Geometry effects on the interaction of two equal-sized drops in simple shear flow at finite Reynolds numbers

Abstract

The effect of geometry on the interaction of two equal-sized drops in shear flow is presented. The full Navier-Stokes equations are solved by a finite difference/front tracking method. The interaction of drops was studied at finite Reynolds numbers for viscosity ratio (λ) of one. The distance between drop centres along the velocity gradient direction (z) was measured as a function of time. The interaction of two drops contains approach, collision, and separation. Based on experimental data, we simulated different geometries by changing the offset and size of drops. It was found that ∆z increases after collision and reaches ∆z, during three stages of interaction, increases with the increasing initial offset. To investigate the drop shape evolution, we calculated the deformation and the orientation angle formed by the drop major axis and horizontal direction. The deformation of the drops is maximum when the drops are pressed against each other and minimum when they are drawn a part. Our results show that the time of approaching of drops at low initial offset is greater than the other ones, but the maximum deformation is the same for equal drop sizes. The deformation decreases with the decreasing size of drops. As the initial offset increases, the drops rotate more quickly and the available contact time for film drainage decreases. We found that the trajectories of drops in the approaching stage are different owing to the different initial offsets. However, after the drops come into contact, it can be seen that they follow the same trajectories, similar to experimental results.