Scaling properties of interfacial flows in tubes of rectangular cross-section.

Lead Research Organisation: University of Manchester
Department Name: Mathematics


This proposal concerns the propagation of air fingers in liquid-filled tubes of rectangular cross-section. This fundamental interfacial flow is encountered in a wide range of applications from thin-film coating to enhanced oil recovery. The aim of the proposed research is to gain an understanding of the dependence of such flows on the aspect-ratio of the tube, alpha (the ratio of the width to the height of the cross-section). Promising experimental results, obtained in Manchester, suggest that certain global features of finger propagation in tubes of different aspect ratios can be obtained by rescaling master curves , obtained for a square tube, by functions of the aspect ratio. This result is of fundamental significance because it suggests a connection between the interfacial dynamics in square or nearly square tubes (alpha =1- 2) and those in Hele-Shaw cells (alpha >> 1). The evolution of the flow between these two limiting geometries will be characterised in detail using the powerful combination of experiments and three-dimensional numerical simulations.


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De Lózar A (2007) Scaling properties of coating flows in rectangular channels. in Physical review letters

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DE LÓZAR A (2008) The steady propagation of an air finger into a rectangular tube in Journal of Fluid Mechanics

Description We characterised the effect of channel width relative to depth on the propagation of air fingers displacing a more viscous liquid. A scaling was obtained experimentally and details three-dimensional numerical simulations revealed the limit of validity of two-dimensional models.
Exploitation Route Fundamental science useful in microfluidic design.
Sectors Manufacturing, including Industrial Biotechology,Other

Description Fundamental knowledge used in microfluidics.
First Year Of Impact 2007
Sector Manufacturing, including Industrial Biotechology,Other
Description BP Exploration
Amount £74,956 (GBP)
Funding ID Pilot study 
Organisation BP (British Petroleum) 
Department BP Exploration Company
Sector Private
Country United Kingdom
Start 08/2012 
End 03/2013
Description EP/H011579/1
Amount £335,214 (GBP)
Funding ID EP/H011579/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 05/2010 
End 06/2013
Description Leverhulme Project Grant
Amount £156,000 (GBP)
Organisation The Leverhulme Trust 
Sector Charity/Non Profit
Country United Kingdom
Start 09/2014 
End 09/2017