300 7.6  High-Throughput Techniques

Worked Case Example 7.2:  Using Microfluidics

A microfluidics channel was constructed consisting of a cylindrical pipe with a diameter of

20 μm using a water-​based fluid of pH 7.5 with volume flow rate of 18.8 nL min⁻¹.

a

State with reasoning whether the flow is laminar or turbulent.

b

Derive Poiseuille’s law starting only from the definition of viscosity and the assumption

of laminar flow, incompressibility and that the fluid is Newtonian. In the case of the

aforementioned channel, what is the maximum flow speed?

Somewhere along the channel’s length, a second side channel joins this main

channel from the bottom to continuously feed small volumes of a solution of the pro­

tein hemoglobin at pH 5.5 at low speed such that the protein is then swept forward

into the main channel. After a given additional length L of the main channel, the

mixed protein at pH 7.5 is injected into a microscope flow cell.

c

If the protein has a lateral diffusion coefficient of 7.0 × 10⁻⁷ cm² s⁻¹ estimate, with

reasoning, what the minimum value of L should be. Comment on this in light of lab-​

on-​a-​chip applications for analyzing a single drop of blood.

(Assume that the density and dynamic viscosity of water are ~10³ kg m⁻³ and ~10⁻³ Pa · s,

respectively.)

FIGURE 7.7  Automated drift correction. A total internal reflected laser beam can be directed

on a split photodiode. When the sample is in focus the voltage from the left (VL) and right (VR)

halves of the photodiode are equal (a). When the sample is out of focus, (b) the voltages from

each half are not equal; this signal can be amplified and fed back into the z-​axis controller of the

nanostage to bring the sample back into focus.