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We develop a mean-field model to examine the stability of a ‘quasi-2-D suspension’ of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by which the anisotropic mobility of particles interacts with long-ranged viscous membrane hydrodynamics. We first show that a system of slender rod-like particles driven by a constant force is unstable to perturbations in concentration – much like sedimentation in analogous 3-D suspensions – so long as membrane viscous stresses dominate. However, increasing the contribution of viscous stresses from the surrounding 3-D fluid(s) suppresses such an instability. We then tie this result to the hydrodynamic disturbances generated by each particle in the plane of the membrane and show that enhancing subphase viscous contributions generates extensional fields that orient neighbouring particles in a manner that draws them apart. The balance of flux of particles aggregating versus separating then leads to a wave number selection in the mean-field model. 

Large gas bubbles can reach the surface of pools of mud and lava where they burst, often through the formation and expansion of circular holes. Bursting bubbles release volatiles and generate spatter, and hence play a key role in volcanic degassing and volcanic edifice construction. Here, we study the ascent and rupture of bubbles using a combination of field observations at Pâclele Mici (Romania), laboratory experiments with mud from the Imperial Valley (California, USA), numerical simulations and theoretical models. Numerical simulations predict that bubbles ascend through the mud as elliptical caps that develop a dimple at the apex as they impinge on the free surface. We documented the rupture of bubbles in nature and under laboratory conditions using high-speed video. The bursting of mud bubbles starts with the nucleation of multiple holes, which form at a near-constant rate and in quick succession. The quasi-circular holes rapidly grow and coalesce, and the sheet evolves towards a filamentous structure that finally falls back into the mud pool, sometimes breaking up into droplets. The rate of expansion of holes in the sheet can be explained by a generalization of the Taylor–Culick theory, which is shown to hold independent of the fluid rheology.