Laboratoire Matière et Systèmes Complexes

Thèse de Mathieu Oléron effectuée sous la direction de Matthieu Roché, de Julien Dervaux et Laurent Limat.

Soutenance en anglais le jeudi 10 février2022 à 14h30 en visio.

Dynamic wetting of viscoelastic subtrates

Abstract :

This work focuses on dynamical elastowetting, which means it investigates the motion of a liquid onto a deformable substrate. However, viscoelastic substrates such as polymeric gels also dissipate energy : the liquid/vapor interface pulls the substrate ; the resulting wetting ridge dissipates energy when the contact line carries it along. Recent theoretical predictions use nonlinear elasticity and suggest that the ratio of these two dissipation sources rules the dynamics of elastowetting systems. The bigger the ratio, the more the substrate dissipates. This thesis probes the so far uncharted implications of this dissipation ratio. Drops slide onto inclined silicon gels, and the dissipation ratio spans four orders of magnitude. We then study both advancing and receding contact lines. This parameter sets the shape of the drops. When the viscoelastic solid dissipates as much energy as the viscous liquid, we observe shapes akin to the rigid case. The drop forms a corner at the rear - the faster, the sharper. We observe rounder corners than the case where the substrate is rigid though. When the viscoelastic solid dissipates much more energy than the viscous liquid, we observe longer and corner-free drops. The relation between the weight and the running speed of the drops confirms the stark difference between systems where the liquid dissipate as much as the solid and systems that mostly dissipate in the substrate. In the first case, the speed increases linearly with the weight, just like the rigid case. In the second case, the rheology of the substrate rules the dynamics. We also mesured the dynamic contact angles between the drop and its substrate. The dissipation ratio strongly modifies the relation between those two parameters. At low dissipation ratio, the curve and the Cox-Voinov relation, that well describes the rigid case, look alike. At high dissipation ratio, the curve steepens at low speed and exhibits two plateaus at large speed (in absolute value). Longer drops stem from this "S"-like curve, called soft hysteresis. The aforementioned model predicts this phenomenon and is in excellent agreement with our experimental data. Local measurements such as dynamic contact angles highlight subtle effects that weighing measurements miss. Viscoelasticity does impact the dynamic of the drop even when the dissipation ratio is close to unity. Despite strong similarities with the rigid case, simply neglecting the dissipation inside the liquid is inapropriate to describe our data. In any case, the drop leaves pearls behind its trail above a certain speed - it’s the pearling instability. Our experiments and the nonlinear theory exhibit the same trend : the instability threshold decreases with increasing dissipation ratio at fixed equilibrium contact angle. This work also opens prospective as regards the curvature at the tip of cornered drops just below the instability threshold. Measurements in the rigid case suggest that nanometric scales regularize the corner. Yet, the characteristic size of the wetting ridge, called the elastocapillary length, impacts the rear curvature in our systems. The smaller the elastocapillary length, the sharper the corner, in agreement with the observed shapes. Further investigation should unveil how does this micrometric length scale couple with the molecular length scale to regularize the corner.