Hydrodynamic Considerations

In continuous and fixed-bed extractors there is a critical throughput rate beyond which flooding will occur. The viscosity of extract usually increases as it moves toward the fitesh solids end of extraction systems. Hence, in crossflow extractors and stationary-basket extractors, progressive changes in recirculation rates may have to be used to compensate for such changes in viscosity. 

In many cases solids progressively soften during extraction. This is particularly true when solids tend to decompose because of solubilization reactions. Flow pressure drop can strongly compact such solids. In such cases, compression permeability measurements sh d be used to determine the flow resistance characteristics of the solid bed. If flow-induced compaction is excessive it may be necessary to reduce bed depth or use a larger than normal flow cross-sectional area. 

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The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is... 

Any hydrodynamic consideration of a drop moving in a liquid field starts with the Navier-Stokes equations of motion, as given in representative books on fluid mechanics (L2, Sll). Using vector notation to conserve space, these equations may be written (B3, B4)... 

Core stream The core stream is the stream-within-a-stream that has been injected into the center of the sheath stream and is maintained there by the hydrodynamic considerations of laminar flow at increasing velocity. The core contains the sample particles that are to be analyzed in the flow cytometer. If the sample is injected too rapidly, the core stream widens and particles may be unequally illuminated. In addition, with a wide core stream, coincidence events are more likely. 

A model for the riser reactor of commercial fluid catalytic cracking units (FCCU) and pilot plants is developed This model is for real reactors and feedstocks and for commercial FCC catalysts. It is based on hydrodynamic considerations and on the kinetics of cracking and deactivation. The microkinetic model used has five lumps with eight kinetic constants for cracking and two for the catalyst deactivation. These 10 kinetic constants have to be previously determined in laboratory tests for the feedstock-catalyst considered. The model predicts quite well the product distribution at the riser exit. It allows the study of the effect of several operational parameters and of riser revampings. 

Hydrodynamic considerations lead to the contention that there are two stable operating points in reactive extrusion - one with a large, fully filled length and a high conversion, and one with a small, fully filled length and a low conversion. Severe... 

To describe emulsion formation two main factors must be considered, namely hydrodynamics and interfacial science. In hydrodynamics, consideration must be given to the type of flow, whether laminar or turbulent, and this depends on the Reynolds number (as wiU be discussed later). 

Adsorption and Capillary Processes in Variably Saturated Porous Media—Pore Scale Hydrostatic and Hydrodynamic Considerations... 

Common conceptual models for liquid distribution and transport in variably saturated porous media often rely on oversimplified representation of media pore space geometry as a bundle of cylindrical capillaries, and on incomplete thermodynamic account of pore scale processes. For example, liquid adsorption due to surface forces and flow in thin films are often ignored. In this study we provide a review of recent progress in modeling liquid retention and interfacial configurations in variably saturated porous media and application of pore scale hydrodynamic considerations for prediction of hydraulic conductivity of unsaturated porous media. 

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