Shrinking microbubbles with microfluidics: mathematical modelling to control microbubble sizes

Microbubbles have applications in industry and life-sciences. In medicine, small encapsulated bubbles (<10 μm) are desirable because of their utility in drug/oxygen delivery, sonoporation, and ultrasound diagnostics. While there are various techniques for generating microbubbles, microfluidic methods are distinguished due to their precise control and ease-of-fabrication. Nevertheless, sub-10 μm diameter bubble generation using microfluidics remains challenging, and typically requires expensive equipment and cumbersome setups. Recently, our group reported a microfluidic platform that shrinks microbubbles to sub-10 μm diameters. The microfluidic platform utilizes a simple microbubble-generating flow-focusing geometry, integrated with a vacuum shrinkage system, to achieve microbubble sizes that are desirable in medicine, and pave the way to eventual clinical uptake of microfluidically generated microbubbles. A theoretical framework is now needed to relate the size of the microbubbles produced and the system's input parameters. In this manuscript, we characterize microbubbles made with various lipid concentrations flowing in solutions that have different interfacial tensions, and monitor the changes in bubble size along the microfluidic channel under various vacuum pressures. We use the physics governing the shrinkage mechanism to develop a mathematical model that predicts the resulting bubble sizes and elucidates the dominant parameters controlling bubble sizes. The model shows a good agreement with the experimental data, predicting the resulting microbubble sizes under different experimental input conditions. We anticipate that the model will find utility in enabling users of the microfluidic platform to engineer bubbles of specific sizes.