The thickness of the falling film of liquid around a Taylor bubble

Llewellin, E. W. and Del Bello, E. and Taddeucci, J. and Scarlato, P. and Lane, Stephen (2012) The thickness of the falling film of liquid around a Taylor bubble. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468 (2140). pp. 1041-1064. ISSN 1364-5021

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 lambda' (the ratio of the film thickness to the pipe radius) is a function only of the dimensionless parameter N-f = rho root gD(3)/mu, where rho is the liquid density, g the gravitational acceleration, D the pipe diameter and mu the dynamic viscosity of the liquid. For N-f less than or similar to 10, the dimensionless film thickness is independent of N-f with value lambda' approximate to 0.33; in the interval 10 less than or similar to N-f less than or similar to 10(4), lambda' decreases with increasing N-f; for N-f greater than or similar to 10(4) film thickness is, again, independent of N-f with value lambda' approximate to 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 lambda' (N-f), which is valid in the range 10 (1) < N-f < 10(5). 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.