By Marius Ungarish
Attention is concentrated on a suspension of buoyant debris (or droplets) in acontinuous fluid. within the presence of a strength box, gravitational or centrifugal, and uncovered to dull boundary constraints, a number of interesting flows might be acquired. those motions are crucial ingre- dients within the everyday separation know-how, the place im- provedand new designs will be useful, yet also they are attention-grabbing from a broader, educational perspective. In those respects, the hot investigations on those flows styles, their underlying mechanisms and mathematical modeling - have gathered to an important, proper physique of data. the most aim of this ebook is to summarize - in a scientific, coherent and constant model - the theoretical modern contributions which look primary in figuring out, simulation and improvement of the subject.
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Additional info for Hydrodynamics of Suspensions: Fundamentals of Centrifugal and Gravity Separation
However, we shall avoid "adjustable parameters" (with one minor exception) in our solutions. Needless to say, the "mixture" and the "two-fluid" 22 2. Physico-Mathematical Formulation models are used here under the assumption that they are consistent - and perhaps interchangeable - approaches to the investigation of the physical problems focussed on in this text. We shall come back to this point in Sect. 3, after mastering the details of the formulations, to which we now proceed. 5) dispersed phase continuity, âa ât• .....
Moreover, in many cases considered here a is either constant or a function of t* only in the mixture region, with corresponding 'V 2 a O. The dimensionless (PeR)- 1 'V 2 a may stiU contribute smoothing boundary layers around the kinematic discontinuities of a introduced in Sect. 3, see Davis & Russell (1989). Similar diffusion term and layer remove boundary-conditions difficulties in the flow over a rotating disk problem studied in Sect. 4. In both cases, however, the length scales involved are so small that the validity of the averaging approach may become questionable.
S been invested in setting the "models" in their present form. Therefore, although stiU on the defensive side when it comes to justification and consistency, it is worthwhile to attempt to solve them for real problems - rather than argue about how to improve the formulation. We believe that important information, insight and suggestions for enhancement can be gained by a critica} study of the solutions obtained in the present framework. st in dimensionless form. Let L* and U* typify the length of the container and the velocity of the global motion of the mixture within.