Characterising fluid flow and solute transport in a gravity driven microfluidic system with surface tension effects

Advanced microfluidic systems are increasingly important for evaluating safety and efficacy in pharmaceutical drug development. For drugs with complex mechanisms of action, it is crucial to understand and control the mixing of relevant compounds and biomolecules in these systems, which in turn requires a detailed understanding of the fluid flow.



We consider a two-dimensional representation of a microfluidic system consisting of two vertical wells connected by a narrow horizontal channel. Fluid flow is gravity-driven and induced by tilting the device, and we work in the regime in which capillary forces are appreciable. We consider driving oscillations for which the Reynolds number is of order unity, and the capillary number is small.



By exploiting the small capillary number and channel aspect ratio, we obtain a reduced ODE model for the volume flow rate through the channel, which depends on the pressure difference between the wells. We analyse how this flow rate depends on the amplitude and frequency of the oscillations and consider the further reductions possible in the limit of low or high frequency oscillations. Furthermore, we examine the effect of contact angle hysteresis and show that this can significantly impact the expected flow rate.



Finally, we discuss how the volume flow rate can be used to determine the full two-dimensional flow profile within the system and hence quantify the mixing of solutes. We discuss how this model can be applied to experimental work, for example to identify the optimal operating regimes for a desired mixing effect.