Download Mathematical Models and Design Methods in Solid-Liquid by A. Rushton (auth.), A. Rushton (eds.) PDF

By A. Rushton (auth.), A. Rushton (eds.)

The separation of finely-divided solids from beverages constitutes an incredible degree in lots of commercial tactics. Separation of combinations starting from hugely focused slurries to somewhat turbid drinks needs to be effected in situations the place the solids, liquid or either stages can have price. Separations can be completed through use of a membrane or clear out medium which, located within the direction of a flowing suspension, will let passage of the fluid while conserving solids at the floor or in the medium. on the other hand the 2 stages can be separated by way of sedimentation approaches regarding gravitational or centrifugal strength. In both mode, separation problems are often skilled with the outcome that solid-liquid separation is usually a bottleneck in advertisement crops. Operational problems and plant mess ups are linked to the random nature of the debris being separated; adaptations in dimension, form, states of aggregation, compressibility, and so on. , produce quite a lot of difficulties. Plugging of the clear out medium or the cave in of the solids lower than utilized rigidity bring about sluggish flowrates of liquid. The colloidal nature of a few precipitates makes separation by means of settling nearly most unlikely with out using chemical brokers to reinforce the dimensions of simple devices and to lessen repulsive floor forces. Unit operations corresponding to filtration, comminution, and so on. , contain a possible bewildering array of machines which makes plant choice a tricky step and displays the uncer­ tainties attaching to operations related to the cast )hase. many varieties of strain, vacuum and centrifugal clear out are available.

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Mathematical Models and Design Methods in Solid-Liquid Separation

The separation of finely-divided solids from beverages constitutes a major level in lots of commercial tactics. Separation of combinations starting from hugely centred slurries to a little turbid beverages needs to be effected in conditions the place the solids, liquid or either stages can have worth. Separations should be completed via use of a membrane or filter out medium which, situated within the course of a flowing suspension, will let passage of the fluid when maintaining solids at the floor or in the medium.

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Tiller, F. , "Revision of kynch sedimentation theory," accepted by AIChE J. (1981). 8. Wakeman, R. , "Numerical integration of the differential equations describing the formation of and flow in compressible filter cakes," Trans. I. Chern. , 56, 258-265 (1978) . 9. , O. Davies, R. Chow and F. M. Tiller, "Clogging phenomena in filtration of liquefied coal," accepted by Chern. Engr. Progr. (1981). 25 FLOW THROUGH POROUS MEDIA AND FLUID-PARTICLE HYDRODYNAMICS Lloyd A. Spielman Departments of Civil and Chemical Engineering University of Delaware, Newark, Delaware CONTENTS Introduction Stokes Eq1Jations General Linearity and Superposition Quasistatic Property Dimensional Analysis and Scaling Packed Bed Hydrodynamics Relationship of Stokes Flow to Darcy's Law Kozeny-Carman Theory Flow through Assemblages of Spheres Particle-Collector Interactions Nomenclat1Jre a a p sphere radius m particle radius m 26 a spherical grain radius s A m porosity function for Happel's model (dimensionless) s b cell radius Fl (H).

If a given flow field satisfies Eqs. (4) and (2). then so must that corresponding to reversal of the velocities and pressure gradient. Eqa. (i) through (vi) then imply that all drag forces exerted by the flow field are Simply reversed also. Quasistatic Property ADother convenient property of Eqs. (4) and (2). which is not in general possessed by Eqs. (l) and (2). is that the former are quasistatic. That is, their time varying flows may be viewed as a smooth sequence of instantaneous steady state flows.

Straightforward reasoning shows that the overall pressure difference ~P should be directly proportional to the bed depth Ax. This is because llP times the bed cross sectional area measures the net force on the opposite faces of the bed and must be equal to the total drag force exerted over all the microscopic surface inside the bed, since it is equal and opposite to the total force necessary to hold the bed fixed. It therefore follows that doubling the bed depth, 6x, will double the pressure drop, because it doubles the aJIlOunt of porous solid over which the internal drag force is exerted, hence 6P must be directly proportional to 6x.

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