Design rules for pumping and metering of highly viscous fluids in microfluidics

The use of fluids that are significantly more viscous than water in microfluidics has been limited due to their high resistance to flow in microscale channels. This paper reports a theoretical treatment for the flow of highly viscous fluids in deforming microfluidic channels, particularly with respect to transient effects, and discusses the implications of these effects on the design of appropriate microfluidic devices for highly viscous fluids. We couple theory describing flow in a deforming channel with design equations, both for steady-state flows and for the transient periods associated with the initial deformation and final relaxation of a channel. The results of this analysis allow us to describe these systems and also to assess the significance of different parameters on various deformation and/or transient effects. To exemplify their utility, we apply these design rules to two applications: (i) pumping highly viscous fluids for a nanolitre scale mixing application and (ii) precise metering of fluids in microfluidics.