Implications of variable fluid resistance caused by start-up flow in microfluidic networks

Electrical circuit analogies are often used to design microfluidic systems because they simplify device design, providing simple relationships between fluid flow rate, driving forces, and channel dimensions. However, such approximations often significantly overestimate flow rates in situations where start-up energy losses from establishing kinetic head are similar in magnitude to the energy required to overcome viscous shear stresses, as is often the case within complex microfluidic networks. These reduced flows can be more accurately predicted within an electrical analogy framework that accounts for the nonlinear flow resistance generated on the transient regime of start-up flow. In this work, standard flow resistance expressions are modified to account for such effects, and the onset of nonlinear resistance is predicted by a dimensionless parameter, which is dependent on the Reynolds number and the channel length. As a demonstration, variable fluid resistance is shown to dramatically affect the flow performance of common microfluidic units such as T-junctions and serpentine channels, and the change in performance is accurately predicted. Experimental and theoretical analysis of T-junctions further shows that variable flow resistance causes the ratio of flows through the junction to converge toward unity with respect to an increasing total flow rate. In addition, serpentine channels are shown to exaggerate these start-up effects, owing to compounded energetic demand associated with changing a flow's direction. As a result, serpentine channels cause the ratio of flow rates exiting a T-junction to diverge from unity with respect to an increasing flow rate.