Microfluidics and Nanofluidics

, Volume 17, Issue 2, pp 359–373

Time limitations and geometrical parameters in the design of microfluidic comparators

Research Paper

DOI: 10.1007/s10404-013-1302-x

Cite this article as:
Cartas-Ayala, M.A. & Karnik, R. Microfluid Nanofluid (2014) 17: 359. doi:10.1007/s10404-013-1302-x

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.

Keywords

Lab-on-a-chipDropletsCellsMicrofluidic manometerMechanical propertiesHydrodynamic resistance

List of symbols

a

Circular channel radius

CR

Sensing channel capacitance

Centrance

Entrance channel capacitance

Cexit

Exit channel capacitance

Ctubing

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

D

Particle diameter measured directly from micrographs

DH

Square channel hydraulic diameter, equivalent to H

E

Young modulus

h

Interface position at different point of the control volume

H

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

HR

Hydrodynamic resistance

I

Sensing channel volumetric flow rate

Ireference

Reference channel volumetric flow rate

IRexit

Exit channel volumetric flow rate

L

Sensing channel length

p

Pressure scalar field

P′

Average channel pressure

P

Injection pressure

P*

Injection pressure varied during calibration procedure

Pexit

Outlet pressure at the device outlet

Q

Sample channel mass flow rate

Qreference

Reference channel mass flow rate

Re

Reynolds number

R

Sensing channel resistance

Rentrance

Entrance channel resistance

Rexit

Exit channel resistance

Rtubing

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

T

Time

u

Average channel velocity

\(\vec{u}\)

Velocity vector field

uout

Velocity leaving the control volume through the measuring channel

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

Average velocity leaving the control volume through the measuring channel

w

Interface position at the measuring point

W

Measuring channel width

x

Horizontal coordinate

y

Vertical coordinate

z

Coordinate perpendicular to the paper plane

\(\alpha^{*}\)

Proportionality constant

\(\alpha\)

Proportionality constant that depends on the junction geometry

\(\beta\)

Positive and real constant

R

Induced hydrodynamic resistance

P

Small changes in injection pressure during manometer calibration

y

Induced interface displacement

\(\lambda\)

Channel length used in the capacitance calculations

\(\mu\)

Dynamic viscosity of the media

\(\tau\)

Inertial unsteady timescale

\(\nu\)

Kinematic viscosity

\(\upsilon\)

Poisson ratio

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA