© 2003 by Oxford University Press
Deformation of a Spherical Bubble in Soft Solid Media under External Pressure
( 1 Los Alamos National Laboratory, Applied Physics Division, MS: T086, Los Alamos, NM 87545, USA 2 Process Science and Engineering Department, Pacific Northwest National Laboratory, PO Box 999, MS K7-15, Richland, WA 99352, USA )
In this paper, a theoretical investigation on the deformation of a spherical bubble embedded in soft solid media under externally applied pressure is presented. The effects that surface tension and mechanical properties have on interactions between the bubble compressibility and the surrounding medium are quantified. Within the framework of classical plasticity theory and following the refined treatment for large plastic displacements set forth by Chadwick, solutions are found for the finite deformation of the bubble radius and the internal bubble pressure in terms of implicit functions. Solutions are applicable to a wide range of material properties and external forcing conditions when soft solid media undergo elastic and finite plastic deformations. The validity of the solutions is not restricted to small values of the ratio between yield stress and elastic modulus. It is hypothesized that the existence of a plastic region in the neighbourhood of the bubble might explain upward bubble migration in soft solids due to pressure fluctuations in the presence of a gravitational field. Examples of the main features of the solutions are discussed in terms of dimensionless parameters.
Received 1 February 2002. Revised 15 November 2002 and 1 February 2003.