Emulsions, or suspensions of droplets of one liquid phase in another, occur in a wide variety of chemical, biological and materials processes. Some examples include liquid-liquid extraction, the flow of blood cells, thermal induced phase separation for the formation of microporous membranes and the formation of the immiscible polymer blends with superior mechanical, thermal and electrical properties. In these and many other applications the emulsion is processed so that drops can undergo large deformations, break-up, and coalesce.

The proposed project is an interdisciplinary collaboration concerned with large-scale micromechanical simulations of low-Reynolds-number or Stokesian emulsions. To deal with numerous challenges associated with this class of problems, the project brings together three researchers with expertise in geometrical modeling and visualization, fluid mechanical modeling and computations, and fast boundary element methods. The principal objectives of the project are twofold. First, explore, develop and implement various tightly integrated computational methods that will significantly advance existing computer simulation capabilities for Stokesian emulsions. Second, conduct simulations critical to the better qualitative understanding of the coalescence-induced-coalescence phenomenon and sheared emulsions containing highly deformable second-phase droplets capable of coalescence and break-up.

The project will build on existing methods and codes developed under prior NSF funding, including Grand Challenge, KDI, and NYI awards. Those include:

• Fast boundary element methods.
• Embedded time-stepping schemes that allow one to control both accuracy and stability.
• Special approximation and integration schemes for handling moderately deformable droplets and droplets near contact.
• Hierarchical geometrical representations, algorithms and data structures for free-form deformable surfaces, computing local and global metrics (curvature, normal, surface area, etc.), topological and combinatorial properties (list of nearest neighbors, location and number of clusters, etc.), and interactive visualization of various function fields.

The proposed work will focus on:

• Efficient iterative methods tailored specifically for Stokesian emulsions.
• Novel time-stepping schemes, with relaxed stability conditions on the time-step size.
• Hierarchical geometrical representations and data structures for locality maintainance, metric, topological and combinatorial query support, and interactive visualization of many droplets undergoing large displacements and deformations, and capable of coalescing and break-up.
• Qualitative understanding of the coalescence-induced coalescence mechanism and the equilibrium behavior of coalescence and break-up and rheology of highly sheared emulsions as a function of droplet volume fraction and droplet to suspending fluid viscosity ratios.

Principal Investigators:
Chandrajit Bajaj, University of Texas at Austin
Roger Bonnecaze, University of Texas at Austin
Gregory Rodin, University of Texas at Austin

This material is based upon work supported by the National Science Foundation under Grant No. 0220037

Any options, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.