Mathematical modelling of a microfluidic system - the effect of surface tension #

Barnum Swannell, Sarah Waters, James Oliver, Daniela Ortiz Franyuti, Olivier Frey, Michal Rudnik

13:30 Tuesday in 4Q08.

Part of the Microfluidics and flow in porous media session.

Abstract #

Advanced microfluidic systems are increasingly important for evaluating safety and efficacy in pharmaceutical drug development. Understanding and controlling solute mixing in these systems is crucial for device design, operation, and interpreting experimental results. This in turn requires a detailed understanding of the fluid flow.

We consider a microfluidic system where fluid flow is gravity driven but capillary forces are appreciable and develop a continuum-based mathematical model to describe the flow. Exploiting the small capillary number and channel aspect ratio, we use asymptotic analysis to derive a reduced ODE model for the overall volume flow rate.

This model can be used to characterise the volume flow rate under a range of operating regimes. Our analysis highlights the importance of capillary effects, and in particular contact angle hysteresis, which can significantly alter the flow rate. Our model is extended to incorporate solute transport and thus provide a relationship between the flow rate and mixing in the system. We discuss applications to experimental work, which include identifying the optimal device operating regimes for a desired mixing effect, as well as informing the design of such systems more broadly.