Osmotic reflection coefficient

by Gaurav Bhalla

Institution: MIT
Department: Chemical Engineering
Degree: PhD
Year: 2009
Keywords: Chemical Engineering.
Record ID: 1854418
Full text PDF: http://hdl.handle.net/1721.1/51614


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…