Microfluidic-drop networks consist of several stable drops-interconnected through microfluidic channels-in which organ models can be cultured long-term. Drop networks feature a versatile configuration and an air-liquid interface (ALI). This ALI provides ample oxygenation, rapid liquid turnover, passive degassing, and liquid-phase stability through capillary pressure. Mathematical modeling, e.g., by using computational fluid dynamics (CFD), is a powerful tool to design drop-based microfluidic devices and to optimize their operation. Although CFD is the most rigorous technique to model flow, it falls short in terms of computational efficiency. Alternatively, the hydraulic-electric analogy is an efficient "first-pass" method to explore the design and operation parameter space of microfluidic-drop networks. However, there are no direct electric analogs to a drop, due to the nonlinear nature of the capillary pressure of the ALI. Here, we present a circuit-based model of hanging- and standing-drop compartments. We show a phase diagram describing the nonlinearity of the capillary pressure of a hanging drop. This diagram explains how to experimentally ensure drop stability. We present a methodology to find flow rates and pressures within drop networks. Finally, we review several applications, where the method, outlined in this paper, was instrumental in optimizing design and operation.
Keywords: capillary pressure; fluid shear stress; hanging-drop network; hydraulic-circuit analogy; hydrostatic pressure; standing-drop network.