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(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 dissipation at the contact line can limit the dynamics and we describe beta(max) by the scaling law beta(max) similar to (Re mu(l)/mu(f))(1/2) that is a function of the droplet viscosity (mu(l)) and its Reynolds number (Re).