Modeling the deformation of a surfactant-covered droplet under the combined influence of electric field and shear flow

A surfactant-covered droplet subject to both electric field and shear flow is studied using a lattice Boltzmann and finite difference hybrid method, which breaks the limitation of asymptotic approaches that allow only small droplet deformation. It is found that in the electric system where electric field induces circulating flows directed from equator to poles, the presence of surfactants promotes droplet deformation for each electric capillary number (CaE), whereas in the electric system where droplets exhibit a prolate shape and circulating flows are directed from poles to equator, the presence of surfactants hinders droplet deformation at high CaE. We also for the first time show that in the electric system where droplet exhibits an oblate shape, the presence of surfactants almost has no effect on droplet deformation at high CaE. Regardless of electric properties and CaE, the inclination angle of surfactant-covered droplets is always smaller than that of clean droplets.