294 7.6  High-Throughput Techniques

approximation can be made by using the hydraulic radius parameter in place of a, which is

defined as 2A/​s where A is the cross-​sectional area of the channel and s is its contour length

perimeter. For well-​defined noncircular cross-​sections, there are more accurate formulations,

for example, for a rectangular cross-​sectional channel of height h that is greater than the

width w, an approximation for RH is

(7.15)

R

l

wh

w h

H ^≈

−

(

)

(

)

12

1

0 63

1 57

2

ι

.

.

tanh

/

The hydraulic resistance is a useful physical concept since it can be used in fluidic circuits in

the same way that electrical resistance can be applied in electrical circuits, with the pressure

drop in a channel being analogous to the voltage drop across an electrical resistor. Thus, for

n multiple microfluidic channels joined in series,

(7.16)

R

R

series,tota

i

n

H i

l ⁼

−^∑

1

,

while, for n channels joined in parallel,

(7.17)

1

1

1

R

R

parallel,total

i

n

H i

=

−^∑

,

Microfluidics devices consist not just of channels but also of several other components to con­

trol the fluid flow. These include fluid reservoirs and pressure sources such as syringe pumps,

but often gravity-​feed systems, for example, a simple open-​ended syringe, which is placed at

a greater height than the microfluidics channels themselves, connected via low-​resistance

Teflon tubing, which generates a small fluid flow but often works very well as it benefits from

lower vibrational noise compared to automated syringe pumps. Other mechanisms to gen­

erate controllable flow include capillary action, electroosmotic methods, centrifugal systems,

and electrowetting technologies. Electrowetting involves the controllable change in contact

angle made by the fluid on the surface of a flow cell due to an applied voltage between the

surface substrate and the fluid.

Other components include valves, fluid/​particle filters, and various channel mixers.

Mixing is a particular issue with laminar flow, since streamlines in a flow can only mix due

to diffusion perpendicular to the flow, and thus mixing is in effect dependent on the axial

length of the pipe (i.e., significant mixing across streamlines will not occur over relatively

short channel lengths; see Worked Case Example 7.2). Often, such diffusive mixing can be

facilitated by clever designs in channel geometries, for example, to introduce sharp corners to

encourage transient turbulence that enables greater mixing between streamline components

and similarly engineer herringbone chevron-​shaped structures into the channels that have

similar effects. However, differences in diffusion coefficients of particles in the fluid can also

be utilized to facilitate filtering (e.g., one type of slow diffusing particle can be shunted into a

left channel, while a rapid diffusing particle type can be shunted into a right channel). Several

types of microvalve designs exist, including piezoelectric actuators, magnetic and thermal

systems, and pneumatic designs.

Microfluidics often utilizes flow cells made from the silicone compound PDMS (discussed

previously in the context of cell stretching devices in Chapter 6). The combination of mech­

anical stability, chemical inertness, and optical transparency makes PDMS an ideal choice for

manufacturing flow cells in microfluidics devices, which involve some form of optical detec­

tion technique inside the flow cell, for example, detection of fluorescence emissions from

living cells. Microfabrication methods can be used to generate a solid substrate mold into

which liquid, degassed PDMS can be poured. Curing the PDMS is usually done either with

UV light exposure and/​or through baking in an oven. The cured PDMS can then be peeled