Liquid Film Thickness in Micro-Scale Two-Phase Flow

Abstract

Liquid film formed between confined vapor bubble and tube wall in micro-scale two phase flow plays an important role in heat exchangers and chemical reactors, since local heat and mass transfer is effectively enhanced at the thin liquid film region (Taha and Cui, 2006). However, characteristics of the liquid film in micro-scale two phase flows are not fully understood, and thus designing two-phase flow systems still remains as a difficult task. It is reported that the thickness of the liquid film is one of the most important parameters for predicting two phase flow heat transfer in micro tubes, see Thome et al., 2004; Kenning et al., 2006; Qu and Mudawar, 2004; Saitoh et al., 2007. For example, in the three zone evaporation model proposed by Thome et al. (2004), initial liquid film thickness is one of the three unknown parameters which must be given from experimental studies. Many researches have been conducted to investigate the characteristics of liquid film both experimentally and theoretically. Taylor (1961) experimentally obtained mean liquid film thickness in a slug flow by measuring the difference between bubble velocity and mean velocity. Highly viscous fluids, i.e. glycerol, syrup-water mixture and lubricating oil, were used so that wide capillary number range could be covered. It was found that the ratio of bubble velocity to mean velocity approaches an asymptotic value of 0.55. This asymptotic value was re-evaluated by Cox (1964), which was reported to be 0.60. Schwartz et al. (1986) investigated the effect of bubble length on the liquid film thickness using the same method as Taylor (1961). It was reported that longer bubbles move faster than shorter ones. Bretherton (1961) proposed an analytical theory for the bubble profile and axial pressure drop across the bubble using lubrication equations. Assuming small capillary number, it is shown that the dimensionless liquid film thickness can be scaled by an exponential function of capillary number, Ca2/3. Liquid film thickness can also be measured from the temperature change of the channel wall under the assumption that the whole liquid film on the wall evaporates and the heat is wholly consumed by the evaporation of the liquid film. Cooper (1969) measured liquid film thickness with this method and investigated the bubble growth in nucleate pool boiling. Moriyama and Inoue (1996) measured liquid film thickness during a bubble expansion in a narrow gap. It was reported that liquid film thickness is affected by the viscous boundary layer in the liquid slug when acceleration becomes large. Their experimental data was correlated in terms of capillary number, Bond number and dimensionless boundary layer thickness. Heil (2001) numerically investigated the inertial