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

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 λ ′ (the ratio of the film thickness to the pipe radius) is a function only of the dimensionless parameter , where ρ is the liquid density, g the gravitational acceleration, D the pipe diameter and μ the dynamic viscosity of the liquid. For , the dimensionless film thickness is independent of N f with value λ ′≈0.33; in the interval , λ ′ decreases with increasing N f ; for film thickness is, again, independent of N f with value λ ′≈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 λ ′( 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.