CNA 2001 Summer School




Mathematical Models of Fluids with Structure

Noel J. Walkington

ABSTRACT: Liquid crystals, fluids containing elastic particles, and polymer fluids, all exhibit non trivial macroscopic behavior due to interactions occurring on micro/mesoscopic scales. The derivation of rational models for these materials is a non-trivial task and results in formidable systems of partial differential equations. Of these problems the most complete theory is for Ericksen's model of liquid crystals, and I will begin with a discussion of this theory. I will then consider fluids containing elastic particles and present an approach which eliminates the need consider different coordinate systems for the particles (Lagrangian) and fluid (Eulerian). This naturally leads to ideas developed in the physics community to model polymer fluids and suggest alternative models for liquid crystals. These latter ideas are not widely known in the mathematical community and their connection with continuum mechanics is not clear.

This is joint work with C. Liu (Pennsylvania State University, USA)

Noel J. Walkington
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213