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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Mathematical modelling of the collapse time of an unfolding shelled microbubble

Cowley, James and Mulholland, Anthony J. and Stewart, Iain W. and Gachagan, Anthony (2016) Mathematical modelling of the collapse time of an unfolding shelled microbubble. [Report]

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Abstract

There is considerable interest at the moment on using shelled microbubbles as a transportation mechanism for localised drug delivery, specifically in the treatment of various cancers. In this report a theoretical model is proposed which predicts the collapse time of an unfolding shelled microbubble. A neo-Hookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. This is achieved by considering a reference configuration (stress free) consisting of a shelled microsphere with a hemispherical cap removed. This is then displaced angularly and radially by applying a stress load to the free edge of the shell. This forms a deformed open sphere possessing a stress. This is then used as an initial condition to model the unfolding of the shell back to its original stress free configuration. Asymptotic expansion along with the conservation of mass and energy are then used to determine the collapse times for the unfolding shell and how the material parameters influence this. The theoretical model is compared to published experimental results.