Translational Stokes flow past particle

Translational Stokes Flow Past Particles of Arbitrary Shape... 

Figure 2.1. Translational Stokes flow past a spherical particle...

Translational Stokes Flow Past Ellipsoidal Particles... 

The axisymmetric problem about a translational Stokes flow past an ellipsoidal particle admits an exact closed-form solution. Here we restrict our consideration to a brief summary of the corresponding results presented in [179],... 

For arbitrary Peclet numbers, the mean Sherwood number (corresponding to the characteristic length ae) for a translational Stokes flow past an ellipsoidal particle can be approximated by the formula [94]... 

At low Peclet numbers, for the translational Stokes flow past an arbitrarily shaped body of revolution, formula (4.10.8) coincides with the exact asymptotic expression in the first three terms of the expansion [358], Since (4.10.8) holds identically for a spherical particle at all Peclet numbers, one can expect that for particles whose shape is nearly spherical, the approximate formula (4.10.8) will give good results for low as well as moderate or high Peclet numbers. 

Figure 4.8. Translational Stokes flow past two identical solid particles...

The dependence of the auxiliary Sherwood number Sho on the Peclet number Pe for a translational Stokes flow past a spherical particle or a drop is determined by the right-hand sides of (4.6.8) and (4.6.17). In the case of a linear shear Stokes flow, the values of Sho are shown in the fourth column in Table 4.4. 

The following general statement was proved in [63] for the case of a uniform translational Stokes flow (Re -4 0) or a potential flow past a particle of an arbitrary shape the mean Sherwood number remains the same if the flow direction is changed to the opposite. 

Here, we consider Stokes problem of uniform, streaming motion in the positive z direction, past a stationary solid sphere. The problem corresponds to the schematic representation shown in Fig. 7-11 when the body is spherical. This problem may also be viewed as that of a solid spherical particle that is translating in the negative z direction through an unbounded stationary fluid under the action of some external force. From a frame of reference whose origin is fixed at the center of the sphere, the latter problem is clearly identical with the problem pictured in Fig. 7-11. Because we have already derived the form for the stream-function under the assumption of a uniform flow at infinity, we adopt the latter frame of reference. The problem then reduces to applying boundary conditions at the surface of the sphere to determine the constants C and Dn in the general equation (7-149). The boundary conditions on the surface of a solid sphere are the kinematic condition and the no-slip condition,... 

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