F.Y. Hunt and J. Bernal, ACMD
J.F. Douglas, Materials Science and Engineering Laboratory
A number of scientists at NIST have undertaken a study of the scientific issues affecting the design and control of a polymer composite manufacturing process known as Resin Transfer Molding. Mold manufacturing processes frequently use materials consisting of a network of fiber bundles that make up a global porous medium and in order to adequately model flow behaviour in these intricate architectures, good estimates of the permeability of the medium are needed. Permeability can be calculated from a solution of the Poiseuille flow equation in a domain with complex geometry. However the use of finite differences or finite element methods can be dfficult to apply. We recently devised a Monte Carlo algorithm for solving the Poiseuille flow problem in two dimensional geometries of interest in experimental studies of permeability of fiber tow configurations. The idea is based on the computation of mean exit times of Brownian motion from the domain in question. Comparisons with the finite element computations of S. Ranganathan and permeability measurements of R. Parnas of the Polymers Division show a relative error of a few percent.
To locate bottlenecks in the Monte Carlo computation the theory of absorbing finite Markov chains is being used to estimate the tails of the exit time distributions of some of the random paths. Our future work will be directed toward calculating the permeability of cross-sections obtained from micrographs of the fiber tow configurations, and to exploring the possibility of extension to 3 dimensional problems.