A surfactant-coated droplet attached to a rough wall subjected to shear flow is investigated using a coupled lattice Boltzmann with the finite difference method, where a contact angle hysteresis model is introduced into the method to characterize the surface roughness. The method is first verified by the equilibrium contact angle of a semi-circular droplet setting on the bottom plane. It is then adopted to explore the surfactant role on the droplet motion and deformation on a rough wall with two representative hysteresis windows. For the hysteresis window of (0°, 180°), i.e., the contact line remains pinned, the addition of surfactants first promotes droplet deformation and then hinders droplet deformation with increasing effective capillary number. However, for the hysteresis window of (70°, 110°), the addition of surfactants always promotes droplet motion and deformation. Finally, the surfactant role on droplet breakup is presented. For the hysteresis window of (0°, 180°), the addition of surfactants hinders droplet breakup. However, for the hysteresis window of (70°, 110°), the addition of surfactants promotes droplet breakup.
A lattice Boltzmann and finite-difference hybrid method is used to simulate the droplet deformation and breakup under the combined action of shear flow and electric field. The hybrid method is first used to validate for the droplet deformation in the combined action of shear flow and electric field. It is then used to simulate the droplet deformation and breakup in two different electric systems. Results of prolate droplets show that the droplet height and deformation both increase with increasing electric capillary number (
C
a
E
). In addition, for the breakup mode of prolate droplets, increasing
C
a
E
makes the long axis of the droplet incline more towards the wall electrodes and droplet breaks up into more daughter droplets. Results of oblate droplets show that the droplet height decreases with increasing
C
a
E
. However, the droplet deformation first decreases and then increases with increasing
C
a
E
, and its minima occurs at
C
a
E
=
0.01
. For the breakup mode of oblate droplets, the droplet deforms into a more oblate shape with a longer neck and finally breakup into more daughter droplets with increasing
C
a
E
.
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