Biomedical Engineering Reference
In-Depth Information
C h a p t e r 5
Diffusion of Biochemical Species
5.1 Introduction
In Chapters 2, 3, and 4 we have analyzed the motion of a liquid under the form
of microfluidics flow and the form of microfluidics drops (digital and droplet mi-
crofluidics). In reality, the fluid that has been studied in these chapters is a buffer
fluid — or carrier fluid — containing the micro- and nanoparticles, macromolecules,
or cells that are of interest.
In the rest of this topic, we focus on the behavior of the microparticles them-
selves in the buffer fluid. Different forces may act on the particles. At a microscopic
scale, diffusion is always present, assuming that the particles are sufficiently small.
This is the case for DNA, micromagnetic beads, and so fourth, but much less so for
large biological objects like cells. Often other physical phenomena superpose with
diffusion. In Chapter 6 we deal with convective transport problems, in Chapter 7
with biochemical reactions, in Chapter 9 with magnetic forces on magnetic beads,
and in Chapter 10 with electric forces on charged and neutral microparticles. In this
chapter we present the basis of the diffusion theory and the different approaches to
solve diffusion problems.
First, we analyze the basis of diffusion that is the random walk of particles due
to the Brownian agitation of the fluid molecules. Next we introduce the diffusion
equation of concentration and present some examples of applications in the bio-
technology domain, and then we introduce the discrete Monte-Carlo approach and
some applications to the diffusion of macromolecules in the human body.
5.2 Brownian Motion
Because Brownian motion is a microscopic scale movement, it is no wonder that
the Brownian motion was first discovered by biologists J. Ingenhousj and R. Brown
[1], the latter after the observation of pollen grains floating at the surface of a drop
of water.
In a gas or a liquid, there is an agitation of the molecules linked to temperature.
A molecule moves in a straight line until it collides with another molecule resulting
in a change of direction. The average linear displacement between two collisions is
called the mean free path.
In biotechnology, we deal with macromolecules and microparticles larger than
the fluid molecules. The basic scheme of displacement is the same; the molecules of
the carrier liquid collide with the macromolecules to make them perform a random
walk (Figure 5.1).
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