Eric K. Dao and Vemuri Balakotaiah

Experiments were conducted to study wave occlusion on falling films in a vertical pipe. Aqueous solutions of glycerine with viscosities in the range 22 to 1250 cp were used. Pipe diameters were varied in the range 0.635 to 1.5875 cm. For each case, the critical liquid flow rate at which the free falling wavy annular flow transforms into slug flow due to wave occlusion was determined. A correlation was found between the critical flow rate (q) expressed in terms of the liquid Reynolds number at occlusion (Re_LS = 4q/pnLD) and two dimensionless groups influencing the transition, the Kapitza number, Ka = s/[nLg)1/3mL] , and the Bond number, Bo = rL_gD2/s. The correlation was found to be Re_LS = 0.062 Ka ^4/3 Bo^2/3 and valid in the range 0.1 < Re_LS < 200, 0.2< Ka < 55 and 7 < Bo < 50.

A simplified two-equation model relating the dimensionless flow rate and film thickness was developed to predict wave occlusion. The model was analyzed in the travelling wave coordinate system in the limit of very small ReLS using local bifurcation techniques to predict the critical flow rate and wave velocity at occlusion as a function of the Kapitza and Bond numbers.