Ismail Tosun

A rigorous cake filtration theory

The currently accepted concepts of the parabolic filtration correlation stipulate that the filtration rate decreases inversely as the flow resistance which is proportional to the extent of the filter cake; that non-parabolic behavior is characteristic of only compressible cakes which exhibit an average resistance which is not constant but depends on slurry concentration, filtrate rate and applied pressure; that the septum resistance is separate from, but additive to, the cake resistance and is obtained from the intercept of the VF− vs VF line; that the average porosity of compressible cakes decreases during a filtration which causes the exit flow rate to exceed the entrance flow rate; that internal variations can only be obtained via compression-permeability simulations; and that the local resistance decreases monotonically from the septum to the cake surface. A filtration theory based on the rigorous, multiphase equations of change finds, contrary to the concepts listed above, that the least permeable part of the cake at the cake-septum interface (K0) controls the filtrate rate and a decreasing pressure gradient across this minimum K0 causes the filtrate rate to decrease; that deviations from parabolic behavior are independent of cake compressibility (incompressible cakes are rare, if they exist at all) but can be expected when ϵα*, s, -ΔPc, K0 and (dP*/dξ)|ξ=0 are not constant; that the septum resistance is intrinsically included in K0 which appears in the slope and not the intercept of VF−1 vs VF; that the average porosity is constant and the exit flow rate exceeds the entrance flow rate due to a difference between the surface porosity and the average porosity; that internal variations can be obtained directly from filtration data alone and do not require a compression-permeability simulation; and that the local filtration resistance can exhibit a minimum as a result of using a non-linear transformation from cake length to cake mass.

Formulation of cake filtration

Abstract For constant pressure cake filtration, combination of the equations of continuity and motion together with the relevant boundary and initial conditions constitutes a moving boundary problem. In this study, Eulerian and Lagrangian formulations of cake filtration as a moving boundary problem are reviewed, deficiencies are pointed out, and a systematic approach and an alternative solution technique are presented.

EXPERIMENTAL STUDIES ON THE EFFECT OF ELECTRODE CONFIGURATION IN ELECTROFILTRATION

Results from the electrofiltration of anatase (TiO2) particles in a water suspension and using three different electrode configurations are presented. The three electrode configurations studied were spot, foil, and mesh. For the first two configurations, the electric field was perpendicular to the direction of flow while for the mesh configuration it was opposite to the direction of flow. The percent gain volume filtrate and power consumption were measured for each electrode configuration. For a given percent gain volume filtrate, it was observed that the foil electrode configuration consumes the least power.

Analysis of drag and particulate stress in porous media flows

Abstract The momentum transfer mechanism between the fluid and solid phases and the practical implications of such a mechanism are investigated for flow through porous media. The continuum-mechanical approach based on the volume averaged equations for multiphase systems is used for the analysis. The results show that the drag between the two phases is equal to the local pressure gradient and that this drag force causes particle movement and not the particulate stress. The pressure gradient identifies regions within the porous media with high drag. Alterations of these regions can change global flow rates in porous media. The resistance function, which is an inverse permeability, has meaning only when it is related to the magnitude of the momentum transfer, or drag, between the phases. If a functionality for the porosity is necessary, then it should depend on the pressure gradient, or, under negligible gravitational effects, the gradient of the particulate or effective intergranular stress.

On the constancy of average porosity in filtration

Abstract To verify the constancy of average cake porosity, constant applied-pressure filtration experiments were conducted under the guidance of a standard 2 3 factorial design. Two types of septa, two levels of slurry concentration and two levels of applied pressure were used. The null hypothesis that there is no influence exerted by the operating factors, i.e. septum, slurry concentration and applied pressure, on the average porosity was tested with an F-distribution and accepted as being true. This indicates that the average porosity remains constant throughout a constant applied-pressure filtration run within a specified statistical significance level.

ANALYSIS OF THE ELECTROFILTRATION MECHANISM BASED ON MULTIPHASE FILTRATION THEORY

A mathematical model based on multiphase filtration theory is developed to describe the electrofiltration process. The model takes both electrophoretic and electroosmotic effects into account. The electrophoretic migration velocity of solid particles is predicted from the model using the filtrate volume time data obtained from electrofiltration experiments.

A WASHING THEORY FOR UNSATURATED FILTER CAKES USING THE CAPILLARY MODEL

A rigorous washing theory is developed using the area averaging technique for unsaturated filter cakes. Limiting cases of the resulting equations are investigated. The assumptions used in the modelling are verified. The mass transfer parameters, which are evaluated by the application of the moment analysis, are shown to be directly proportional with the volumetric flow rate of the wash liquor. Experimental results also indicate that, for a given wash liquor volumetric flow rate, the increase in the cake thickness causes an increase in the mass transfer parameters. It should be noted that the proposed model is applicable for large particle sizes. As particle size becomes finer and the size distribution becomes wider, the model should be modified by including dead void spaces containing pockets of the mother liquor in the filter cake

OPTIMIZATION OF THE LOCATIONS OF SIDE STREAMS IN A FILTER CAKE WASHING PROCESS

A macroscopic model was developed to perform optimization studies for countercurrent, non-equilibrium, displacement filter cake washing on a belt filter with incoming side streams. Each washing stage was assumed to contain a number of perfect mixing cells connected in series. The optimum locations of the side streams, which yielded the minimum exit solute concentration for the washed cake, were evaluated. Three cases were considered: Incoming side stream added to the wash liquor flow, incoming side stream added to the cake flow and incoming side streams added to both flows simultaneously. A parameter study was performed systematically to determine the effect of washing parameters on the optimum side stream locations.

A comment on the concentration polarization build-up in hollow fibers

Abstract In this short note we correct an error by Aimar et al. [J. Membrane Sci., 59 (1991) 81]. Based on the corrected values of σ, the wall concentration and mass transfer coefficient values are recalculated for linear and exponential models.

LOSS COEFFICIENTS IN ENTRANCE REGION FLOWS OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IN ECCENTRIC ANNULI

Abstract Loss coefficients for laminar flow of an incompressible Newtonian and non-Newtonian fluids flowing in an eccentric annulus are calculated by modelling an eccentric annulus as a slit of variable height. While the loss coefficients for a power-law fluid are smaller than those for a Newtonian one, the reverse is true for a Bingham fluid. In the limiting case of a concentric annulus, the results are found to be in good agreement with those reported in the literature.