The role of surface tension gradient in determining microscopic dynamic contact angle

Following Gibb's interpretation of an interface as a dividing surface, we derive a model for the microscopic dynamic contact angle by writing a force balance for a control volume encompassing the interfaces and the contact line. In doing so we identify that, in addition to the surface tension of respective interfaces, the gradient of surface tension plays an important role in determining the dynamic contact angle. This is because not only does it contribute towards an additional force, but it also accounts for the deviation of local surface tension from its static equilibrium value. It is shown that this gradient in surface tension can be attributed to the convective acceleration in the vicinity of the contact line, which in turn is a direct result of varying degree of slip in that region. In addition, we provide evidence that this gradient in surface tension is one of the key factors responsible for the difference in contact angle at the leading and trailing edge, of a steadily moving contact line. These findings are validated using molecular dynamics simulations.