Year: 2025
Type: article
Abstract: We investigate the motion of a thin liquid drop on a pre-stretched, highly bendable elastic sheet. Under the lubrication approximation, we derive a system of fourth-order partial differential equations, along with appropriate boundary and contact line conditions, to describe the evolution of the fluid interface and the elastic sheet. Extending the classical analysis of Cox and Voinov, we perform a four-region matched asymptotic analysis of the model in the limit of small slip length. The central result is an asymptotic relation for the contact line speed in terms of the apparent contact angles. We validate the relation through numerical simulations. A key implication of this result is that a soft substrate retards drop spreading but enhances receding, compared to the dynamics on a rigid substrate. The relation remains valid across a wide range of bending modulus, despite the distinguished limit assumed in the analysis.
Source: Journal of Fluid Mechanics
Authors: Zhixuan Li, Weiqing Ren
Institution: National University of Singapore
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7101418087