Drops Moving in Gas at High Reynolds Numbers

The dependence of drop deformation on the Weber number and the vorticity inside the drop was studied in [336]. It was shown that the drop is close in shape to an oblate ellipsoid of revolution with semiaxis ratio 1 If there is no vortex inside the drop, then this dependence complies with the function We(x) given in (2.8.3). The ratio x decreases as the intensity of the internal vortex increases. Therefore, the deformation of drops moving in gas is significantly smaller than that of bubbles at the same Weber number We. The vorticity inside an ellipsoidal drop, just as that of the Hill vortex, is proportional to the distance TZ from the symmetry axis, 

The steady-state velocity of fall in gas (for example, of a rain drop in air) can be calculated by 

Formulas (2.8.12)—(2.8.14) together with the dependence x(We, A) completely determine the motion of a drop in gas. A condition related to the exponential growth of the oscillation amplitude under which the failure of a drop starts, was obtained in [336]. For a rain drop, this condition approximately corresponds to the values X - f We = 5, and ae = 3.8 mm. 

Under strong deformations, drops split into smaller ones, that is, are destroyed. The destruction process for drops is very complicated and is determined by surface tension, viscosity, inertia forces and some other factors. For various characteristic velocities of the relative phase motion, the character of destruction may be essentially different. A comparative analysis of many experimental and theoretical studies of drop destruction was given in [154, 312]. It was pointed out that there are six basic mechanisms of drop destruction, which correspond to different ranges of the Weber number. 

The motion of a particle in infinite fluid creates some velocity and pressure fields. Neighboring particles move in already perturbed hydrodynamic fields. Simultaneously, the first particle itself experiences hydrodynamic interaction with the neighboring particles and neighboring moving or fixed surfaces. Since in the majority of actual disperse systems, the existence of an ensemble of particles and the apparatus walls is inevitable, the consideration of the hydrodynamic interaction between these objects is very important. One of the methods for obtaining the required information about the interaction is based on the construction of exact closed-form solutions. However, even within the framework of Stokes hydrodynamics, to describe the motion of an ensemble of particles is a very complicated problem, which admits an exact closed-form solution only in exceptional cases. 

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