Biomedical Engineering Reference
In-Depth Information
C h a p t e r 6
Transport of Biochemical Species and
Cellular Microluidics
6.1 Introduction
In general, biotechnology deals with the manipulation of biological targets, such as
DNA strands, proteins, cells, or cluster of cells. One of the goals of biotechnology
is
the manipulation of very small amounts of targets, even a single target, for example
a single cell. To do so, different methods are used successively to allow for more and
more selectivity. Figure 6.1 schematizes the different methods from the less selective to
the most selective.
The first step is the transport by microfluidic means. For example, the targets are to
be extracted and concentrated from a liquid sample, or they have to be guided towards
a reactive surface, mixed with a reagent, dispersed in another liquid, or transported to
a mass spectrometer. In any case, the knowledge of transport mechanism is mandatory.
The next steps in selectivity depend on the particular application.
Transport phenomena depend on the velocity of the carrier flow and on the size
and nature of the biological objects. It is characterized by the Peclet number (Pe)
that has been defined in Chapter 1. Figure 6.2 schematizes the different observed be-
havior. Very small particles diffuse while being transported; their location becomes
stochastic. Larger particles have a lesser diffusion and are guided by the carrier flow
streamlines. At larger velocities, they gain inertia and can abandon the streamlines
when the curvature is important. Still larger (and heavier) particles sediment.
We present first the governing equations of transport (advection-diffusion equa-
tion) under the continuum assumption and their nondimensional form, which intro-
duces the characteristic Peclet number, and then we analyze some characteristic cases,
such as the flow in a microchannel, and present the Taylor-Aris model. This model will
lead us to the major problem of mixing in microfluidics. To complete the approach,
Langevin's equation is introduced for particles experiencing a strong Brownian motion
and a particle trajectory approach for larger particles less affected by the Brownian mo-
tion. Applications of particle trajectory to field flow fractionation and chromatography
columns are presented next. Finally, a section is devoted to cellular microfluidics.
6.2 Advection-Diffusion Equation
6.2.1 Governing Equation for Transport
As we have done for the mass conservation equation and for the momentum equa-
tion, we write the concentration balance in an elementary volume (D
x
, D
y
). For
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