Abstract
Objective: The equations for transport of hydrophilic solutes through aqueous pores provide a fundamental basis for examining capillary–tissue exchange and water and solute flux through transmembrane channels, but the theory remains incomplete for ratios, α, of sphere diameters to pore diameters greater than 0.4. Values for permeabilities, P, and reflection coefficients, σ, from Lewellen [Citation], working with Lightfoot et al. [Citation], at α = 0.5 and 0.95, were combined with earlier values for α < 0.4, and the physically required values at α = 1.0, to provide accurate expressions over the whole range of 0 < α < 1.
Methods: The “data” were the long-accepted theory for α < 0.2 and the computational results from Lewellen and Lightfoot et al. on hard spheres (of 5 different α's) moving by convection and diffusion through a tight cylindrical pore, accounting for molecular exclusion, viscous forces, pressure drop, torque and rotation of spheres off the center line (averaging across all accessible radial positions), and the asymptotic values at α = 1.0. Coefficients for frictional hindrance to diffusion, F(α), and drag, G(α), and functions for σ (α) and P(α), were represented by power law functions and the parameters optimized to give best fits to the combined “data.”
Results: The reflection coefficients = {1 − [1 − (1 − ϕ)2]G′(α)} + 2α2fF′(α), and the relative permeability P/Pmax = ϕF ′(α)[1 + 9α5.5 · (1.0−α5)0.02], where ϕ is the partition coefficient or volume fraction of the pore available to solute. The new expression for the diffusive hindrance is F′(α) = (1−α2)3/2ϕ/[1+0.2 · α[p2·(1 − α2)16], and for the drag factor is G′(α) = (1−2α2/3−0.20217α5)/(1 − 0.75851α5) − 0.0431[1 − (1 − α10)]. All of these converge monotonically to the correct limits at α = 1.
Conclusions: These are the first expressions providing hydrodynamically based estimates of σ (α) and P(α) over 0 < α < 1 They should be accurate to within 1–2%.
This work was supported by NIH grant EB01973 and HL073598. The author is highly appreciative of the editorial assistance of James E. Lawson, and the figure preparation assistance of Kay A. Sterner.