Microfluidics and Nanofluidics

, Volume 17, Issue 2, pp 359–373 | Cite as

Time limitations and geometrical parameters in the design of microfluidic comparators

Research Paper


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.


Lab-on-a-chip Droplets Cells Microfluidic manometer Mechanical properties Hydrodynamic resistance 

List of symbols


Circular channel radius


Sensing channel capacitance


Entrance channel capacitance


Exit channel capacitance


Capacitance generated by the tubing connecting the device to the injection reservoirs


Particle diameter measured directly from micrographs


Square channel hydraulic diameter, equivalent to H


Young modulus


Interface position at different point of the control volume


Device height, in the square channel it is also its width and hydraulic diameter


Hydrodynamic resistance


Sensing channel volumetric flow rate


Reference channel volumetric flow rate


Exit channel volumetric flow rate


Sensing channel length


Pressure scalar field


Average channel pressure


Injection pressure


Injection pressure varied during calibration procedure


Outlet pressure at the device outlet


Sample channel mass flow rate


Reference channel mass flow rate


Reynolds number


Sensing channel resistance


Entrance channel resistance


Exit channel resistance


Resistance generated by the tubing connecting the device to the injection reservoirs




Average channel velocity


Velocity vector field


Velocity leaving the control volume through the measuring channel

\(\overline{{u_{out} }}\)

Average velocity leaving the control volume through the measuring channel


Interface position at the measuring point


Measuring channel width


Horizontal coordinate


Vertical coordinate


Coordinate perpendicular to the paper plane


Proportionality constant


Proportionality constant that depends on the junction geometry


Positive and real constant


Induced hydrodynamic resistance


Small changes in injection pressure during manometer calibration


Induced interface displacement


Channel length used in the capacitance calculations


Dynamic viscosity of the media


Inertial unsteady timescale


Kinematic viscosity


Poisson ratio


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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