Abstract
The problem of drop deformation and breakup in shear flow represents academic and practical interest and has attracted close attention over the intervening decades. Drop breakup is important for a wide range of engineering and biomedical applications including production and processing of emulsions, aerosols, etc. Although drop breakup operations are widely used in various industries, however, till quite presently there is no unequivocal treatment of the physical mechanism, which causes the fragmentation of dispersions in shear flows. In this paper the principles of constructing a mathematical model, which predicts the evolution of initially spherical droplet in shear flows of viscous liquid over a wide range of flow regimes as well physical parameters of both liquid phases, are considered. A mathematical model is presented that describes the deformation of a single drop suspended in another immiscible liquid under the combined action of three forces, namely, hydrodynamic force, capillary force and dissipative viscous force. The influence of each of these forces on the process of droplet deformation is discussed in the paper.
 The focus of the study is to more deeply analyze the dynamics of droplet deformation in shear flows and the transitional effects associated with current droplet shapes. Particular attention is paid to the analysis of critical conditions for the onset of irreversible deformation of droplets, which leads to their destruction. The deformed droplet is assumed to be in the form of prolate ellipsoid of revolution. The drop deformation is regarded as motion of the centers mass of the half-drops, symmetrical with respect to the drop center.
 The results of numerical calculations for droplet deformation in shear flows in comparison with experimental data of other authors are presented. A simple criterion for destruction of droplets in shear flows has been obtained. The results of the analysis confirm the reliability of the model and the competency of the assumption made. The model is able to predict the nature of droplet deformation and the conditions for their destruction in shear flows with known operating parameters with a greater degree of accuracy than the existing empirical relationships.
Highlights
Представлена математическая модель, описывающая деформацию капли, находящуюся в сдвиговом потоке другой несмешивающейся с ней жидкости
A mathematical model is presented that describes the deformation of a spherical fluid drop located in a shear flow of another liquid immiscible with it
It is shown that the model makes it possible to predict the behavior of deformed drops in shear flows in a wide range of flow regimes and physical parameters of both liquid phases
Summary
Представлена математическая модель, описывающая деформацию капли, находящуюся в сдвиговом потоке другой несмешивающейся с ней жидкости. A mathematical model is presented that describes the deformation of a spherical fluid drop located in a shear flow of another liquid immiscible with it. Ці положення використовуються при розробці моделі поведінки крапель в зсувних потоках.
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