Calculation of motion of a spherical drop in the Bingham medium

Mathematical modeling of the experimentally observed process of approaching of two identical oil drops located in an alcohol-water solution (matrix) with an identical density is performed. It is found that the drop moves in cycles consisting of the state at rest, acceleration, and deceleration; the cycle time is about 10$^{-2}$ s. Violation of the balance of forces on the drop boundary in the state at rest is caused by the fact that the shear stresses on this boundary cannot exceed the yield stress of the matrix, and the normal stresses are determined by solving the problem of the elasticity theory, because intermolecular bonds in the quiescent matrix make it similar to a solid. The results of drop motion calculations and experimental data agree well during the entire process of drop approaching, except for the final stage, which can be attributed to the neglect of hydrodynamic interaction of the drops.