Mass transfer plane shear flow

To describe the solution of the mass transfer problem for an arbitrary plane shear flow at high Peclet numbers, we introduce dimensionless quantities by the formulas ... 

Instead of polarized noble gases, thermally polarized NMR microimaging was used to study of liquid and gas flow in monolithic catalysts. Two-dimensional spatial maps of flow velocity distributions for acetylene, propane, and butane flowing along the transport channels of shaped monolithic alumina catalysts were obtained at 7 T by NMR, with true in-plane resolution of 400 xm and reasonable detection times. The flow maps reveal the highly nonuniform spatial distribution of shear rates within the monolith channels of square cross-section, the kind of information essential for evaluation and improvement of the efficiency of mass transfer in shaped catalysts. The water flow imaging, for comparison, demonstrates the transformation of a transient flow pattern observed closer to the inflow edge of a monolith into a fully developed one further downstream. 

Let us investigate convective mass transfer to the surface of a solid sphere freely suspended in an arbitrary plane shear Stokes flow. In this case, the fluid velocity distribution remote from the particle is given by formulas (4.5.1) with... 

In Chapters 3 and 4 we analyze mass and heat transfer in plane channels, tubes, and fluid films. We consider the mass and heat exchange between particles, drops, or bubbles and uniform or shear flows at various Peclet and Reynolds numbers. The results presented are of great importance in obtaining scientifically justified methods for a number of technological processes such as dissolution, drying, adsorption, aerosol and colloid sedimentation, heterogeneous catalytic reactions, absorption, extraction, and rectification. 

Velocity fluctuations can also cause extra apparent shear stress components. An element of fluid with a non-zero velocity component in the x-direction possesses an x-component of momentum. If this element of fluid also has a non-zero velocity component in the y-direction then as it moves in the y-direction it carries with it the x-component of momentum. The mass flow rate across a plane of area 8x8z normal to the y-coordinate direction is pvy8x8z and the x-component of momentum per unit mass is vx, so the rate of transfer of x-momentum in they-direction is given by the expression... 

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