TY - JOUR

T1 - Instabilities in two-dimensional flower and chain clusters of bubbles

AU - Fortes, M. A.

AU - Vaz, M. Fatima

AU - Cox, Simon

AU - Teixeira, Paulo

N1 - M.A. Fortes et al., Instabilities in two-dimensional flower and chain clusters of bubbles, Colloids and Surfaces A: Physicochemical and Engineering Aspects Volume 309, Issues 1-3, 1 November 2007, Pages 64-70 A Collection of Papers Presented at the 6th Eufoam Conference, Potsdam, Germany, 2-6 July, 2006

PY - 2007/11

Y1 - 2007/11

N2 - 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>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.

AB - 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>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.

U2 - 10.1016/j.colsurfa.2007.02.039

DO - 10.1016/j.colsurfa.2007.02.039

M3 - Article

SN - 0927-7757

VL - 309

SP - 64

EP - 70

JO - Colloids and Surfaces A: Physicochemical and Engineering Aspects

JF - Colloids and Surfaces A: Physicochemical and Engineering Aspects

IS - 1-3

ER -