| Abstract: | Problems of diffusion to particles of nonspherical shape at large Peclet numbers have been analyzed in many papers (see 1–7], for example). The solution of the problem of mass exchange of an ellipsoidal bubble at low Reynolds numbers was obtained in 1] while the solution at high Reynolds numbers was obtained in 2, 3]. In 4] an expression is given for the diffusional flux to the surface of a solid ellipsoidal particle over which a uniform Stokes stream flows. Generalization to the case of particles of arbitrary shape was done in 5, 6], while generalization to any number of critical lines on the surface of the body was done in 7, 8]. The two-dimensional problem of steady convective diffusion to the surface of a body of arbitrary shape is analyzed in the approximation of a diffusional boundary layer (ADBL). The simple analytical expressions obtained are more suitable for practical calculations than those in 5-8], since they allow one to determine at once, in the same coordinate system in which the field of flow over the particle was analyzed, the value of the diffusional flux to its surface (from the corresponding hydrodynamic characteristics). The plane problem of the diffusion to an elliptical cylinder in a uniform Stokes stream is solved. The problems of the diffusion to a plate of finite dimensions (in the plane case) and a disk (in the axisymmetric case) whose planes are normal to the direction of the incident stream are considered. It is shown that, in contrast to the results known earlier (see 4, 6-15], for example), where the total diffusional flux was proportional to the cube root of the Peclet number, here it is proportional to the one-fourth power.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 104–109, November–December, 1978.The authors thank Yu. P. Gupalo, Yu. S. Ryazantsev, and Yu. A. Sergeev for a useful discussion. |
