Transport Phenomena: Computational Models for Convective and Diffusive Transport in Capillaries and Tissue

A review of computational procedures for convective and diffusive transport, developed by the authors, is presented in this chapter. The presented finite element computational framework is directed to transport within capillaries and tissue. The convective transport includes modeling of motion of deformable bodies within fluid flow. It is based on a strong coupling concept and remeshing procedure. It was found by the authors that this approach has advantages in reliability and accuracy with respect to others available in literature, although it is not computationally efficient. A hierarchical multiscale model for diffusion couples molecular dynamics and continuum FE method by evaluating equivalent continuum diffusive parameters; these parameters include commonly used diffusion coefficients, but also parameters which account for physicochemical interactions between diffusingmolecules and microstructural solid surfaces. A numerical homogenization is used in this multiscale model. Coupled convective and diffusive transport is also considered. A number of typical solved examples illustrate generality, robustness, and accuracy of the presented computational methodology.