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Authors: Llewellin, E. W.* 
Del Bello, E.* 
Taddeucci, J.* 
Scarlato, P.* 
Lane, S. J.* 
Title: The thickness of the falling film of liquid around a Taylor bubble
Issue Date: 24-Feb-2012
Series/Report no.: /468 (2012)
DOI: 10.1098/rspa.2011.0476
Keywords: gas slug
slug flow
long bubble
turbulent falling film
pipe flow
transitional flow
Subject Classification04. Solid Earth::04.01. Earth Interior::04.01.99. General or miscellaneous 
04. Solid Earth::04.01. Earth Interior::04.01.05. Rheology 
04. Solid Earth::04.08. Volcanology::04.08.99. General or miscellaneous 
04. Solid Earth::04.08. Volcanology::04.08.02. Experimental volcanism 
04. Solid Earth::04.08. Volcanology::04.08.03. Magmas 
05. General::05.02. Data dissemination::05.02.03. Volcanic eruptions 
Abstract: We present the results of laboratory experiments that quantify the physical controls on the thickness of the falling film of liquid around a Taylor bubble, when liquid–gas interfacial tension can be neglected. We find that the dimensionless film thickness l (the ratio of the film thickness to the pipe radius) is a function only of the dimensionless parameter Nf = rgD3/m, where r is the liquid density, g the gravitational acceleration, D the pipe diameter and m the dynamic viscosity of the liquid. For Nf 10, the dimensionless film thickness is independent of Nf with value l ≈ 0.33; in the interval 10 Nf 104, l decreases with increasing Nf; for Nf 104 film thickness is, again, independent of Nf with value l ≈ 0.08. We synthesize existing models for films falling down a plane surface and around a Taylor bubble, and develop a theoretical model for film thickness that encompasses the viscous, inertial and turbulent regimes. Based on our data, we also propose a single empirical correlation for l(Nf), which is valid in the range 10−1 < Nf < 105. Finally, we consider the thickness of the falling film when interfacial tension cannot be neglected, and find that film thickness decreases as interfacial tension becomes more important.
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