Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 10

2.6.1.6 Ohmic model for electrolyte solutions .......................................................................63
2.6.2 Electrophoresis............................................................................................................64
2.6.3 Dielectrophoresis .........................................................................................................65
2.7 Magnetic and Electromagnetic Effects ............................................................................................. 66
2.7.1 Magnetic effects..........................................................................................................66
2.7.1.1 Electromagnetic effects............................................................................................68
2.8 Scaling Law and Fluid Flow in Microscale ....................................................................................... 68
References ........................................................................................................................................... 71

2.1 TRANSPORT PHENOMENA
Transport phenomena in micromixers can be described theoretically at two basic levels: molecular
level and continuum level. The two different levels of description correspond to the typical length scale
involved. Continuum model can describe most transport phenomena in micromixers with a length
scale ranging from micrometers to centimeters. Most micromixers for practical applications are in this
range of length scale. Molecular models involve transport phenomena in the range of one nanometer to
one micrometer. Mixers with length scale in this range should be called “nanomixer.” The term
“micromixer” in this topic will cover devices with submillimeter length dimension.
At the continuum level, the fluid is considered as a continuum. Fluid properties are defined
continuously throughout the space. At this level, fluid properties, such as viscosity, density, and
conductivity, are considered as material properties. Transport phenomena can be described by a set of
conservation equations for mass, momentum, and energy. These equations of change are partial
differential equations, which can be solved for physical fields in a micromixer, such as concentration,
velocity, and temperature.
Miniaturization technologies have pushed the length scale of microdevices further. In the event of
nanotechnology, scientists and engineers will encounter more phenomena at molecular level. At this
level, transport phenomena can be described through molecular structure and intermolecular forces.
Because many micromixers are used as microreactors, a fundamental understanding of molecular
processes is important for designing devices with length scale in the micrometer to centimeter range.

2.1.1 Molecular level
At molecular level, the simplest description of transport phenomena is based on the kinetic theory of
diluted monatomic gases, which is also called the Chapman-Enskog theory. The interaction between
nonpolar molecules is represented by the Lennard-Jones potential, which has an empirical form of:

4 3 c ij s
r

6

12

d ij s
r

f ij ð r Þ¼ ; (2.1)

where s is the characteristic diameter of the molecule, r is the distance between the two molecules, and
3 is the characteristic energy, which is the maximum energy of attraction between the molecules. In
(2.1) , the term ( s / r ) 12 represents the repulsion potential, while the term ( s / r ) 6 represents the attraction
potential between the pair of molecules. The coefficients c ij and d ij are determined by molecule types