Cox, Simon

Fortes, M. A.

Teixeira, Paulo

Vaz, M. Fatima

English

We assess the stability of simple two-dimensional clusters of bubbles relative to small displacements of the vertices, at fixed bubble areas. The clusters analysed are: 1) flower clusters consisting of a central bubble of area l surrounded by N shells each containing n bubbles of unit area, 2) periodic chain clusters consisting of N 'parallel' rows of n bubbles of unit area and width w. The energy and bubble pressures of the symmetrical, unbuckled clusters are found analytically as a function of l and w for given N and n. Both types of clusters studied show a single energy minimum at a critical lm or wm. At the energy minimum for flower clusters, the pressure in the central bubble vanishes. The clusters show a symmetry-breaking buckling instability under compression at a critical lb or wb. The corresponding critical energy Eb was determined with the Surface Evolver software. While for N=1 the conditions lb = lm, wb = wm and Eb = Em hold, for N&gt;1 buckling requires further compression beyond the minimum, for which the energy increases with increasing compression (decreasing l or w), and the excess pressure in the central bubble of the flower clusters becomes negative

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Instabilities in two-dimensional flower and chain clusters of bubbles

http://pure.aber.ac.uk/ws/files/71866/multipetal12b.pdf

Instabilities in two-dimensional flower and chain clusters of bubbles

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