General Microscopic Approach for Biofluid Transport

Abstract

Many problems in biofluid mechanics can be treated with the one-dimensional shell balance approach described in Chap. 6. However, the solution of multidimensional problems requires a more general approach. The result of this approach is a set of partial differential equations that can be applied to a variety of different problems, including many of the one-dimensional problems we have already solved in Chap. 6. It is not our intention to provide extensive methods for solving partial differential equations in this chapter. We will solve some multidimensional problems with relevant biofluids applications, but our main goals are to show how the general equations are derived, what restrictions are placed on them, how to simplify them by applying scaling concepts and reasonable assumptions, and how to specify auxiliary conditions, such as initial conditions and boundary conditions, that will provide us with a well-posed problem.