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.
We investigate the equilibrium of an axisymmetric system consisting of sessile and pendent drops on pre-stretched nonlinear elastic membranes. The membrane experiences large deformations due to the drop's weight and interfacial interactions. We first show that force balance alone leads to non-unique equilibrium solutions. Identifying the system's equilibrium with the minimum of its free energy, we then demonstrate that the equilibrium solution is made unique by requiring the continuity of meridional stretches across the three-phase contact circle. For a special class of nonlinear elastic materials – $I_2$ materials – we then compute the equilibrium configurations of the drop–membrane system for a range of drop volumes and membrane pre-tensions. Finally, the present work facilitates two important applications: (a) the membrane's pre-tension and current tension are related exactly to help in utilizing the system as an elastocapillary probe for membrane pre-tension and (b) we suggest an experimental protocol for measuring the membrane's surface properties.
No abstract
New experimental results on the hindered settling of model glass bead suspensions in non‐Newtonian suspending media are reported. The data presented encompass the following ranges of variables: 7.38 × 10−4 ≤ Re1∞ ≤ 2; 0.0083 ≤ d/D ≤ 0.0703; 0.13 ≤ C ≤ 0.43 and 1 ≥ n ≥ 0.8. In these ranges of conditions, the dependence of the hindered settling velocity on concentration is adequately represented by the corresponding Newtonian expressions available in the literature. The influence of the power law flow behaviour index is completely embodied in the modified definition of the Reynolds number used for power law liquids.
We study the equilibrium of planar systems consisting of sessile and pendent drops on pre-stretched, nonlinear elastic membranes. The membrane experiences large deformations due to both capillary forces and the drop's weight. The membrane's surface energies are allowed to depend upon stretches in the membrane. We minimize the free energy of the system to obtain the governing equations. This recovers all equations found by force balance, in addition to an extra condition that must hold at the triple point. The latter closes the system's mathematical description and defines a unique equilibrium given the membrane's material and pre-stretch, and the properties of drop's fluid and its volume. The extra condition simplifies to continuity of stretches at the triple point when the surface energies are strain-independent. We then solve these coupled nonlinear equations to obtain the global equilibria of the drop–membrane system. We report the effects of drop's volume and membrane's pre-tension on the system's geometry and tension distribution in the membrane. Through this, we align the theory closely with experiments, which will then allow the use of the present system both as an elastocapillary tension probe and as a device to measure solid surface energies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.