Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates

Abstract

A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius $\beta_\mathrm{max}$. By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter $\mu_f$. Moreover, our analysis shows that at low and intermediate impact speeds dissipation at the contact line limits the dynamics and we describe $\beta_\mathrm{max}$ by the scaling law $\beta_\mathrm{max} \sim (Re \mu_\mathrm{l}/\mu_f)^{1/2}$ that is a function of the droplet viscosity ($\mu_\mathrm{l}$) and its Reynolds number ($Re$).