(742f) Three-Dimensional Simulations of Charged Droplets in Electric Fields and Shear

Fluid interfaces are often charged and these charges play an important role in determining the behaviour of droplets in electric fields and during collisions in flow. We have previously coupled solvers for binary-liquid flow and electrostatic potential as described by the linearized Poisson-Boltzmann equation (Debye-Hückel equation). With this two-dimensional hybrid simulation code, we simulated electroosmotic flow in charged channels, the electrophoresis of a charged droplet, and a collision of two charged droplets. A sample flow field around a drop during electrophoresis is shown in the figure below.

We present an extension of the previous work to three dimensions. To simulate the flow of two immiscible liquids, we use the free-energy lattice Boltzmann method. We employ an iterative method to solve the Debye-Hückel equation. Both the flow and electrostatic potential solvers were implemented on graphics processing units to achieve short simulation times. We present the results of several benchmarks of electroosmotic flow between charged surfaces. A comparison of the computed flow and an analytical solution for the flow between two charged parallel plates in a uniform electric field is shown below. We also simulate the electrophoresis of a charged droplet and collisions of two charged droplets. We compare the results of the two- and three-dimensional simulations as well as the collisions of charged and uncharged droplets. These simulations provide insight into the role of surface charge on the coalescence of charged drops in emulsions.