Flow-Induced Coalescence: Evaluation of Some Approximations

Collision efficiency, Pc, is one of the crucial quantitative characteristics of flow-induced coalescence, which consists in collisions of droplets dispersed in a flowing matrix followed by their fusion. The basic step of Pc estimation is the calculation of droplet pair trajectories from all possible start positions to find whether droplets fuse when they are in a given start position. The trajectories can be calculated by exact solution of equations expressing the change of all coordinates with time for Newtonian systems. Since involving of viscoelastic properties into this exact description appeared difficult, we used simplifications and approximations. However, the approximations were too gross and lead to inconsistencies for some systems. To find such approximations level that avoids inconsistencies but still allows us to reach the solution, we decided to evaluate and demonstrate effects of individual approximations. Comparison made on a Newtonian system has shown that neglecting of parameters dependence on viscosity ratio and droplet size ratio has not critical consequences for spherical droplets. However, the abandonment of the switch between free-flow and near-approach approximations, and involving of the reliable description of hydrodynamic interaction for broader range of inter-droplet distances should be considered.