Multiphase systems dispersion coefficient

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

In Sections II and VI, the stability of multiphase systems was analyzed for unbounded and bounded beds, respectively. In the unbounded case, it was dispersion that was the most important parameter in deciding the stability of the system. An increase in the dispersion coefficient led to a... 

It will be useful to develop an understanding of the relationship between turbulent flow field and dispersion. Measurement techniques need to be developed for the measurement of turbulent flows in multiphase systems. The relationship between eddy diffusion and the dispersion coefficient needs to be brought out over a wide range of particle sizes, setthng velocities, column diameters, column heights, phase velocities, and physical properties. 

For sound process design, we need values of numerous design parameters such as fractional phase holdups, pressure drop, dispersion coefficients (the extent of axial mixing) of all the compounds, heat and mass transfer coefficients across a variety of fluid-fluid and fluid-solid interfaces depending on the type of multiphase system, type of reactor, and the rate-controlling steps. To clarify the scope of the case studies selected, their salient features are next listed. 

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