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.

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.

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 Extracting Interface Correlations from the Pair Distribution Function of Composite Materials

2021 ◽  
Author(s):  
Harry Geddes ◽  
Henry D. Hutchinson ◽  
Alex R Ha ◽  
Nicholas P. Funnell ◽  
Andrew Goodwin
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Functional Materials ◽  
Model System ◽  
Complex Mixtures ◽  
Proof Of Concept ◽  
X Ray ◽  
The Individual ◽  
Theory And Experiment ◽  
Matrix Factorisation

<div> <div> <div> <p>Using a non-negative matrix factorisation (NMF) approach, we show how the pair distribution function (PDF) of complex mixtures can be deconvolved into the contributions from the individual phase components and also the interface between phases. Our focus is on the model system Fe||Fe3O4. We establish proof-of-concept using idealised PDF data generated from established theory-driven models of the Fe||Fe3O4 interface. Using X-ray PDF measurements for corroded Fe samples, and employing our newly-developed NMF analysis, we extract the experimental interface PDF (‘iPDF’) for this same system. We find excellent agreement between theory and experiment. The implications of our results in the broader context of interface characterisation for complex functional materials are discussed. </p> </div> </div> </div>

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

Study on the Effect of Tool Rake Angle on Cutting Vibration in Precision Machining

2004 ◽  
Vol 471-472 ◽  
pp. 127-131
Author(s):  
Gui Cheng Wang ◽  
Li Jie Ma ◽  
Hong Jie Pei
Keyword(s):  
Theoretical Analysis ◽  
High Speed ◽  
Cutting Speed ◽  
Rake Angle ◽  
Precision Machining ◽  
Turning Operation ◽  
Cutting Vibration ◽  
Main Factors ◽  
Theory And Experiment

The cutting vibration is one of the main factors to affect precision machining. In this paper, the influence of tool rake angle on cutting vibration is studied at different cutting speed in turning operation, and corresponding theoretical analysis is made. The experiment results show that: the amplitude of machining vibration gradually decreases with tool rake angle increasing; while rake angle o g <0°, the biggest amplitude occurs at V=50~70m/min; While o g ≥0°, it is at V=160~180m/min. Moreover, theory and experiment foundation is presented on avoiding the biggest amplitude range so as to guarantee quality of precision machining at high speed.

LIQUID FOAM DRAINAGE: AN OVERVIEW

2008 ◽  
Vol 22 (15) ◽  
pp. 2333-2354 ◽  
Author(s):  
QICHENG SUN ◽  
LIANGHUI TAN ◽  
GUANGQIAN WANG
Keyword(s):  
Surfactant Solution ◽  
Two Dimensions ◽  
Limiting Factors ◽  
Liquid Foams ◽  
Measuring Techniques ◽  
Substantial Progress ◽  
The Stability ◽  
Liquid Foam ◽  
Concentrated Dispersions ◽  
Foam Drainage

Liquid foams are concentrated dispersions of gas bubbles in a small amount of surfactant solution, which are perpetually out of equilibrium systems. The process of liquid draining through networks of Plateau borders in a fresh foam is so-called foam drainage, as a result of both gravitational and capillary forces, which has great effect on the stability of foams. From the view of foam physics and dynamics, this paper briefly introduces foam structure and major lifetime limiting factors of foam. The substantial progress on the theory of drainage, measuring techniques for liquid fractions, drainage in both one dimension and two dimensions, and drainage in microgravity circumstances are overviewed throughout. Remaining tasks are discussed and a multiscale methodology for foam drainage is proposed for future investigations.

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
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