Dynamics of Haines jumps for compressible bubbles in constricted capillaries

Abstract

AbstractThe unsteady, impulsive motion of a compressible bubble expanding out of a constricted capillary is quantified with a macroscopic momentum balance. Numerical solution demonstrates the importance of the Ohnesorge number, the geometry of the constriction, the length of the initial gas bubble, and the surface tension, density, and unconstricted capillary radius, which combine to form a characteristic scaling time. Experimental data for the position of the bubble front as a function of time confirm the theoretical result when the time scale for the bubble jump is longer than that required to achieve fully developed parabolic flow. Theory also predicts the capillary number of the bubble jump which, in conjunction with previous theoretical results, determines the time to snap‐off of gas bubbles moving through constricted capillaries. Excellent agreement is found with existing experimental data for Ohnesorge numbers ranging from 5 × 10−3 to 0.3.