Soft wetting: Models based on energy dissipation or on force balance are equivalent

In Newtonian mechanics, an overdamped system at steady state is governed by a local balance of mechanical stress but also obeys a global balance between injected and dissipated energy. In the classical literature of purely viscous drop spreading, apparent differences in “dissipation” and “force” approaches have led to unnecessary debates, which ultimately could be traced back to different levels of mathematical approximation (1). In the context of wetting on a soft solid, Zhao et al. (2) interpret their experiments by a model based on viscoelastic dissipation inside the substrate. It is claimed that this global dissipation model is fundamentally different from the local mechanical model presented by Karpitschka et al. (3). The purpose of this letter is to demonstrate that (i) the models in refs. 2 and 3 are in fact strictly equivalent … ↵1To whom correspondence should be addressed. Email: stefan.karpitschka{at}ds.mpg.de.