Transfer in Linear Shear Flows at Low Peclet Numbers

Mass Transfer in Linear Shear Flows at Low Peclet Numbers 

Mass transfer to a particle in a translational flow, considered in Section 4.4, is a good model for many actual processes in disperse systems in which the velocity of the translational motion of particles relative to fluid plays the main role in convective transfer and the gradient of the nonperturbed velocity field can be neglected. 

In Section 1.1 we briefly described the velocity field for some cases of gradient flows with nonuniform structure. For particles whose size is much less than the characteristic scale of spatial nonuniformity of the flow, the velocity distribution (1.1.15) can be used as the velocity distribution remote from the particle in problems about mass transfer to a particle in a linear shear flow. 

In practice, one often deals with the case in which particles are completely entrained by the flow and convective transfer due to the shear flow plays the main role. In studying the corresponding diffusion processes, it is convenient to attach the frame of reference to the particle center of gravity then this frame moves translationally at the particle velocity, and the particle itself can freely rotate around the origin. For linear shear flow, the fluid velocity components have the form 

For a spherical particle in an arbitrary linear shear flow (4.5.1), the first four terms of the asymptotic expansion as Pe - 0 of the mean Sherwood number have the form [5] 

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