Algorithm for direct numerical simulation of emulsion flow through a granular material

  • Authors:

  • Alexander Z. Zinchenko;Robert H. Davis

  • Affiliations:

  • Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA;Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

Quantified Score

Hi-index 31.46

Visualization

Abstract

A multipole-accelerated 3D boundary-integral algorithm capable of modelling an emulsion flow through a granular material by direct multiparticle-multidrop simulations in a periodic box is developed and tested. The particles form a random arrangement at high volume fraction rigidly held in space (including the case of an equilibrium packing in mechanical contact). Deformable drops (with non-deformed diameter comparable with the particle size) squeeze between the particles under a specified average pressure gradient. The algorithm includes recent boundary-integral desingularization tools especially important for drop-solid and drop-drop interactions, the Hebeker representation for solid particle contributions, and unstructured surface triangulations with fixed topology. Multipole acceleration, with two levels of mesh node decomposition (entire drop/solid surfaces and ''patches''), is a significant improvement over schemes used in previous, purely multidrop simulations; it remains efficient at very high resolutions (10^4-10^5 triangular elements per surface) and has no lower limitation on the number of particles or drops. Such resolutions are necessary in the problem to alleviate lubrication difficulties, especially for near-critical squeezing conditions, as well as using ~10^4 time steps and an iterative solution at each step, both for contrast and matching viscosities. Examples are shown for squeezing of 25-40 drops through an array of 9-14 solids, with the total volume fraction of 70% for particles and drops. The flow rates for the drop and continuous phases are calculated. Extensive convergence testing with respect to program parameters (triangulation, multipole truncation, etc.) is made.