Calculating the approach of two spherical droplets located in a Bingham fluid

The experimentally observed process of approach of two identical oil droplets in an alcohol-water solution (matrix) which have identical density and move cyclically in the rest – acceleration – deceleration mode with a cycle time of 0.01 s is mathematically modeled. The imbalance of forces on the boundaries of the droplets at rest is due to the fact that the shear stresses on them cannot exceed the yield strength of the matrix and the normal stresses are determined from the solution of the elastic problem because the intermolecular bonds in the resting matrix make it similar to a solid. The calculation and experimental results are compared, and it is noted that they are in good agreement.