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Towards the Collapse of Bubbles in a Viscous Liquid

Nail S. Khabeev, A. Karim Alnooh

Abstract


The present paper is devoted to a model of lling empty spherical bubble in a New-tonian viscous liquid caused by an initial bubble wall motion. The existence of two different types of motion predicted in [1] is conrmed numerically: bubbles, which are smaller than a critical size, are filled slowly in an innitely long time; the filling of large bubbles takes place rapidly with an unlimited accumulation of energy during collapse.
In [1] the way of calculation of the critical parameter was not done in details. Here we did it by using qualitative theory of dierential equations, we also did a numerical verification of this basic result.


Keywords


bubbles, viscous liquid, Navier-Stokes equations, critical radius of bubble

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