The effective diffusivity of a solute within a pore of comparable size is frequently found to be less than its value in bulk solution. This phenomenon is known as "hindered" or "restricted" diffusion and it arises fundamentally from the fact that the characteristic dimension of the solute molecule is no longer small compared to that of the pore through which it passes. Hindered diffusion is observed in a number of important fields such as gel permeation chromatography, heterogeneous catalysis, and membrane separations. Hindered diffusion of narrow molecular weight fractions of two polysaccharides was measured in microporous membranes with well-defined pore geometry. The two polysaccharides examined were dextran, a flexible coiled polymer of 1,6-glucopyranose units, and ficoll, a highly branched copolymer of sucrose and epichlorohydrin. The ratio of the membrane diffusion coefficient (D) to the bulk solution diffusion coefficient (D"), determined by light scattering, was examined as a function of the relative solute size to membrane pore size (r8/rp). Values of D/D" were found to be significantly greater for dextran than ficoll over most of the range of rs/rp examined.The ficoll data agree very well with a hydrodynamic model of diffusion based on a hard sphere in a tube.

Effects of molecular size and configuration on hindered diffusion were examined by measuring diffusion of two series of uncharged macromolecules through track-etch membranes with uniform and well-defined pore geometry. At any given Stokes-Einstein radius, diffusivities in small pores were lower for ficoll (crosslinked structure) than for dextran (more nearly linear structure). SCOPEThe effective diffusivity of a solute within a finely porous medium (e.g., a membrane or porous catalyst support) is frequently found to be less than its value in bulk solution. This phenomenon is known as "hindered or "restricted diffusion and it arises fundamentally from the fact that the characteristic dimension of the solute molecule is no longer small compared to that of the pore through which it passes. Several theoretical descriptions of liquid-phase mass transfer in fine pores have been developed based on hydrodynamic models of diffusion. These generally treat the membrane or other finely porous structure as an array of identical cylindrical pores, and the solute molecules as solid spheres. The advantages of such physical models over phenomenological approaches, such as that based on nonequilibrium thermodynamics, is that they offer the possibility of predicting mass transfer rates from a limited number of independently measurable properties of the solute and porous barrier, or alternatively, allow structural or other inferences to be made regarding the transport barrier when transport rates are known.The development in recent years of track-etch membranes has provided an excellent model system with which to test theories of hindered diffusion. These membranes are generally formed from thin sheets of mica or polycarbonate, with pores created by a two step process of bombardment with heavy fission fragments followed by chemical etching. The resultant pore geometry is highly regular and closely resembles the idealized cylindrical pores considered in the theories. These membranes have been employed in several previous investigations of restricted diffusion, but data remain somewhat limited. One objective of the present study was to extend the available data on diffusion of uncharged solutes to include substantially higher ratios of molecular size to pore size than had been considered previously, for comparison with existing theory. A second objective was to examine the effects of molecular configuration on restricted diffusion, for which little theoretical analysis is available. This was done by measuring diffusion of dextran, a slightly branched polysaccharide, and ficoll, a crosslinked copolymer of sucrose and epichlorohydrin, over a wide range of molecular sizes in polycarbonate tracketch membranes. CONCLUSIONS AND SIGNIFICANCEMeasurements of bulk solution diffusivity (D,) performed in membranes with large pores revealed that the tritiated dextran and ficoll used in this study have Stokes-Einstein radii ranging from about 2.3-6.0 nm and 1.6-3.5 nm, respectively. This was taken as the measure of molecular size. Characterization...

To investigate the mechanism(s) of angiotensin II-induced proteinuria, polydisperse [3H]dextran (D) (radius = 18-42 A) was infused into seven Munich-Wistar rats before and during intravenous infusion of angiotensin II (AII), 0.35 microgram/kg per min. During AII infusion, UprotV rose approximately twofold, and the fractional clearances of D [(U/P)D/(U/P)In] increased significantly for dextrans with radii greater than 22 A. Single nephron filtration fraction increased, due to a measured rise in the glomerular transcapillary hydraulic pressure difference from 34 to 43 mmHg. Near constancy of single nephron glomerular filtration rate resulted, however, from the offsetting effect of a decrease in glomerular plasma flow rate from 83 to 60 nl/min. These measured hemodynamic changes were found, by the use of pore theory, to account to a large extent for the measured increases in (U/P)D/(U/P)In. In seven other rats, fractional clearances of polyanionic dex-ran sulfate (a more reliable marker of albumin filtration than D) were also found to increase significantly with AII, suggesting that the proteinuria induced by AII can be explained, in large part, by hemodynamic factors.

A B S T R A C T To investigate the mechanism(s) of increased filtration of serum proteins after glomerular injury, polydisperse samples of uncharged [ 42A were determined in these rats, together with direct measurements of the forces governing the glomerular filtration rate of water. Whole kidney and single nephron glomerular filtration rates were -40% lower in PAN-treated rats, relative to controls, due mainly to a marked reduction in the glomerular capillary ultrafiltration coefficient and, to a lesser extent, to a small reduction in glomerular plasma flow rate as well. In PAN-treated rats, as in normal controls, inulin was found to permeate the glomerular capillary wall without measurable restriction, and both D and DS were shown to be neither secreted nor reabsorbed. Fractional clearances of uncharged D were reduced after PAN administration, falling significantly for effective D radii from 22 to 38A. Utilizing a theory based on macromolecular transport through pores, these results indicate that in PAN-treated rats, effective pore radius is the same as in controls, -44A. In PAN nephrosis, however, the ratio of total pore surface area/pore length, a measure of pore density, is reduced to approximately one-third that of control, due very likely to a reduction in filtration surface area. In contrast to the results with uncharged D, fractional clearances of DS were found to increase after PAN

Developments in the hydrodynamic theory of solute transport through porous membranes are reviewed, with emphasis on their application to macromolecule movement across capillary walls. A model that treats the capillary wall as a barrier containing uniform cylindrical pores, and permeating solutes as hard spheres, is shown to be successful in describing the size-selectivity of the glomerulus. Influences of various hemodynamic perturbations on solute transport are also accounted for by this approach. Possible extensions and modification of the theory, to account for the influence of molecular charge and other factors on glomerular permeability properties, are discussed.