The Constrained Brownian Movement of Spherical Particles in Cylindrical Pores of Comparable Radius: Models of the Diffusive and Convective Transport of Solute Molecules in Membranes and Porous Media

Abstract

Abstract Rigorous calculations are presented for the effect of a constraining circular cylindrical boundary upon the translational Brownian motion of an isolated spherical particle suspended in a Poiseuille flow. These results also apply to dilute, multiparticle systems. Results are presented in the format of modifications of the Taylor—Aris theory of dispersion, arising from nonzero values of the dimensionless parameter λ = sphere radius/tube radius. Differences between present, continuum-mechanical, results and those derived from global forms of the thermodynamics of irreversible processes are reconciled. An outline of a more general theoretical framework is presented, with a view toward eventual applications to nonspherical particles and noncylindrical boundaries, such as occur, for example, in problems of aerosol deposition.