A computational study of pair-wise interactions between drops and the dynamics of concentrated emulsion is undertaken using a three-dimensional front-tracking finite difference method. The study is motivated by numerous industrial and domestic applications of multi-fluid flow.

We first investigate the effects of inertia on pair-wise interaction between drops in a Newtonian system. It is seen that at high Re, increase in the initial cross-stream separation between the two interacting drops slightly increases the drops deformation. In addition, it is observed that if the separation position of the two interacting drops along the flow direction is so small that the drops can slide past each other even at high Re, increase in Re leads to an increase in the drops' lateral displacement after separation. However, if the separation position of the two interacting drops is more than twice the undeformed radius of the drops, the drops may not be able to slide past each other if Re is sufficiently large. The deformability of the drops also affects their lateral displacement. We observe that deformable drops are not able to slide past each other under the same conditions where drops with very low Ca can slide past each other. It appears that the flow modification caused by the drops deformation creates a downward force on the left drop.

Next, we examine the effects of inertia on drop dynamics in a concentrated emulsion. We observe that the effects of inertia on weak hydrodynamic interaction at low dispersed phase volume fraction do not result in increased volume-averaged drop deformation. However, for concentrated emulsions, interaction between drops at increased Re leads to an increase in volume-averaged drop deformation especially when Ca of the drops is low. A single drop tends to rotate towards the vertical direction at increased Re. However, interactions between drops suppress this tendency.

Finally, we investigate the effects of viscoelasticity on interactions between drops. We notice that the interaction between viscoelastic drops is similar to that between Newtonian drops. However, we observe that the interaction in the case of Newtonian drops in a viscoelastic matrix is different from that of Newtonian fluids. Viscoelastic stresses in the matrix-phase viscoelastic system inhibit the drops' lateral displacement and cause the drops to align more with the flow direction. Similar to what has been observed in single-drop deformation, the De of the matrix-phase viscoelasticity has non-monotonic effects on the drops' deformation when the drops are aligned with each other along the compressional quadrant of the shear flow.