ABSTRACTS

Contributed Talks

  1. Viscous Fingering in Non-Newtonian Fluids

    2. Petri Fast
    Courant Institute, New York University, NY

    Thin gap flows of non-Newtonian liquids are important technologically, and can exhibit a rich variety of dynamical behaviors. To study such problems, I use the thin gap limit to reduce a continuum viscoelastic model to a two-dimensional nonlinear generalization of Darcy's law. This leads to a nonlinear elliptic boundary value problem to be solved in a time-dependent domain. Recent intermediate time-scale simulations of the resulting dynamical system show intriguing consistency with experiments. I present the current state of a project to develop a moving overset grid scheme for the accurate and efficient long-time simulation of this problem.
  2. Simulation of Gravity Flow of Granular Materials in Silos

    3. John V Mathews III
    Department of Mathematics, NC State Univeristy, Raleigh, NC

    Despite its importance in industrial applications, the flow of granular materials through silos and bins is poorly understood. A particular model of steady granular flows under the influence of gravity is studied. The corresponding equations form a system of hyperbolic conservation laws. A higher order numerical method, the Discontinuous Galerkin method, is applied to this model. Computational results are presented.
  3. Tracking Interfaces in Multi-phase Fluid Flow

    4. William Miles
    Clemson University, Clemson, NC

    The tracking of interfacial boundaries between fluids is of critical importance in many fluid dynamic problems. The development of numerical schemes to do such tracking must take into account the possibility of numerical diffusion (for stable methods) as well as spurious oscillatory behavior (for higher order methods). Thus, the usual finite difference (volume) schemes face a contradictory situation of maintaining accuracy and stability simultaneously. This presentation will begin by discussing some of the previously mentioned difficulties encountered in modeling the interface between two fluids. The discussion will also indicate some of the differences between Newtonian and non-Newtonian fluids, which can cause further difficulty in dealing with fluid flow problems. The flux-corrected transport algorithm, one of the latest algorithms designed to achieve both accuracy and stability, will then be presented. Following this, the methodology will be translated into a finite element scheme designed to track the fluid interface.
  4. Gravitationally - Driven Drainage of Thin Films
    5. Shailesh Naire, R. J. Braun
    Department of Mathematical Sciences, University of Delaware, Newark, DE 19716
    and
    S. Snow Dow Corning Corporation Midland, MI 48686-0994
    The evolution of the free surface of a thin film draining under gravity is examined for the case where there is a dilute insoluble surfactant with finite surface viscosity. Three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity and surfactant transport are obtained at leading order. Interfacial stresses resulting from surface viscosity and Marangoni effects are included. Numerical solutions are compared with data obtained at Dow Corning Corp.