Eur. Phys. J. Spec. Top.
https://doi.org/10.1140/epjs/s11734-025-01648-2

Review

Unsteady dynamical wetting: a review

¹ Université Paris Cité, CNRS, Matière et Systèmes Complexes, 75013, Paris, France
² Laboratory of Fluid Mechanics and Instabilities, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

^a philippe.brunet@u-paris.fr

Received: 31 December 2024
Accepted: 24 April 2025
Published online: 20 May 2025

Abstract

The wetting dynamics is often considered in the frame of stationary conditions, i.e., when the contact-line advances or recedes at constant velocity. The purpose of many corresponding studies is then to determine a relationship between the contact-line velocity and the shape of the free surface in the vicinity of the line, the latter being often quantified by a dynamical contact-angle ${\theta }_d$, which is velocity-dependent. The present review aims to consider the dynamics of wetting in unsteady cases, which have been so far less investigated, where inertia is susceptible to play a significant, if not major, role. This includes various situations as the first stages of spreading after the liquid has contacted a substrate, drops sliding along low-friction surfaces, the spreading or receding of liquids with a stick–slip dynamics, the fast and/or oscillating rising of menisci in capillaries and the response of drops or menisci to periodic mechanical forcing. This latter case is particularly remarkable in the fact that the relationship between instantaneous velocity $V_{\text{CL}}$ and dynamical contact-angle ${\theta }_d$ shows a complex, multi-valued dependence. After having summarized some of the most significant experimental and theoretical studies, we present the results of an original experiment where a liquid bridge of height h is sheared by the periodic motion of its lower basal substrate. By varying the frequency and therefore the thickness $\delta$ of the viscous boundary layer, we show that this aforementioned complex behavior appears if $\delta /h$ is below a critical value, otherwise one recovers a relation between velocity and contact-angle compatible with the classical Cox–Voinov hydrodynamic framework. We finally conclude on some remaining questions and challenges in unsteady wetting.