Two touching/self-assembly droplets in uniform Stokes flow: Viscous energy dissipation of the flow in droplets

Abstract

Viscous energy dissipation of the flow in two touching or self-assembly droplets in uniform Stokes flow is investigated in this paper. Based on the Stokes solution, the energy dissipation per unit time of the two droplets is calculated and validated by comparing with the result of one droplet Stokes flow, and then a theoretical model to calculate the energy dissipation is established. The investigation reveals that the energy dissipation per unit time of either droplet increases with the increasing droplet viscosity at constant continuous fluid viscosity and reaches a peak value when the two viscosities are equal. Moreover, the energy dissipation per unit time of either droplet changes with the sizes of both droplets. The total energy dissipation per unit time of the two droplets is less than the sum of the energy dissipation per unit time of the two droplets before their contact or self-assembly, and in particular, it reaches the minimum value which is about 1/6 of the result of one droplet flow when the two droplets’ sizes are equal. Two droplets’ contact or self-assembly will minimize the energy dissipation of droplets, so it can save energy for the flow system. This study proposes a new perspective for droplet self-assembly study and can promote droplet collision and coalescence studies and then bring benefits to relevant applications.