Dynamics of imbibition into a pore with a heterogeneous surface

We use large-scale molecular dynamics simulations to study the dynamics of liquid penetration into a cylindrical pore having a randomly heterogeneous surface comprising areas of differing wettability. Our results confirm that the equilibrium contact angle in the heterogeneous pore is well described by Cassie's law. As in the case of the uniform pore studied previously, the dynamics of penetration can be described by the Lucas-Washburn equation corrected to include the effect of a dynamic contact angle. The dissipation at the three-phase line, which gives rise to the dynamic contact angle, may be characterized in terms of a friction coefficient. Interestingly, the wetting-line friction on the heterogeneous surface also turns out to be a linear function of the fractional concentration of the areas of different wettability, analogous to Cassie's law. These results can be interpreted in terms of an independent random walk mechanism.