Mass transfer nonspherical particle

In this chapter, we extend the discussion of the previous chapter to nonspherical shapes. Only solid particles are considered and the discussion is limited to low Reynolds number flows. The flow pattern and heat and mass transfer for a nonspherical particle depend on its orientation. This introduces complications not present for spherical particles. For example, the net drag force is parallel to the direction of motion only if the particle has special shape properties or is aligned in specific orientations. 

Very few solutions have been obtained for heat or mass transfer to nonspherical solid particles in low Reynolds number flow. For Re = 0 the species continuity equation has been solved for a number of axisymmetric shapes, while for creeping flow only spheroids have been studied. 

A review of the theoretical analysis at high Peclet number is given by Yaron and Gal-Or,147 Although all these studies were carried out for spherical particles, Lochiel and Calderbank77 have shown that they can be extended to nonspherical particles, if the particle diameter in the relation is replaced by a diameter corresponding to a sphere having the same ratio of external surface to volume as the nonspherical particle. It should be noted that Eq. (9-51) can be applied to mass transfer from a sphere falling at terminal velocity. The Peclet number in this case is defined as... 

Mass Transfer Between Nonspherical Particles or Bubbles and Flow 185... 

The dependence (4.12.3) can also be used to estimate the intensity of transient mass transfer for nonspherical particles, drops, and bubbles at Pe 1. In this case, all dimensionless variables r, Sh, Shst, and Pe must be defined on the basis of the same characteristic length a. Under this condition, the expression (4.12.3) provides valid asymptotic results for small as well as large times. Equation (4.12.3) can be rewritten as follows ... 

Here Sho is the Sherwood number corresponding to mass transfer of a particle in a stagnant medium without the reaction. Each summand in (5.3.6) must be reduced to a dimensionless form on the basis of the same characteristic length. The value of Sho can be determined by the formula Sho = all/S , where a is the value chosen as the length scale and, is the surface area of the particle the shape factor II is shown in Table 4.2 for some nonspherical particles. 

Equation (170) applies to low flux mass transfer between liquid and fluidized spheres, all of which and the total surface of which are contributing to the mass transfer. For nonspherical particles, Limas-Ballesteros et al. (1982b) found that with both Shp and Ar based... 

Grashof number for mass transfer L is a characteristic dimension, i.e., the diameter of a spherical particle, or the equivalent diameter of a nonspherical particle, etc. v is the kinematic viscosity D is the binary diffusion coefficient U is the linear velocity of the gas stream flowing past the particle (measured outside the boundary layer surrounding the particle) g is the acceleration due to gravity is a characteristic concentration difference, and... 

Application To develop more robust models and efficient computer codes by using advanced computer techniques so that the capability of particle scale simulation can be extended, say, from two- to three-dimensional and/or from simple spherical to complicated nonspherical particle system involving not only multiphase flow but also heat and mass transfer and chemical reactions, which is important to transfer the present phenomenon simulation to process simulation and hence meet real engineering needs. 

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