Biophotonics_Concepts_to_Applications

The two basic categories offluidflow are laminarflow and turbulentflow. Fluids
in alaminarflowexhibit a smooth and constantflow, whereasturbulentflowis
characterized by vortices andflowfluctuations. For microfluidic systems theflow is
essentially laminar, whereas macroscopicflows are characterized by turbulentflows
that are random in space and time. The two basic factors that characterizefluidflow
are viscous forces and inertial forces. Theflow types are measured by the dimen-
sionlessReynolds numberRe, which is given by

Re¼

Inertial force

Viscous force

¼

quDh

l

¼

uDh

m

ð 11 : 5 Þ

Hereρis thefluid density,μis the dynamic viscosity (a measure of the internal
resistance of the channel),ν=μ/ρis the kinematic viscosity (the resistance toflow
under the influence of some force acting on thefluid), and u is the velocity of the
fluid. Thehydraulic diameterof the channel Dhdepends on the geometry of the
channel and is given by

Dh¼

4A

Pwet

ð 11 : 6 Þ

where A and Pwetare the cross-sectional area and the wetted perimeter (the surface
of the microfluidic channel that is in direct contact with the liquid) of the channel,
respectively. The value of Re depends on factors such as the shape, surface
roughness and aspect ratio (ratio of width to height) of the channel. For largefluid
channels the value of Re ranges from about 1500 to 2500. Its value is less than 100
for microfluidic channels, which represents a laminarflow.

Example 11.4Compare the hydraulic diameter of two square channels that

have channel dimensions of 50μm and 80μm, respectively.

Solution: (a) The cross-sectional area for the 50-μm channel is A(50

μm) = (50μm)^2 = 2500μm^2 and the perimeter is Pwet= 4(50μm) = 200

μm. Thus from Eq. (11.6) it follows that Dh(50μm) = 4(2500μm^2 )/(200

μm) = 50μm.

(b) Similarly, Dh(80μm) = 4(6400μm^2 )/(320μm) = 80μm.

Several examples from many types of microfluidic chips and associated interface
devices are listed in Table11.2. TheLab-on-a-Chip Catalogue(from the company
microfluidic ChipShop) is an example of an online resource for a wide variety of
microfluidic chips and implementation accessories [ 15 ].

330 11 Biophotonics Technology Applications