Compact Empirical Model for Droplet Generation in a Lab-on-Chip Cytometry System

This study describes the construction of a droplet generation speed compact empirical mathematical model for a flow-focusing microfluidic droplet generator. The application case is a portable, low-cost flow cytometry system for microbiological applications, with water droplet sizes of 50-70 micrometer range and droplet generation rates of 500-1500 per second. In this study, we demonstrate that for the design of reliable microfluidic systems, the availability of an empirical model of droplet generation is a mandatory precondition that cannot be achieved by time-consuming simulations based on detailed physical models. When introducing the concept of a compact empirical model, we refer to a mathematical model that considers general theoretical estimates and describes experimental behavioral trends with a minimal set of easily measurable parameters. By interpreting the experimental results for different water- and oil-phase flow rates, we constructed a minimal 3-parameter droplet generation rate model for every fixed water flow rate by relying on submodels of the water droplet diameter and effective ellipticity. As a result, we obtained a compact model with an estimated 5-10% accuracy for the planned typical application modes. The main novelties of this study are the demonstration of the applicability of the linear approximation model for droplet diameter suppression by the oil flow rate, introduction of an effective ellipticity parameter to describe the droplet form transformation from a bullet-like shape to a spherical shape, and introduction of a machine learning correction function that could be used to fine-tune the model during the real-time operation of the system.