Effect of substrate flexibility on non-Newtonian droplet impact dynamics on flexible superhydrophobic surfaces

Non-Newtonian drops are known to suppress rebounds off rigid horizontal superhydrophobic substrates (SHS). The arrest of drop rebound on SHS, known as the Cassie to Wenzel transition (CWT) or impalement, occurs due to several factors such as normal stress, enhanced extensional viscosity and increased adsorption of polymers. In the case of a rigid surface, drop deposition occurs when the two conditions of rigid substrate (the ratio of dynamic pressure (P_D) to capillary pressure (P_C) exceeding one i.e., P_D/P_C > 1 and Weissenberg number Wi > 1) are satisfied [34]. On the other hand, flexible substrates exhibit an interesting coupled dynamics of drop impact and substrate oscillations. We envisage that flexible substrates will have an additional feature i.e. substrate stiffness to influence the rebound suppression mechanism.

We have performed drop impact experiments with aqueous solution of polyacrylamide droplets on cantilever beams and varied the concentration to study the effect of fluid elasticity. By varying the heights of drop release, we have changed the drop impact velocities to study the inertial effects, manifested by Weber number (We). We have also studied the effect of stiffness by varying the substrate materials.

Unlike rigid substrates, stiffness is a critical parameter for CWT in case of flexible substrates. With decreasing stiffness or higher flexibility, drops rebound even if these two conditions are satisfied. The parametric dependence of polymer concentration, Weber number, and substrate stiffness produces distinct impact outcomes, which are summarized in a regime map expressed in terms of the Elasticity number and a modified Weber number that accounts for stiffness effects.