Dissolution Arrest and Stability of Particle-Covered Bubbles

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Original entry: Tom Kodger, APPHY 226, Spring 2009


Reference

M. Abkarian, A.B. Subramaniam, S.Kim, R.J. Larsen, S.Yan, H.A. Stone. PRL 99, 188301 (2007);

Keywords

Armored bubbles, surface evolver, Laplace overpressure

Abstract

Experiments show that bubbles covered with monodisperse polystyrene particles, with particle to bubble radius ratios of about 0.1, evolve to form faceted polyhedral shapes that are stable to dissolution in ir-saturated water. We perform SURFACE EVOLVER simulations and find that the faceted particle-covered bubble represents a local minimum of energy. At the faceted state, the Laplace overpressure vanishes, which together with the positive slope of the bubble pressure-volume curve, ensures phase stability. The repulsive interactions between the particles cause a reduction of the curvature of the gas-liquid interface, which is the mechanism that arrests dissolution and stabilizes the bubbles.

Capillarity In Action

FIG. 1. (a) Experimental images of dissolution of a partially covered bubble, 3 s between each frame. Interparticle distances are reduced and the bubble develops planar facets as it stabilizes (white dashed lines). (b)–(d) Various stable crumpled and faceted shapes of armored bubbles, a/R: (b) 0.008, (c) 0.19, (d) 0.22. The white arrows indicate missing particle defects at the vertices of the bubble. Bubble shapes like these remain stable for days if not longer. Scale bars 8μ m.

A spherical gas bubble within a liquid, saturated with the entrained gas, has a positive Laplace pressure and therefore is unstable. If this 'overpressure' can be mitigated, the stability of bubble can be lengthened several orders of magnitude. The authors shot that the stability of armored bubbles (bubbles with particles at the interface), which adopt various nonspherical and irregular shapes can be understood in terms of the local geometry of the liquid-gas interface as characterized by the mean and Gaussian curvatures at the scale of individual particles.



For armored bubbles with 'a/R ~ 0.1', where 'a' is the stabilizing particle diameter and 'R' is the bubble radius, the authors observe facets with a fivefold disclination at the intersections typically unoccupied by a particle (Fig. 1).

FIG. 2. (a) Simulated bubble shapes obtained for V=Vp equal to (1) 203, (2) 138, and (3) 120. The darker particles represent fivefold disclinations. The arrow indicates the facet which has buckled inward. (b) Top graph. Left vertical axis: (filled circle) Laplace pressure, δP, vs V/Vp of the armored bubble. (+) For comparison, P of a bubble without particles is shown. (open circle) 2 times the absolute value of the fluid-fluid interface mean curvature, 2<H>, vs V/Vp. Right vertical axis: (X) asphericity of the armored bubble vs V/Vp. Bottom graph. Left vertical axis: (filled circle) the surface energy ES of the fluid-fluid interface and (open circle) the total energy E of the armored bubble vs V/Vp. Right vertical axis: (X) total repulsive energy EP between particles vs V/Vp.


To further investigate, surface evolver simulations are performed. Where the surface tension of the particles is 30 times that of the bubble, a contact angle of 40degrees is applied, and a simple exponential repulsion is applied due to the anionic nature of the particles, which is justified due to limited large scale surface rearrangements near the jammed state, as verified experimentally. The volume of one particles, Vp per bubble volume, V, is incrementally simulated and the equillibrium particle positions measured. (Fig. 2).



Where buckling occurs, the asphericity of the particle stabilized bubble shows distinct transitions. The pressure difference is also calculated and found to be 0 at a distinct Vp/V value of ~130. At this point, the mean curvature, <H> is 0, the bubble overpressure become mitigated and its stability increased dramatically.