Hydrodynamic Relations

Based on the two-phase model of fluidization, the following basic relations hold  

The superficial velocity at minimum fluidizing conditions is given by the correlation 

The mass- and heat-transfer coefficients between the bubble and dense phases are connected via the following relations  

The above relations and parameter values are all taken from the literature. 

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Existing statistical methods permit prediction of macroscopic results of the processes without complete description of the microscopic phenomena. They are helpful in establishing the hydrodynamic relations of liquid flow through porous bodies, the evaluation of filtration quality with pore clogging, description of particle distributions and in obtaining geometrical parameters of random layers of solid particles. 

Rotation remains the best candidate for extra-mixing in RGB stars. The present modelling of the rotational mixing is however still incomplete, and agreement between self-consistent models and observations might be achieved by improving the description of the hydrodynamics related to rotation. 

Accdg to Schmidt (Ref 1, as quoted from rdsumd in CA) "That the detonation velocity (D) of explosives increases regularly with the density (d) follows directly from hydrodynamic relations when the thermodynamic.behavior of very dense gases is considered. D increases in proportion as the gas vol (v) is decreased by the covol (a) ... 

By substituting (7.102) into equation (7.101) and using the known previous hydrodynamic relations, equation (7.101) becomes... 

A qualitative verification of this hot-model hydrodynamics relates with a seesaw phenomenon. For this phenomenon, Grace et al. have... 

In the steady state simulation and design, the state variables are the flowrates and the pressure drops or terminal pressures for each branch of the net. Each of the branches between two nodepoints are described by a mathematical model of the hydrodynamics relating the pressure drop to the fluid flow between the nodes. The material balance sums up the flow into and out of a node no is... 

The rotational diffusivity dyadic is origin-independent. These origin-displacement theorems are the counterparts of the comparable hydrodynamic relations set forth in Eqs. (51) and (52). 

Also, Valerius et al. [28, 29] show by exact formulation that the balance of the solid-phase (catalyst) actually is a balance of the liquid phase and/or gas phase in the catalyst pellet. Nevertheless, this text will follow the international trend and designate the trickle-bed reactor balance equations for the gas/liquid phase in the catalyst grain as balance for the solid phase or catalyst . The complex hydrodynamic relations in trickle-bed reactors together with the various assumptions or neglects result in widely different structured mathematical models. Two basic types of models, the differential models and the cascade or cell models, are most frequently used in the literature. 

The preceding survey suggests that the binary mixture of GB fluid has not been studied so far by simulation or numerical methods although, as already mentioned, this is important because real systems are more likely to possess either size, shape, or interaction asymmetry, or any combination of them. The veriflcation of hydrodynamic relations is important for uncovering the nature of solute-solvent interactions in these more complex but model systems. This will certainly help to understand the composition dependence of the binary mixture of GB fluids. One expects in these studies a high degree of nonlinearity in composition dependence because asymmetric interaction-induced nonideal solution behavior has been observed for LJ mixtures of size-symmetric particles [22,23]. 

Fig. 5.7 Weight-average molar mass (Af ) dependence of ratio of two hydrodynamics-related radii (average viscometric radius, and average hydrodynamic radius,...

The Stokes-Einstein(SE) relation is one of hydrodynamic relations for transport properties. In normal liquids, the relation... 

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