An exactly solvable ogston model of gel electrophoresis. 7. Diffusion and mobility of hard spherical particles in three-dimensional gels

We extend our lattice model of gel electrophoresis (and diffusion) to the study of the continuum limit (no lattice effect) for hard spherical particles migrating in periodic and random three-dimensional gels. To reach the continuum limit, the mesh size of the system is progressively decreased until a clear extrapolation to the continuum limit (where the size of the lattice parameter is infinitely small in comparison to the size of the gel fibers) can be done. Various types of gel are studied, starting from simple periodic parallel and straight fibers to a representation of a more realistic gel formed of irregular, cross-linked fibers placed along random directions. Our mobility data for pseudospherical particles in the continuum limit are interpreted in terms of the obstruction model of diffusion.