Interplay of density ratio, viscosity ratio, and initial offset on the coalescence of droplet pairs in confined shear flow.

The hydrodynamic collision between droplet pairs dispersed in another continuous fluid matrix is critical to diverse engineering and real-life applications. Simulating such phenomena is more challenging due to the impact of small-scale interactions that determine large-scale behavior. We investigate the effect of density ratios (60 to 800), viscosity ratios (12 to 60), and the initial offset between two droplets on the collision mode in confined shear flow through simulation based on the free-energy binary-liquid lattice Boltzmann method. For all the case studies performed, Reynolds number and Capillary number were kept 1.0 and 0.01, respectively. There has been found both upper and lower critical initial offset which lead to three different modes of collision, namely reverse-back, coalescence, and pass-over. Our results further reveal that the effect of density and viscosity ratios is significant on such collision modes. Near the critical initial offset, competition between inertia and shear forces causes to show unusual revolution of each droplet around the other and eventual coalescence, as we vary density and viscosity ratios. The effect of all these parameters along with the confinement ratio considered in this study will be discussed in detail.