Dual role of local contact angles in spontaneous drop motion on gradient surfaces

Description

Frieder Mugele1, Sander Reuvekamp1, and Sissi de Beer1

1 University of Twente, Fac. Science and Technology, MESA+ Institute, PO Box 217, 7500 AE Enschede (The Netherlands)

The friction between a moving drop and a solid surface induces a deformation of the drop shape, as widely studied for the generic case of gravity-driven drops sliding down an inclined plane. In this case, the friction-induced distortions are most pronounced at the drop’s front and back apex, where the contact angle displays a local maximum and minimum because the normal component of the drop velocity is maximum (see e.g. [1]). In contrast, functional surfaces with a wettability gradient pull droplets towards regions of reduced contact angle in such a manner that the front apex typically probes the lowest equilibrium contact angle whereas the back apex experiences the highest equilibrium contact angle, leading to an antagonistic effect of driving wetting forces and viscous friction.
Here, we demonstrate how this situation induces to a peculiar distribution of the local dynamic contact angle with three local maxima and minima along the circumference instead of the conventional single local maximum and single minimum at the front and at the back for drops driven by body forces. To show this effect, we measure the local contact angles of dodecane drops on an oleophilic polymer brush coating. The system displays very low but finite advancing and receding contact angles of 1-3° – depending on the degree of oil saturation – that we measure with 0.1° accuracy using optical interferometry [2]. Combining the imposed wettability gradient with a Cox-Voinov expression for the local contact line friction explains the observed contact angle distribution.

Figure 1. Left: top view of moving drop on brush with a swelling gradient between left and right (dark rim) reflecting the wettability gradient. Right: local contact angles extracted from interference fringes with three local maxima around the circumference.

[1] E. Rio, A. Daerr, B. Andreotti, L. Limat, Phys. Rev. Lett. 94 (2005), 024503.
[2] Ö. Kap, S. Hartmann, H. Hoek, S. de Beer, I. Siretanu, U. Thiele, F. Mugele, J. Chem. Phys. 158 (2023), 174903.
 
Drops on gradient surfaces spontaneously move toward more wetting regions such that the leading edge experiences the lowest and the trailing edge the highest equilibrium contact angle. At the same time, viscous friction induces a contact angle increase at the leading edge and a reduction at the trailing edge of a moving drop. Here we use high resolution interferometric imaging of alkane drops on an oleophilic polymer brush surface with a vapor-induced wettability gradient to demonstrate that these antagonistic effects lead to a non-monotonic variation of the local contact angle with three local maxima and minima along the contact line. This generic phenomenology is explained by combining a wettability gradient with Cox-Voinov’s expression for the dynamic contact angle.

The friction between a moving drop and a solid surface induces a deformation of the drop shape, as widely studied for the generic case of gravity-driven drops sliding down an inclined plane. In this case, the friction-induced distortions are most pronounced at the drop’s front and back apex, where the contact angle displays a local maximum and minimum because the normal component of the drop velocity is maximum (see e.g. [1]). In contrast, functional surfaces with a wettability gradient pull droplets towards regions of reduced contact angle in such a manner that the front apex typically probes the lowest equilibrium contact angle whereas the back apex experiences the highest equilibrium contact angle, leading to an antagonistic effect of driving wetting forces and viscous friction.
Here, we demonstrate how this situation induces to a peculiar distribution of the local dynamic contact angle with three local maxima and minima along the circumference instead of the conventional single local maximum and single minimum at the front and at the back for drops driven by body forces. To show this effect, we measure the local contact angles of dodecane drops on an oleophilic polymer brush coating. The system displays very low but finite advancing and receding contact angles of 1-3° – depending on the degree of oil saturation – that we measure with 0.1° accuracy using optical interferometry [2]. Combining the imposed wettability gradient with a Cox-Voinov expression for the local contact line friction explains the observed contact angle distribution.

Soft materials are ubiquitous in technological applications that require deformability, for instance, in flexible, water-repellent coatings. However, the wetting properties of prestrained soft materials are only beginning to be explored. Here we study the sliding dynamics of droplets on prestrained soft silicone gels, both in tension and in compression. Intriguingly, in compression we find a nonmonotonic strain dependence of the sliding speed: mild compressions decelerate the droplets, but stronger compressions lead again to faster droplet motion. Upon further compression, creases nucleate under the droplets until, finally, the entire surface undergoes the creasing instability, causing a “run-and-stop” motion. We quantitatively elucidate the speed modification for moderate prestrains by incremental viscoelasticity, while the acceleration for larger prestrains turns out to be linked to the solid pressure, presumably through a lubrication effect of expelled oligomers.

Period	1 Jul 2025 → 3 Jul 2025
Event title	6th International Conference on Droplets, 2025
Event type	Conference
Conference number	6
Organisers	Universite Libre de Bruxelles, University of Liege
Sponsors	Photron, Fluigent, Fonds De La Recherche Scientifique - FNRS
Location	Liege, BelgiumShow on map