Stability and folds in an elastocapillary system

We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of simply connected and doubly connected menisci. Using variational and spectral methods, stability is related to the slope of equilibrium branches in the liquid content versus pressure diagram for the constrained and unconstrained problems. The second-variation spectra are separately determined for the membrane and meniscus, showing that the membrane out-of-plane spectrum and the in-plane spectrum at large elatocapillary numbers are both positive, so that only meniscus perturbations can cause instability. At small elastocapillary numbers, the in-plane spectrum has a negative eigenvalue, inducing wrinkling instabilities in thin membranes. In contrast, the smallest eigenvalue of the meniscus spectrum always changes sign at a pressure turning point where stability exchange occurs in the unconstrained problem. We also examine configurations in which the meniscus and membrane are individually stable, while the elastocapillary system as a whole is not; this emphasizes the connection between stability and the coupling of elastic and capillary forces

Drop deposition on surfaces with contact-angle hysteresis: Liquid-bridge stability and breakup

We study the stability and breakup of liquid bridges with a free contact line on a surface with contact-angle hysteresis under zero-gravity conditions. Theoretical predictions of the stability limits are validated by experimental measurements. Experiments are conducted in a water-methanol-silicon oil system where the gravity force is offset by buoyancy. We highlight cases where stability is lost during the transition from a pinned-pinned to pinned-free interface when the receding contact angle is approached---rather than a critical state, indicating that the breakup length is not always associated with the static maximum-length stability limit. We demonstrate that the dynamic contact angle controls the contact-line radius following stability loss, and that interface evolution following stability loss can increase the dispensed-drop size if the contact angle is fixed.Comment: To be submitted to Phys. Fluid