Particles, Drops, and Bubbles in Fluid

Solving the problem on the interaction of a solid particle, drop, or bubble with the surrounding continuous phase underlies the design and analysis of many technological processes. The industrial applications of such interaction include classification of suspensions in hydrocyclones, sedimentation of colloids, pneumatic conveyers, fluidization, heterogeneous catalysis in suspension, dissolving solid particles, extraction from drops, absorption, and evaporation into bubbles [69, 107, 111, 122,137,478,505], 

The description of a large variety of meteorological phenomena is also based on the analysis of motion of a collection of drops in air. The recent increase in atmosphere pollution is a serious problem, which requires understanding the transfer of mechanical, chemical, and radioactive particles in the atmosphere. 

In rarefied systems of particles, drops, or bubbles, the particle-particle interaction can be neglected in the first approximation then one deals with the behavior of a single particle moving in fluid. In this case, the streamline pattern depends on the particle shape, the flow type (translational or shear), and a number of other geometric factors. 

One of the main methods for obtaining approximate closed-form solutions of the corresponding hydrodynamic problems is to linearize the Navier-Stokes equations for low Reynolds numbers. This method is often used in this chapter when we study the motion of small particles, drops, and bubbles in a fluid. 

A number of physical and mathematical statements of problems on motion of particles, drops, and bubbles in fluid, as well as various formulas and experimental data, can be found, for example, in [94, 179, 183, 255, 270, 287, 517], 

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