Numerical simulations to determine the size of microdroplets without visualization by measuring pressure fluctuations

A novel pressure-fluctuation-based method is proposed for measuring the size of microdroplets without the need for visualization through a microscope. In the present work, numerical simulations are carried out in a co-flow geometry to verify this concept. First, the droplet formation frequency is determined by applying the fast Fourier transform to measured pressure fluctuation data with respect to time at any point on the outer wall. Then, the size of dispersed phase microdroplets is determined using a relationship between dispersed-phase flow rate and the droplet formation frequency. The droplet size obtained using the pressure fluctuation method is compared with that from the volume fraction method, and it is found that the error is less than 5%. The deviation is attributed to the formation of satellite droplets in the simulations. The relationship between the nondimensional parameters flow-rate ratio, capillary number, and normalized droplet diameter is investigated systematically, and empirical relations are obtained through power-law regression. The effects of interfacial tension, flow-rate ratio, and viscosity ratio on the magnitude of pressure oscillations and the corresponding droplet size are studied. All the parameters are found to have significant effects on droplet size. The ability of the proposed method to predict microdroplet size is significant with regard to potential applications to biomedical systems and drug delivery.