Pressure drop and bubble velocity in Taylor flow through square microchannel

Interface tracking simulations of gas–liquid Taylor flow in horizontal square microchannels were carried out to understand the relation between the pressure drop in the bubble part and the curvatures at the nose and tail of a bubble. Numerical conditions ranged for 0.00159 ≤ Ca_T ≤ 0.0989, 0.0817 ≤ We_T ≤ 25.4, and 8.33 ≤ Re_T ≤ 791, where Ca_T, We_T, and Re_T are the capillary, Weber, and Reynolds numbers based on the total volumetric flux. The dimensionless pressure drop in the bubble part increased with increasing the capillary number and the Weber number. The curvature at the nose of a bubble increased and that at the tail of a bubble decreased as the capillary number increased. The variation of the curvature at the tail of a bubble was more remarkable than that at the nose of a bubble due to the increase in the Weber number, which was the main cause of large pressure drop in the bubble part at the same capillary number. The relation between the bubble velocity and the total volumetric flux was also discussed. The distribution parameter of the drift-flux model without inertial effects showed a simple relation with the capillary number. A correlation of the distribution parameter, which is expressed in terms of the capillary number and the Weber number, was developed and was confirmed to give good predictions of the bubble velocity.