Invariant analysis and conservation laws for the time fractional foam drainage equation

2015 ◽  
Vol 130 (10) ◽  
Author(s):  
Wenjuan Rui ◽  
Xiangzhi Zhang
Keyword(s):  
Conservation Laws ◽  
Invariant Analysis ◽  
Foam Drainage Equation ◽  
Foam Drainage

Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation

2017 ◽  
Vol 72 (3) ◽  
pp. 261-267 ◽  
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Series Solution ◽  
Power Series Solution ◽  
One Dimensional ◽  
Symmetry Classification ◽  
Symmetry Operators ◽  
Foam Drainage Equation ◽  
Foam Drainage

AbstractWe perform a complete Lie point symmetry classification of the generalised foam-drainage equation and then construct an optimal system of one-dimensional subalgebra of the admitted symmetry operators and use them to reduce the equations under study. A power series solution of the reduced equation is constructed. Moreover, we find all multipliers of the equations and apply them to construct conservation laws.

Numerical solutions of the fractal foam drainage equation

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Siddra Habib ◽  
Asad Islam ◽  
Amreen Batool ◽  
Muhammad Umer Sohail ◽  
Muhammad Nadeem
Keyword(s):  
Numerical Solutions ◽  
Foam Drainage Equation ◽  
Fractal Foam ◽  
Foam Drainage

Exact solutions for nonlinear foam drainage equation

2016 ◽  
Vol 91 (2) ◽  
pp. 209-218 ◽  
Author(s):  
E. M. E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Exact Solutions ◽  
Foam Drainage Equation ◽  
Foam Drainage

scholarly journals Theoretical analysis of the performance of a foam fractionation column

2014 ◽  
Vol 470 (2165) ◽  
pp. 20130625 ◽  
Author(s):  
S. T. Tobin ◽  
D. Weaire ◽  
S. Hutzler
Keyword(s):  
Theoretical Analysis ◽  
Surfactant Solution ◽  
Model System ◽  
Foam Fractionation ◽  
Fractionation Column ◽  
Foam Drainage Equation ◽  
Limiting Case ◽  
Alternative Set ◽  
Theory And Experiment ◽  
Foam Drainage

A model system for theory and experiment which is relevant to foam fractionation consists of a column of foam moving through an inverted U-tube between two pools of surfactant solution. The foam drainage equation is used for a detailed theoretical analysis of this process. In a previous paper, we focused on the case where the lengths of the two legs are large. In this work, we examine the approach to the limiting case (i.e. the effects of finite leg lengths) and how it affects the performance of the fractionation column. We also briefly discuss some alternative set-ups that are of interest in industry and experiment, with numerical and analytical results to support them. Our analysis is shown to be generally applicable to a range of fractionation columns.

Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation

1999 ◽  
Vol 82 (21) ◽  
pp. 4232-4235 ◽  
Author(s):  
Stephan A. Koehler ◽  
Sascha Hilgenfeldt ◽  
Howard A. Stone
Keyword(s):  
Liquid Flow ◽  
Aqueous Foams ◽  
Flow Through ◽  
Foam Drainage Equation ◽  
Foam Drainage

A foam drainage equation generalized for all liquid contents

2001 ◽  
Vol 14 (3) ◽  
pp. 331-342 ◽  
Author(s):  
S J Neethling ◽  
H T Lee ◽  
J J Cilliers
Keyword(s):  
Foam Drainage Equation ◽  
Foam Drainage
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