Osmotic reflection coefficient
Author(s)Bhalla, Gaurav, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Chemical Engineering.
William M. Deen.
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The presence of a discriminating barrier separating two solutions differing in concentration generates a net volume flux called osmotic flow. The simple case is of the ideal semi-permeable membrane which completely excludes the solute. The flow through such a membrane is directly proportional to the thermodynamic pressure drop less the osmotic pressure drop. For membranes which partially exclude the solute the osmotic contribution to flow is less than that of the semi-permeable membrane, and the reduction is given by the osmotic reflection coefficient [sigma]o,. This work was motivated by understanding the mechanistic aspects of osmotic flow through such membranes, in order to predict [sigma]o. One of the main goals of the research was to develop computational models to predict [sigma]o for charged porous membranes and charged fibrous membranes. The effects of molecular shape on [sigma]o for rigid macromolecules in porous membranes were analyzed using a hydrodynamic model. In this type of model, employed first by Anderson and Malone, steric exclusion of the solute from the periphery of the pore induces a concentration-dependent drop in pressure near the pore wall, which in turn causes the osmotic flow (Anderson and Malone 1974). Results were obtained for prolate spheroids (axial ratio, [gamma] > 1) and oblate spheroids ([gamma] < 1) in cylindrical and slit pores. Two methods, one of which is novel, were used to compute the transverse pressure variation. Although conceptually different, they yielded very similar results; the merits of each are discussed. For a given value of a/R, where a is the prolate minor semiaxis or oblate major semiaxis and R is the pore radius, [sigma]o, increased monotonically with increasing [gamma]. When expressed as a function of aSEIR, where asE is the Stokes-Einstein radius, the effects of molecular shape were less pronounced, but still significant. The trends for slits were qualitatively similar to those for cylindrical pores. When [sigma]o was plotted as a function of the equilibrium partition coefficient, the results for all axial ratios fell on a single curve for a given pore shape, although the curve for cylindrical pores differed from that for slits. For spheres ([gamma]= 1) in either pore shape, [sigma]o was found to be only slightly smaller than the reflection coefficient for filtration (of). That suggests that [sigma]o can be used to estimate of for spheroids, where results are currently lacking. A computational model was developed to predict the effects of solute and pore charge on [sigma]o, of spherical macromolecules in cylindrical pores. Results were obtained for articles and pores of like charge and fixed surface charge densities, using a theory that combined low Reynolds number hydrodynamics with a continuum, point-charge description of the electrical double layers. In this formulation steric and/or electrostatic exclusion of macromolecules from the vicinity of the pore wall creates radial variations in osmotic pressure. These, in turn, lead to the axial pressure gradient that drives the osmotic flow. Due to the stronger exclusion that results from repulsive electrostatic nteractions, ao, with charge effects always exceeded that for an uncharged system with the same solute and pore size. The effects of charge stemmed almost entirely from particle positions within a pore being energetically unfavorable. It was found that the required potential energy could be computed with sufficient accuracy using the linearized Poisson-Boltzmann equation, high charge densities notwithstanding. In principle, another factor that might influence o in charged pores is the electrical body force due to the streaming potential. However, the streaming potential was shown to have little effect on [sigma]o, even when it markedly reduced the apparent hydraulic permeability. A model based on continuum hydrodynamics and electrostatics was developed to predict the combined effects of molecular charge and size on the o, of a macromolecule in a fibrous membrane, such as a biological hydrogel. The macromolecule was represented as a sphere with a constant surface charge density, and the membrane was assumed to consist of an array of parallel fibers of like charge, also with a constant surface charge density. The flow was assumed to be parallel to the fiber axes. The effects of charge were incorporated into the model by computing the electrostatic free energy for a sphere interacting with an array of fibers. It was shown that this energy could be approximated using a pairwise additivity assumption. Results for [sigma]o, were obtained for two types of negatively charged fibers, one with properties like those of glycosaminoglycan chains, and(cont.) the other for thicker fibers having a range of charge densities. Using physiologically reasonable fiber spacings and charge densities, [sigma]o, for BSA in either type of fiber array was shown to be much larger than (often double) that for an uncharged system. Given the close correspondence between [sigma]o and the [sigma]f; the results suggest that the negative charge of structures such as the endothelial surface glycocalyx is important in minimizing albumin loss from the circulation.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2009.Includes bibliographical references (leaves 149-152).
DepartmentMassachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology