The stress-strain relationship of liquid marbles under compression

Abstract

Liquid marbles can be characterized using elastic solid models consisting of a liquid surrounded by a soft solid membrane. The elastic properties of liquid marbles determine the amount of compression under a given external force. This is an important property as the elasticity of liquid marbles determines their morphology under a given stress. We show that the stress-strain relationship of liquid marbles can be described by σ∗Bo=0.6[1/(1−εhro)2−1], where Bo is the Bond number, σ* is the normalised stress, and εhr0 is the strain measured with respect to the equivalent radius of the liquid marble. This stress-strain relationship could pave the way for the development of microfluidic devices with robust liquid marbles. Liquid marbles are classified as non-wetting liquid droplets with the characteristics of soft solids. As there is no direct physical contact between the liquid interior and the surroundings, liquid marbles are capable of virtually lossless transport of small liquid volumes. Their low cost and ease of preparation make liquid marbles highly desirable instruments in digital microfluidics.1 Research on the elasticity of liquid marbles has been steadily gaining attention in the research arena, and this includes the controllable deformation of liquid marbles coated with monolayer nanoparticles.2–4 The rationale behind such works could be that the survivability of a liquid marble heavily depends on its elasticity. Furthermore, it is important to note that large deformations of liquid marbles may lead to substantial internal mixing which is conducive to cell viability, a critical aspect in using liquid marbles as bio-reactors. The simple parallel plate compression test was usually conducted with the goal of comprehending the robustness of liquid marbles.5–7 This well-established method has been used to investigate the properties of liquids,8 solids,9 and gels.10 Asare-Asher et al. investigated the Young's modulus of a liquid marble and reported its non-linear elastic characteristics.6 Whyman and Bormashenko determined the surface tension of liquid marbles under compression by applying some geometrical assumptions.11 Rendos et al. also investigated the surface tension of liquid marbles under compression, albeit using the energy conservation approach.5 Liu et al. characterised the robustness of a liquid marble by quantifying the surface coverage of the coating particles.7 In principle, the combination of a liquid interior and a thin coating necessitates a more comprehensive model than a model that uses a single-phase. Also, liquid marble coatings consist of loose powder that cracks readily, which could render the membrane encapsulated liquid model unsuitable. As such, the development of a universal model is motivated by this prevailing challenge. The developed model aims to describe the elasticity of a liquid marble with more rigour without resorting to geometric assumptions. Also, the development of the universal stress-strain relationship for liquid marbles can be fundamental in designing microfluidic devices with robust liquid marbles. In this study, we investigate the elasticity of a liquid marble using a large-strain, parallel plate compression test with high resolution. To obtain large strains whilst maintaining the integrity of the liquid marble, the plates have been coated with the same hydrophobic powder as the marble. A coarse grained liquid marble model12 is employed to obtain the stress-strain relationship of a 10 μl water droplet coated with polytetrafluoroethylene (PTFE) particles. After validating the liquid marble model against the experimental results, the model is used to evaluate the effect of the volume of the droplet, the density, and the surface tension of the liquid on the stress-strain relationship of the liquid marbles. Then, the model predictions are used to develop a generalised stress-strain relationship applicable to any liquid marble. Finally, the validity of the generalised equation is assessed using the experimental results.