Translational Stokes flow past drop

Figure 2.2. Translational Stokes flow past a spherical drop...

For the special case of a translational Stokes flow past a spherical drop, Eq. (4.7.11) passes into (4.7.4). 

In the case of nonstationary mass transfer in a steady-state translational Stokes flow past a spherical drop with limiting resistance of the continuous phase, the steady-state value Shst is presented in the first row of Table 4.7. By substituting this value into (4.12.3), we obtain... 

At high Peclet numbers, for an nth-order surface reaction withn=l/2, 1,2, Eq. (5.1.5) was tested in the entire range of the parameter ks by comparing its root with the results of numerical solution of appropriate integral equations for the surface concentration (derived in the diffusion boundary layer approximation) in the case of a translational Stokes flow past a sphere, a circular cylinder, a drop, or a bubble [166, 171, 364], The comparison results for a second-order surface reaction (n = 2) are shown in Figure 5.1 (for n = 1/2 and n = 1, the accuracy of Eq. (5.1.5) is higher than for n = 2). Curve 1 (solid line) corresponds to a second-order reaction (n = 2). One can see that, the maximum inaccuracy is observed for 0.5 < fcs/Shoo < 5.0 and does not exceed 6% for a solid sphere (curve 2), 8% for a circular cylinder (curve 3), and 12% for a spherical bubble (curve 4). 

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. 

For a first-order volume reaction and a translational Stokes flow past a spherical drop, the asymptotic solution of the inner problem (5.3.1), (5.3.2) as Pe -4 oo results in the following expression for the mean Sherwood number [104] ... 

To emphasize the role of a chemical reaction, such thermocapillary effects will be called chemo-thermocapillary. The problem on the steady-state translational Stokes flow past a drop is conventionally divided into three parts. 

Let a be the outer radius of the compound drop, and let ae be the radius of the core (0 < e < 1). The exact solution of the problem on the flow past a compound drop in a translational Stokes flow with velocity U can be found in [416], where the stream functions in the phases are given. The drag force is also... 

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