Dynamics of the Deformable Fluid Interface Interacting with an Approaching Solid under the Electrostatic Field

A theoretical model was developed to describe the dynamics of a deformable fluid interface interacting with an approaching solid without contact by both the attractive electrostatic and van der Waals (i.e., vdW) interaction, analogous to the situation in the experiments by electric force microscopy (i.e., EFM) or electric-surface force apparatus (i.e., E-SFA) involved in the soft fluid interface. On the basis of this model, a numerical study of the deformation of the fluid interface, the force-vs-separation behavior, and the critical limiting conditions of contact has systematically been carried out. Our results show that the surface pressure induced by the electrostatic interaction plays a more prominent role in the deformation of the fluid interface than the vdW interaction does, and there exists a principal length scale associated with the relative strength of the electrostatic field to the surface tension, affecting the fluid interface shape under the electrostatic field. It was also shown that both the force-distance curves and the corresponding curves of fluid interface deformation peak versus distance for various electrostatic fields satisfy the universal scaling power law. Moreover, an analytical solution to the Euler-Lagrange differential equation governing the deformation of the fluid interface under the external electric field is obtained, and two extended formulas for explicitly describing the principal length scales that respectively characterize the lateral and longitudinal deformations of the fluid interface were determined.