ABSTRACTS

Invited Talks

  1. Exact and modulated patterns in flows of liquid crystal polymers

    2. Greg Forest
    Department of Mathematics, University of North Carolina, Chapel Hill, NC

    We study the moment-averaged, kinetic equations for flows of liquid crystal polymers as developed by Doi, Edwards, and others. These equations provide a mesoscale description of averaged, nonlinear information about molecular-scale orientation. As such, the theory captures behavior of anisotropic, viscoelastic flows. The usual momentum equations couple to an orientation tensor and its associated "nematodynamics". We analyze these equations in the presence of short-range and intermediate-range elasticity potentials, both with and without simple flow (shear and elongation), producing remarkable exact patterns and their phase transitions. The modulation of selected patterns is proposed as a description for the larger lengthscale textures that are routinely observed in experiments with liquid crystal polymers. This is joint work with Qi Wang, IUPUI, and Hong Zhou, University of North Carolina and UC-Santa Cruz.
  2. At-Line Capillary Viscometer Measurements
    3. L. Pamela Cook, G. Schleiniger, B. Wood
    Department of Mathematical Sciences, University of Delaware, Newark, DE. 19716 and
    C. Nwankwo
    DuPont Company, Wilmington, DE
     The goal of this work is to gain insight into flow referenced differential capillary viscometry (FRDCV) and to extend its capability to real-time measurement of polymer diffusivities. This work will make possible the determination of the characteristic composition of polymer solutions in real time online, instead of at a remote laboratory, leading to significant savings for industry.
    Online (or experimenatally) a plug of dilute polymer solution from the reaction is introduced into a fully developed flow of a solvent in a capillary. Measurements of pressure are taken downstream resulting in a polymer mixture profile. The fluid equations governing a two fluid mixture, with one fluid being a dilute viscoelastic mixture, the other a Newtonian solvent, are written in non-dimensional form and analyzed, both numerically and asymptotically, for their dependence on the dilution parameter epsilon and especially for their dependence on the Reynolds number and on the Schmidt (or inverse diffusivity) numbers. The governing process is a convective-diffusion balance.
  3. Exploring Stability and Dynamics of Viscoelastic Flows using Numerical Simulations

    4. Radhakrishna Sureshkumar, Department of Chemical Engineering and Materials Research Laboratory, Washington University, St. Louis, MO 63132.
    Numerical simulation of viscoelastic flows will prove to be most useful if it can predict the steady state, linear stability, and the non-linear dynamics of geometrically complex flows. Research in the past decades has resulted in the development of robust software for the numerical simulation of isothermal, multidimensional and steady viscoelastic flows. However, in comparison, the state of the art in the numerical simulation of time-dependent viscoelastic flows is still in the developing stage. This presentation will discuss promising approaches for the computation of stability boundaries, the construction of bifurcation diagrams and the exploration of post-critical nonlinear dynamics of viscoelastic flows with multiple inhomogeneous spatial directions for the base (steady) state. Results will be presented for a special class of flows, namely flows in periodic geometries, such as periodically constricted channel, eccentric cylinders and periodic arrays of cylinders in a channel.
    Work Supported by NSF Career Award, ACS/PRF and SDSC.
  4. Entanglement Friction and Dynamics of Macromolecules Near Surfaces

    5. Lynden Archer
    Department of Chemical Engineering, Texas A & M University
    College Station, TX

    The quiescent structure and transient dynamics of uncharged, flexible macromolecules near solid surfaces are quite different from those in bulk liquids. Surfaces are known, for example, to reduce configurational freedom, induce density fluctuations, and to slow-down molecular relaxation dynamics of flexible polymer molecules. In this presentation various aspects of polymer dynamics near surfaces will be discussed. I will focus in particular on the effect of a tightly bound surface layer on dynamic friction between surface and bulk polymer chains. A recent proposal for flow-induced changes in entanglement friction between deformed macromolecules at surfaces, will also be extended to address some unresolved problems in non-linear rheology of bulk polymers in fast shearing flows.
  5. Undercompressive Shocks in Driven Film Flow

    6. Andrea Bertozzi
    Departments of Mathematics and Physics, Duke University, Durham, NC

    Nonlinear hyperbolic conservation laws have solutions with propagating `shocks' or discontinuities. Compressive shocks satisfy an `entropy condition' in which characteristics enter the shock on each side. Undercompressive shocks violate this condition. We show that scalar laws with non-convex fluxes and fourth order diffusion have stable undercompressive fronts, yielding such unusual behavior as double shock structures from simple jump (Riemann) initial data. Thermal/gravity driven thin film flow is described by such equations and the signature of undercompressive fronts has been observed in recent experiments. Unlike compressive fronts, undercompressive film fronts are stable to fingering instabilities [1,2].
    [1] A. L. Bertozzi, A. Muench, X. Fanton, and A. M. Cazabat, Phys. Rev. Lett. 81(23), December 7, 1998.
    [2] A. L. Bertozzi, A. Muench, and M. Shearer, preprint.
  6. Uniaxial Stretching, Stress Relaxation and Failure of Viscoelastic Fluid Filaments (or why some fluids are stickier than others)

    7. Gareth H. McKinley
    Department of Mechanical Engineering, M.I.T., Cambridge MA 02139, USA

    The uniaxial extensional viscosity is a fundamental material property of a fluid which characterizes the resistance of the material to stretching deformations The intimate connection between the degree of strain-hardening that develops during transient uniaxial elongational stress growth in a viscoelastic fluid and the dynamical evolution in the profile of a thin polymeric filament is important in many industrial processing operations and is manifested in heuristic concepts such as 'spinnability', 'tackiness' and 'stringiness'. Common examples encountered in every-day life include the spinning of ultra-thin filaments of silk by orb-weaving spiders, removal of Band-aids and other pressure-sensitive adhesive materials, and the unexpectedly long life-time of strands of saliva. The strain-hardening in the fluid properties is directly connected to molecular properties of the fluid such as molecular weight, topology and concentration/entanglement-density. This dependence is reflected in the predictions of the particular viscoelastic constitutive equation characterizing a specific fluid, and being able to generate and understand stretching flows thus provides an important route for understanding the dynamical response of the material in a strong transient flow such as fiber-spinning, extrusion or film blowing and coating operations. A Filament Stretching Rheometer (FiSER) provides one of the few ways of unambiguously measuring the transient elongational response of 'mobile' polymer solutions that are viscous, but not rigid enough to test in the extensiometers commonly employed for extremely viscous melts. In this talk we outline the kinematic principles behind the design of such devices, analyze the dynamics of the resulting bulk fluid motion and show how the measurements can be used to probe the molecular stretching and stress relaxation of polymer chains and also to investigate instabilities associated with the necking and breakup of viscoelastic fluids