Hydrodynamic mixing in a granular bed with irregular packing
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In investigating longitudinal [1–4] and transverse  mixing in a granular bed described by a cellular model it has so far been assumed that all the cells are identical, while the parameters of the distribution function of the residence time in the individual cell (henceforth called the microdistribution) are strictly fixed. In an actual granular bed with irregular packing the identical cell condition is obviously not satisfied and the microdistribution parameters may be regarded as random quantities. This paper is concerned with an investigation of the effect of the spread of microdistribution parameters on the characteristics of the process of longitudinal and transverse transport of a neutral fluid in a granular bed.
While retaining the general structure of the cellular model , we assume that the gas or liquid passing through the bed flows from the cells on one horizontal level into the cells on the next level downstream, its motion in the transverse direction being random. Obviously, a particle of the fluid passing through the granular bed can then occupy one cell on each horizontal level. Dropping the identical cell condition, we assume that the bed is homogeneous and that the parameters of the cells successively occupied by a fluid particle are statistically independent. This assumption means that cells with different values of the parameters have been “well mixed,” so that inside the bed there are no fluctuations significantly exceeding the cell dimension in extent.
KeywordsMathematical Modeling Distribution Function Mechanical Engineer General Structure Industrial Mathematic
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