The Cole-Hopf Transformation for Solving Rayleigh-Plesset Equation in Bubble Dynamics

The Cole-Hopf Transformation for Solving Rayleigh-Plesset Equation in Bubble Dynamics

Ali F. Abu-BakrAly M. Abourabia 

Mathematics and Computer Science Department, Menoufia University, Shebin El-Kom 32511, Egypt

Theoretical and Mathematical Physics Department, Ural Federal University, Ekaterinburg 620083, Russia

Corresponding Author Email: 
alibakrm@yahoo.com
Page: 
82-87
|
DOI: 
https://doi.org/10.18280/ama_a.550207
Received: 
20 March 2018
|
Accepted: 
18 May 2018
|
Published: 
30 June 2018
| Citation

OPEN ACCESS

Abstract: 

In this paper, we investigate the solution of the behaviour of bubble growth in Newtonian fluid by using extended Rayleigh-Plesset equation. The transformation of Cole-Hopf has been applied on the nonlinear ordinary differential equation of the non-dimensional extended Rayleigh-Plesset equation in order to obtain the exact solution of bubble radius. We have also introduced the study of phase portrait of growth problem. The results studied analytically and indicated in graphics.

Keywords: 

Cole–Hopf transformation, Rayleigh-Plesset equation, phase portrait, bubble dynamics

1. Introduction
2. Mathematical Model
3. The Cole-Hopf Transformation and the Analytical Solution of Rayleigh-Plesset Equation
4. The Phase Portrait of Extended Rayleigh-Plesset Equation
5. Results and Discussion
6. Conclusions
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