Linear Straining Shear Flow. Arbitrary Peclet Numbers

Linear Straining Shear Flow. Arbitrary Peclet Numbers 

Spherical particle. First, we consider an axisymmetric shear flow, where the dimensional fluid velocity components remote from the particle have the following form in the Cartesian coordinates X, X2, Xy 

For a spherical particle in an axisymmetric shear Stokes flow (Re — 0), numerical results for the mean Sherwood number can be well approximated in the entire range of Peclet numbers by the expression (4.7.9), where the asymptotic value Shpoo must be taken from the first row in Table 4.4. As a result, we obtain the formula 

For an arbitrary straining shear flow (Gkm = Gmk), the mean Sherwood number for a solid sphere can be expressed by the similar formula 

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The solution of hydrodynamic problems for an arbitrary straining linear shear flow (Gkm = Gmk) past a solid particle, drop, or bubble in the Stokes approximation (as Re -> 0) is given in Section 2.5. In the diffusion boundary layer approximation, the corresponding problems of convective mass transfer at high Peclet numbers were considered in [27, 164, 353]. In Table 4.4, the mean Sherwood numbers obtained in these papers are shown. 

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