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

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 ${\beta }_{\mathrm{m}\mathrm{a}\mathrm{x}}$. 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 ${\beta }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ by the scaling law $\beta_$\mathrm{m}\mathrm{a}\mathrm{x}$ \sim (Re \mu_$\mathrm{l}$/\mu_f)^{1/2}$ that is a function of the droplet viscosity (${\mu }_{\mathrm{l}}$) and its Reynolds number ($Re$).