Configurational effect on the reflection coefficient for rigid solutes in capillary pores

Osmosis-driven flow through a leaky porous membrane is analyzed by combining the relevant equations describing spatial and orientational distributions of rigid non-spherical solute particles with the equations of fluid flow in a single capillary which is very narrow compared to its length. The capillary cross-section is either circular or rectangular and connects two bulk solution reservoirs having equal pressures but unequal concentrations of solute (osmotic pressure). The objective of this analysis is to study the effect of particle and pore shape on the reflection coefficient (σ₀). The most significant result is that for solute particles of any eccentricity from one (sphere) to infinity (needle) in either the circular or rectangular pores, σ₀ ≈ (1?K)², where K is the pore-bulk equilibrium partition coefficient. A corollary of this result is that, comparing solute particles of equal volume, the more elongated a solute is the higher is its reflection coefficient; furthermore, for a given solute, the reflection coefficient is higher for pores that are more eccentric compared to a circle of equal area.