Hydrodynamic and rejection properties of a coil dialyzer.

Compliance of coil dialyzers follows a linear dependence on pressure when measured in saline; compliance measurements with non-wetting fluids are inappropriate and underestimate the blood compartment expansion experienced with pressure. The arithmetic mean of inlet and outlet pressures can be used to predict ultrafiltration rate independent of venous outlet pressure, and blood compartment volume varies both with inlet pressure and blood flow. The rejection of carbohydrate marker solutes increases from about 10% for 1,200 Daltons to 100% for 12,000 Dalton species.

Appraisal of equations for neutral solute flux across porous sieving membranes.

General transport equations, based on irreversible thermodynamics applied to membranes without regard to their structures, are compared with results based upon specific membrane models. It is pointed out that the range of validity of the general linear transport equations of irreversible thermodynamics may be extremely small, and that attempts to extend the range by thermodynamic considerations have always involved subtle assumptions of a nonthermodynamic nature. Simple membrane models are used as diagnostic tools to pinpoint such assumptions, with particular reference to the often-concealed assumption of membrane homoporosity. It is shown that it is not possible to write an exact equation for solute flux across an inert porous membrane only in terms of the three customary membrane parameters sigma (reflection coefficient), Ps (permeability coefficient), and Lp (hydraulic conductivity), unless the membrane is strictly homoporous. Even in the linear range heteroporosity imposes a hidden condition of delta p greater than delta pi for such a three-parameter description to be valid. Useful results in the nonlinear regime require more detailed information on membrane structure than is contained in just three parameters.

Effect of heteroporosity on flux equations for membranes.

An investigation is made of the possible errors in simple integrated equations for solute flux across both non-sieving and sieving porous membranes that can result from variations in the membrane structure. Detailed structural models are used, beginning with a membrane consisting of a parallel array of pores and progressing to series--parallel combinations of pore segments of various lengths and cross-sectional areas, with internal cross connections among pore segments allowed. It is shown that there are both upper and lower mathematical bounds on the possible variations that can be produced in a curve of solute flux versus volume flow by arbitrary variation in the membrane structure, subject only to certain general conditions. In particular, the flux equation for a homoporous membrane is a lower bound. The maximum deviations from this lower bound for a membrane of arbitrary structure are only moderately large, and require rather extreme pore size distributions; most distributions introduce only small errors. Implications of these results in studies of real membrane structure and in the design of experiments are discussed.

Equations for membrane transport. Experimental and theoretical tests of the frictional model.

Frictional models for membrane transport are tested experimentally and theoretically for the simple case of a solution consisting of a mixture of two perfect gases and a membrane consisting of a porous graphite septum. Serious disagreement is found, which is traced to a missing viscous term. Kinetic theory is then used as a guide in formulating a corrected set of transport equations, and in giving a physical interpretation to the frictional coefficients. Sieving effects are found to be attributable to entrance effects rather than to true frictional effects within the body of the membrane. The results are shown to be compatible with nonequilibrium thermodynamics. Some correlations and predictions are made of the behavior of various transport coefficients for general solutions.

Steady-state sieving across membranes.

The constraint of steady-state operation for sieving or ultrafiltration across membranes greatly restricts possible theoretical mechanisms. Effective sieving in the steady state requires the coexistence of a removal mechanism with the rejection mechanism. These points are illustrated without elaborate mathematics by a model of membranes in a series array with intervening compartments. This model also shows that in certain regimes the structure of the first membrane alone determines the overall sieving characteristics of the array.

Diffusion and convective flow across membranes: irreversible the thermodynamic approach.

The experimentally verified hydrodynamic approach to a description of diffusive and convective flow of solute across mutual membrane pathways is compared with the phenomenological equation resulting from the application of irreversible thermodynamics. Inherent nonlinearities in this equation severely, if not absolutely, limit its usefulness.