Time limitations and geometrical parameters in the design of microfluidic comparators

Abstract

The ability to control the flow of particles (e.g., droplets and cells) in microfluidic environments can enable new methods for synthesis of biomaterials (Mann and Ozin in Nature 382:313–318, 1996), biocharacterization, and medical diagnosis (Pipper et al. in Nat Med 13:1259–1263, 2007). Understanding the factors that affect the particle passage can improve the control over the particles’ flow through microchannels (Vanapalli et al. in Lab Chip 9:982, 2009). The first step to understand the particle passage is to measure the resulting flow rate, induced pressure drop across the channel, and other parameters. Flow rates and pressure drops during passage of a particle through microchannels are typically measured using microfluidic comparators. Since the first microfluidic comparators were reported, a few design factors have been explored experimentally and theoretically, e.g., sensitivity (Vanapalli et al. in Appl Phys Lett 90:114109, 2007). Nevertheless, there is still a gap in the understanding of the temporal and spatial resolution limits of microfluidic comparators. Here we explore, theoretically and experimentally, the factors that affect the spatial and temporal resolution. We determined that the comparator sensitivity is defined by the device geometry adjacent and upstream the measuring point in the comparator. Further, we determined that, in order of importance, the temporal resolution is limited by the convective timescale, capacitive timescale due to channel expansion, and unsteady timescale due to the flow inertia. Finally, we explored the flow velocity limits by characterizing the transition between low to moderate Reynolds numbers (Re <<1 to Re ~ 50). The present work can guide the design of microfluidic comparators and clarify the limits of this technique.