coefficients) and have in addition only two dissipative constants: the shear viscosity and the relaxation time of transient elasticity. This simple model can account for many experimentally observed rheological effects qualitatively and sometimes even quantitatively. Flow phenomena discussed include the Weissenberg effect, overshoot, relaxation spectra and elongational flows.

10:45  Plastic flow of solids
A. Minami, A. Onuki
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
A phase field model is presented to study dislocation formation (coherency loss) in one- and two-phase binary alloys. In our model, the elastic energy density is a periodic function of the strain components, which allows multiple formation of dislocations. The composition is coupled to the elastic field twofold via lattice misfit and via composition-dependence of the elastic moduli. By numerically integrating the dynamic equations in two and three dimensions, we find that dislocations appear in pairs in the interface region in two dimensions and as a loop with the ends trapped at the interface in three dimensions. They glide under uniaxial stretching in the softer region and do not penetrate into the harder domains. This process gives rise to a plastic flow, where stress increases gradually with increasing applied strain. Particularly in three dimensions, we follow the dislocation loop formation and growth around hard domains. We also observe growth of spiral-shaped domains rich in the softer component around screw dislocations.

[1] Akihiko Minami and Akira Onuki ''Dislocation formation and plastic flow in binary alloys in three dimensions'' Phys. Rev. B 72, 100101(R) (2005).
[2] Akihiko Minami and Akira Onuki, ''Dislocation formation in two-phase alloys'' Phys. Rev. B 70, 184114 (2004).

11:10  Thermodynamics of Non-Isothermal Polymer Flows: Experiment, Theory and Simulation
T.C. Ionescu¹, B.J. Edwards¹, D.J. Keffer¹, V.G. Mavrantzas^2
1 Department of Chemical Engineering, University of Tennessee, Knoxville, TN 37996-2200, USA
² Department of Chemical Engineering, University of Patras, Patras GR 26504, Greece
We provide a critical evaluation of the so-called ''Theory of Purely Entropic Elasticity'', which states that the free energy change of a flowing, non-isothermal viscoelastic fluid is entirely due to entropic effects, and contains no contributions due to elastic energy changes. Our investigation consists of both theoretical and experimental parts. In the theoretical part, we perform non-equilibrium Monte Carlo simulations to calculate both the energetic and entropic contributions to the free energy of the material under uniaxial elongational flow. This results in measurable energetic effects at higher strain rates, and these effects increase as temperature decreases. Experimentally, we measured the heat capacity at constant volume of LDPE under steady-state shear and uniaxial elongational flow conditions, and calculated the conformational contribution to this quantity. According to the Theory of Purely Entropic Elasticity, the conformational contribution to the heat capacity should be negligible, however, significant non-vanishing contributions are measurable at high strain rates. Results are qualitatively consistent between theory and simulation.

11:35  Discussion
M. Grmela

12:05  Lunch

   Day 3: Tuesday afternoon, September 5, 2006

14:00  A general methodology to predict the linear rheology of branched polymers
E. van Ruymbeke¹, R. Keunings², C. Bailly², D. Vlassopoulos^1,3
1 IESL - FORTH, Heraklion, Greece
² UCL, Louvain La Neuve, Belgium
³ University of Crete, Department of Materials Science and Technology, Heraklion, Greece
We present a general coarse-grained model for predicting the linear viscoelasic properties of branched polymers from the knowledge of their molecular structure and three viscoelastic parameters, i.e. the Rouse time of an entanglement segment, the plateau modulus and the entanglement molecular weight. The model uses the ingredients of the tube-based theories of McLeish and co-workers, and its implementation is based on a time-marching algorithm, this conceptual approach was already successfully applied to linear and star polymers, and is appropriately modified here to account for more complex branched architectures, within the framework of dynamic tube dilation (using the extended criteria of Graessley). While the fluctuations of the external branches segments are quite well described in literature, the motion of the molecular segments localized between two branching points is still an open question that we study in this work. With proper account of polydispersity and use of macromolecular coordinates for the diffusion of the branching points, successful description of a wide range of rheological data of H, pom-pom, tree-like or comb polymers is obtained. The good quality of predictions gives us confidence about this approach. More notably, we do not need to use ad hoc parameter modifications (in particular the p2 parameter) to get good results. The proposed methodology thus represents a generic approach for predicting the linear rheology of branched polymers.

14:25  2-Fluid Viscoelasticity
H. Pleiner¹, J.L. Harden^2
1 Max Planck Institute for Polymer Research, 55021 Mainz, Germany
² Dept. Physics, University of Ottawa, Ottawa Ontario K1N 6N5, Canada
We combine the nonlinear hydrodynamic description of viscoelastic fluids with a general 2-fluid hydrodynamics of 2-component (mass density) and 2-momentum (velocity) systems to give a generalized hydrodynamics model for disperse polymers and colloids. This description deals with hydrodynamic equations for the two (generally conserved) mass densities, the total (conserved) momentum density and for the non-hydrodynamic, relaxing relative velocity, the thermal degree of freedom, and either the relaxing elasticity, or transient orientation dynamics. There are special problems with this 2-fluid extension of ordinary hydrodynamics, like the choice of the transport and convection velocities or the separation of the stress tensor between the two subsystems. Generally it turns out that transport and convective velocities are material dependent and can be different for the different variables or even from each other. However, there are certain restrictions and interdependencies among them due to thermodynamic requirements. In addition, the stress division problem is not independent from the transport and convective velocity problem.

14:50  Selected nonlinear physical properties of liquid crystalline elastomers
A.M. Menzel, H.R. Brand
Theoretical Physics III, University of Bayreuth, Germany
Side-chain liquid single crystal elastomers (SCLSCEs) are unique materials combining the properties of ordinary rubbers with those of a liquid crystalline phase. Furthermore the director describing the broken symmetry in the liquid crystalline phase is coupled to deformations of the elastomer, which allows for example the reorientation of the director by external mechanical forces. In a linearized continuum theory this coupling is determined by two terms in the free energy density, which were introduced by de Gennes and contain relative rotations between the director and the polymer network. A central goal of our studies, where we analyze the macroscopic behavior of SCLSCEs in external fields, is to generalize these two terms and the complete expression for the free energy into the nonlinear domain. Physical consequences of the nonlinear terms will be discussed.

15:15  Suspensions of rodlike molecules: phase transition and equlilibration time scale for a shear flow
F. Otto, C. Löschke, J. Wachsmuth
University of Bonn, Germany
We consider the Doi-model for suspensions of rodlike molecules. We perform a bifurcation analysis for the isotropic-nematic phase transition in the force-free case. It shows that the type of bifurcation almost does not depend on the choice of the integral kernel modelling the excluded volume effect. We rigorously show the existence of exactly two branches of steady states up to rotations near the point where the isotropic phase becomes unstable. We consider as well a dilute solution exposed to a shear flow with large Deborah-number. The rod distribution will converge to an equilibrium asymptotically concentrated in flow direction. However the mean flux does not vanish (but the rods are constantly rotated). We prove that the equilibration is exponential on a time scale (Deborah number)^(-2/3). The difficulty is that the generator of the stochastic process is not symmetric. We give a hypocoercivity argument based on commutators between diffusion and mean flux in the equilibrium.

15:40  Coffee break

15:45  Poster Session »

16:35  Free time

17:00  Excursion