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

MULTIPLE EXACT SOLUTIONS OF THE GENERALIZED TIME FRACTIONAL FOAM DRAINAGE EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050062
Author(s):  
DANDAN SHI ◽  
YUFENG ZHANG ◽  
WENHAO LIU
Keyword(s):  
Exact Solutions ◽  
Expansion Method ◽  
Transformation Method ◽  
Vertical Density Profile ◽  
New Exact Solutions ◽  
Vertical Density ◽  
Foam Drainage Equation ◽  
Physical Phenomena ◽  
Generalized Time ◽  
Foam Drainage

In this paper, we investigate the exact solutions of the generalized time fractional foam drainage equation. The Lie-group scaling transformation method and improved [Formula: see text]-expansion method are adopted here. The equation describes the evolution of the vertical density profile of a foam under gravity. New exact solutions and maple diagrams of the generalized time fractional foam drainage equation can help us better understand the physical phenomena.

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

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

scholarly journals A model system for foam fractionation

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120727 ◽  
Author(s):  
S. Hutzler ◽  
S. T. Tobin ◽  
A. J. Meagher ◽  
A. Marguerite ◽  
D. Weaire
Keyword(s):  
Theoretical Analysis ◽  
Surfactant Solution ◽  
Model System ◽  
Foam Fractionation ◽  
Numerical Computations ◽  
Foam Drainage Equation ◽  
Theory And Experiment ◽  
Foam Drainage

A model system for theory and experiment that 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 and its variants are used for a theoretical analysis of this process. In the limit in which the lengths of the two legs is large , exact analytic formulae may be derived for the key properties of the system. Numerical computations and experiments support these results.

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