Mahendra R. Doshi

LIMITING FLUX IN ULTRAFILTRATION OF MACROMOLECULAR SOLUTIONS

Abstract The mass transfer equation describing the process of gel polarized ultrafiltration is solved using an integral method. A concentration profile is assumed to be an nth degree polynomial. In conventional integral method, “n”is arbitrarily assigned an integer value. In this paper we have taken the first moment of the convective diffusion equation to determine “n” as a function of the system parameters. The agreement between the closed form integral method solution and the exact numerical solution is excellent while the widely used film theory deviates considerably.

Ultrafiltration in an unstirred batch cell

The ultrafiltration of bovine serum albumin (BSA) in .15 M NaCl (pH = 7.40) and .10 M sodium acetate (pH = 4.70) was investigated in an unstirred batch cell. Data were analyzed to minimize the effects of inter-membrane variations and other experimental errors. BSA systems were studied over a wide range of concentration (1–10 g/100cc) and at higher pressures than previously reported (150 psig). Results confirm that BSA does reach a pressure-independent flux region. A constant property integral method solution, which has the simplicity of the popular film theory model, compared quite well with the exact solution. Agreement between acquired BSA data and theoretical predictions is excellent, with the maximum error less than 3%. Not only is the assumption of constant diffusion coefficient shown to be reasonable for the unstirred batch cell, but also that the difference in the calculated value of the diffusion coefficient for BSA at pH = 4.70 and pH = 7.40 is small. This finding is further confirmed by separate diffusion coefficient determinations by ultracentrifuge technique. The values of Cgel as determined from ultrafiltration data are 37.0 g/100cc at pH 4.7 and 57.5 g/100cc at pH 7.4. These values correspond reasonably well to literature values.

Hollow fiber reverse osmosis: experiments and analysis of radial flow systems

The performance of a hollow fiber reverse osmosis system was determined experimentally by measuring the fraction of feed recovered as product, φ, and the concentration reduction ratio, θp. A predictive model for these two quantities was developed which yields results that agree with the experimental data very well for applied pressures of 300–450 psig., feed rates from 75 to 525 cc/sec and feed concentrations up to 15000 ppm of sodium chloride. The concept of distributed sinks in a continuum is used for the shell side, and a diffusion model is used to describe solute transport across the fiber wall. The principal assumptions made are negligible concentration polarization, small radial pressure drop in the shell and small solute transport, compared with solvent transport, through the fiber. Simple closed form expressions for φ and θp, given by eqns (43a) and (51), were obtained which are accurate over the range of experimental conditions employed.

Unsteady reverse osmosis or ultrafiltration in a tube

Abstract The unsteady behavior of a tubular hyperfiltration system, with both a pulse and a continuous feed, is analyzed using a significant extension of miscible dispersion theory. The extension permits one to treat unsteady convective diffusion in systems with convection at interfacial boundaries in a relatively straightforward manner. It is shown that such convection can effect an enormous reduction in axial dispersion in such systems. A superposition integral is used to generalize the solution for the pulse input to reverse osmosis systems with continuous feeds which may be subject to arbitrary fluctuations in feed concentrations.

Pressure field-flow fractionation or polarization chromatography

Abstract When a pressurized fluid mixture flows past a reverse osmosis or ultra-filtration membrane the components of the mixture diffuse to, and permeate the membrane, at different rates and the extent to which a component is polarized at the membrane surface depends on its wall Peclet number, Pwi. Pressure field flow chromatography utilizes this phenomenon, and the resulting differential retardation (or increase in residence time) of the polarized solute particles in the slower moving concentrated fluid layers immediately adjacent to the membrane creates a chromatographic separation of the components of the mixture. The results of the present analysis of separation by pressure field flow fractionation (PFFF) between flat, narrowly spaced membranes are compared with those in a tube and with those obtained when a cross-flow in one membrane and out the other (flow field flow fraction) exists. The results suggest that all three approaches appear to have reasonably good potential for practical applications. Perturbation results for the large time values of Ki in the generalized dispersion equation, valid for large and small values of the parameter Pew are given in convenient algebraic forms for PFFF. For large values of Pew, solute retardation is very pronounced and axial dispersion is reduced very substantially, both of which suggest potentially favorable separations. A significant difference between PFFF and FFFF system is the exponential increase in Cm caused by the loss of carrier fluid along the conduit in the case of PFFF. The effect is reflected in the value of Ko.

A MODEL FOR FREENESS MEASUREMENT OF PAPERMAKING SUSPENSIONS

In the pulp and paper industry, it is often necessary to characterize the drainage capability or a pulp on the paper machines. The industry uses a standard measure called the freeness to represent this and other properties for papermaking pulps. The freeness is the total volume of water discharged from a side orifice of a specific configuration while the pulp suspension drains freely under gravity. In this paper, a model for the gravity filtration of pulp suspensions forming a compressible pulp mat is along with some empirical treatment of the flow is used to model the freeness test. The gravity drainage process is assumed to be described by a cake filtration process with the pressure at each instant being given by the gravity head. From the model, the critical parameters governing the freeness of a pulp suspension are shown to be the specific surface area and the specific volume of the pulp fibers in addition to the compressibility of the pulp mat. When these parameters are available from independent gra...

SEDIMENTATION BEHAVIOR OF VARIOUS PULP FIBERS

Abstract Wood pulp fibers form floes which settle by “zone settling.” These fiber floes do not exhibit Stokes’ Law settling behavior. A new filtration model was developed. This model describes quite well the settling of most types of pulp fibers, and its application generates a parameter, K’, which can be used to monitor pulp refining. However, decrilled samples, i.e., pulp from which fines have been removed, do not follow the new model. More work is needed to understand the settling behavior of fines-free pulp.

THE GENERALIZED LEVEQUE SOLUTION

In the conventional Leveque analysis, three assumptions are made: (a) that the curvature effect is negligible; (b) that the velocity profile can be linearized; and (c) that the symmetry condition can be replaced by an infinity condition. In the present, more exact, analysis all three assumptions have been relaxed by introducing a new transverse coordinate. The results indicate that the curvature effect is quite important and that the assumption of an infinity condition is reasonable. Consequently, results obtained by neglecting the curvature effects should be used with caution.