Taking a closer look: A molecular-dynamics investigation of microscopic and apparent dynamic contact angles

Molecular dynamics (MD) may be used to investigate the velocity dependence of both the microscopic and apparent dynamic contact angles (θ_m and θ_app).

We use large-scale MD to explore the steady displacement of a water-like liquid bridge between two molecularly-smooth solid plates under the influence of an external force F⁰. A coarse-grained model of water reduces the computational demand and the solid-liquid affinity is varied to adjust the equilibrium contact angle θ⁰. Protocols are devised to measure θ_m and θ_app as a function of contact-line velocity U_cl.

For all θ⁰, θ_m is velocity-dependent and consistent with the molecular-kinetic theory of dynamic wetting (MKT). However, θ_app diverges from θ_m as F⁰ is increased, especially at the receding meniscus. The behavior of θ_app follows that predicted by Voinov: (θ_app)³ = (θ_m)³ + 9Ca·ln(L/L_m), where Ca is the capillary number and L and L_m are suitably-chosen macroscopic and microscopic length scales. For each θ⁰, there is a critical velocity U_crit and contact angle θ_crit at which θ_app→0 and the receding meniscus deposits a liquid film. Setting θ_app=0, θ_m=θ_crit and U_cl=U_crit in the Voinov equation yields the value of L/L_m. The predicted values of θ_app then agree well with those measured from the simulations. Since θ_m obeys the MKT, we have, therefore, demonstrated the utility of the combined model of dynamic wetting proposed by Petrov and Petrov.