TY - JOUR

T1 - The thickness of the falling film of liquid around a Taylor bubble

AU - Llewellin, E. W.

AU - Del Bello, E.

AU - Taddeucci, J.

AU - Scarlato, P.

AU - Lane, Stephen

PY - 2012/4/8

Y1 - 2012/4/8

N2 - 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.

AB - 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.

KW - gas slug

KW - slug flow

KW - long bubble

KW - turbulent falling film

KW - pipe flow

KW - transitional flow

KW - VERTICAL TUBES

KW - SLUG FLOW

KW - STAGNANT LIQUIDS

KW - MASS-TRANSFER

KW - GAS-BUBBLES

KW - ROUND TUBE

KW - VELOCITY

KW - RISE

KW - EXPLOSIONS

KW - REYNOLDS

UR - http://www.scopus.com/inward/record.url?scp=84859568900&partnerID=8YFLogxK

U2 - 10.1098/rspa.2011.0476

DO - 10.1098/rspa.2011.0476

M3 - Journal article

VL - 468

SP - 1041

EP - 1064

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2140

ER -