Analysis of the diameter of microbubbles formed in a cross flow microchannel

Two microfluidic devices for generating microbubbles are considered in the study presented in this paper. The first device consists of a liquid channel and a gas channel that is perpendicular to each other. In this device, the microbubble diameter varies inversely with the liquid flow rate (i.e. with flow velocity) but at the expense of high pressure drop. This device is modified by introducing a solid structure in front of the orifice to become the second device. This modification causes an increase in fluid velocity only in front of the orifice. In this paper a model is developed for determining the diameter of microbubbles generated in both of these devices. The model is developed by balancing the forces acting on the microbubble during growth and at the moment of detachment from the orifice. The detachment of the microbubble is assumed to happen when the sum of all detaching forces equals the net attaching force acting on the microbubble during the growth. Non-slip boundary condition is assumed on the walls of the channels in this model. Based on these assumptions a mathematical model is developed and solved numerically for different values of liquid and gas flow rate to obtain the microbubble diameter at the moment of detachment. A MATLAB® code is developed for solving the force balance equation. The superiority of the second device over the first one is validated by comparing the results obtained from the models in both cases.