Dynamic hysteresis of an oscillating contact line

The behavior of contact line is conventionally described by the single-valued dependence between the dynamic contact angle θ_d  and contact line velocity U_CL. However, by experimentally investigating the mobile contact line of a sessile droplet supported by a vertically vibrating substrate, a distinct multivalued contact line relation is found on fluorosilane coated surface.

To understand the cause of the multivaluedness, we first evaluate the dynamic contact line (DCL) friction coefficient μ_f, which is quantified by balancing the work done by the unbalanced Young's force and the frictional dissipation on DCL. Using this metric, we gauge μ_f of different systems. It is found that both surface coating (molecule species, chain length) and liquid properties (viscosity) have impact on the DCL friction. The results suggest that μ_f is a complex phenomenological parameter, which incorporates the dissipative effects from both molecular interaction and viscous resistance in the vicinity of DCL. Moreover, instead of being a constant, μ_f is found to increase dramatically as DCL decelerates, indicating the transition between dynamic and static friction regimes.

Finally, the multivaluedness in the contact line relation is attributed to the asymmetry in μ_f  distribution between approaching and leaving the turning points. To validate this relevance, we incorporate dynamical μ_f model in the DCL mobility relation in volume of fluid simulation, expecting to reproduce the multivaluedness in the numerical solution.