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 Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Hadi Hosseini Fadravi ◽  
Hassan Saberi Nik ◽  
Reza Buzhabadi
Keyword(s):  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Convergent Series ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Foam Drainage Equation ◽  
Foam Drainage

The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.

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

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.

Drainage dynamics controlled by corner flow: Application of the foam drainage equation

2016 ◽  
Vol 52 (11) ◽  
pp. 8402-8412 ◽  
Author(s):  
Frouke Hoogland ◽  
Peter Lehmann ◽  
Dani Or
Keyword(s):  
Corner Flow ◽  
Foam Drainage Equation ◽  
Foam Drainage
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