Air bubble collapse in liquid. 

An asymptotic solution of the differential  equation.
 
Emmanuil Agrest, Ph. D. 

Associate professor at Johnson and Wales University 
Adjunct professor at Mathematics Department 
College of Charleston 


 

Abstract

Cavitation is a process of formation of gas or vapor filled bubbles similar to boiling in heated water. It is well known that practically any liquid usually contains numerous microscopically small bubbles. The pressure change of a big enough intensity may generate the process of cavitation. This occurs in part on the surface of a high-speed vessel propeller. An ultrasonic wave may also be responsible for the cavitation.
The motion of a cavitation gas bubble in a liquid under the action of an alternating pressure field is being investigated. Nolting - Neppiras second order differential equation to describe radial pulsation is used. An analytical asymptotic solution to the equation is derived for the collapsing stage of the motion. The minimum radius of the collapsing bubble before it starts to grow again is obtained in the form of an algebraic expression.
 
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