PNNL

Abstract

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 the mechanical properties of the medium have on the interaction between the compressibility of the bubble 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, closed-form solutions are found for the finite deformation of the bubble radius and the internal bubble pressure. Results are discussed in terms of dimensionless parameters applicable to a wide range of material properties and external forcing conditions when the soft solid medium undergoes elastic and finite plastic deformations in the vicinity of the bubble caused by the external driving pressure. It is hypothesized that the existence of a plastic region in the neighborhood of the bubble might explain upward bubble migration in the presence of a gravitational filed.