| Abstract: |
| We investigate the motion of a thin liquid drop on highly bendable elastic sheets. Under the lubrication approximation, we derive a coupled system of fourth-order partial differential equations, together with appropriate boundary and contact line conditions, to describe the evolution of both the fluid interface and the elastic sheet. Using matched asymptotic analysis in the limit of small slip length, we extend the classical Cox-Voinov relation to incorporate the effects of substrate elasticity. The extended relation is validated through numerical simulations. One key implication is that, compared with a rigid substrate, a soft substrate retards drop spreading but enhances receding dynamics. |
|