Planar equilibria of sessile and pendant liquid drops on geometrically non-linear elastic membranes

Abstract

Equilibrium shapes are obtained for sessile and pendant liquid drops placed on elastic membranes in two-dimensions. The membrane is allowed to undergo large deformations under the action of capillary forces and fluid pressure. We focus on the global characteristics of the system, like the equilibrium shape of the drop, the membrane’s deformed shape, the apparent contact angle and contact size, and their variation with the volume of the drop for different membrane tensions and drop apex curvatures. It is found that the apparent contact angle is not simply a function of material property but of the system’s geometry as well. The contact size for sessile drops shows a non-monotonic behavior with the volume for all drop apex curvatures. However, for pendant drops, the behavior is strictly monotonic below a critical value of the drop apex curvature.

Equilibrium shapes of liquid drops on pre-stretched nonlinear elastic membranes

“…For pendent drops in figure 5(b), however, the membrane deforms by bulging upwards, with the bulge reducing as the drop volume is raised. The upward bulge in pendent drops has been observed in experiments (Nadermann et al 2013;Schulman & Dalnoki-Veress 2015) and has also been predicted in planar systems (Hui & Jagota 2015;Nair et al 2018). We also note that the dry membrane does not remain flat, and we will return to this point later when we discuss the dry membrane angle in § 6.2.…”

“…For a choice of non-dimensional apex curvature of the drop β and contact radius ā, the governing equation (2.19) for the drop together with the end conditions (2.20) is numerically solved to obtain the drop's profile zd (r d ) and, thereby, the drop angle θ d . We follow the algorithm of Nair et al (2018) to compute shapes when zd is not a single-valued function of rd , such as for sessile drops when θ d > 90 • .…”

“…In passing we also mention investigations into two-dimensional systems. The planar equilibrium of drops on thin structures was studied by Nair, Sharma & Shankar (2018), who characterized the effect of volume on the global features of the drop-membrane system, by Hui & Jagota (2015), who employed it to elaborate the difference between solid surface energy and solid surface tension, and by Neukirch, Antkowiak & Marigo (2013) and Neukirch et al (2014), who computed the direction of the external force on a beam exerted by the liquid-vapour phase in the absence and presence of extensional deformations. Neukirch et al (2013Neukirch et al ( , 2014 and Nair et al (2018) took the solid structures to be made of linear elastic material but accommodated large rotations, but Hui & Jagota (2015) employed a neo-Hookean material model.…”

“…(2013, 2014) and Nair et al. (2018) took the solid structures to be made of linear elastic material but accommodated large rotations, but Hui & Jagota (2015) employed a neo-Hookean material model.…”

Transient deformation and swelling of paper by aqueous co-solvent solutions

“…The second is the elastocapillary deformation of the paper sheet due to the interfacial tension and capillary pressure of the deposited droplet, which both lead to a deformation towards the underside of the paper sheet. [52][53][54][55] This deformation mechanism is facilitated by the drastic decrease of the elastic modulus of paper with increasing moisture content. The gravitational force scales with r liq V drop g, where g is the gravitational acceleration.…”