A NEW COMPUTATIONAL METHOD FOR THE SOLUTION OF FLOW PROBLEMS OF MICROSTRUCTURED FLUIDS .1. THEORY

The theoretical basis for a new computational method is presented for the solution of flow problems of microstructured fluids: examples include suspensions of rigid particles and polymeric liquids ranging from liquid crystals to concentrated solutions or melts of flexible chains. The method is based on a Lagrangian conservation statement for the distribution function of the conformation of the local structure, which can be derived from the conventional, Eulerian conservation statement and is exactly equivalent. The major difference, which is reflected in the numerical technique, is that the Lagrangian representation of the distribution function allows for computation of the Brownian contribution and of moments of distribution functions in ways that do not require explicit knowledge of the distribution function, and involve no approximation whatsoever. This suggests a new type of efficient, self-adaptive numerical scheme that is suitable for the solution of flow problems of microstructured fluids, in which macroscopic properties depend on the state of the microstructure.