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

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.