Bubble Growth under Nonuniform Initial Conditions

Bubble Growth Under Nonuniform Initial Conditions 1. Introduction 

In actual practice vapor bubbles almost always originate at solid surfaces, rather than in the midst of a large body of uniformly superheated liquid. This introduces a number of additional complications, whose effect in most cases is still largely unknown. Even for isolated bubbles the spherical shape is 

Note that this is not a Lagrangian transformation, although the bubble wall is immobilized. The initial temperature function is taken to be a quadratic 

The bubble wall is assumed to be at the saturation temperature corresponding to the ambient pressure  

New independent variables are now introduced into Eq. (63) s =y/R as a position variable, and jR(f) as a time variable, giving 

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