Page 192 - An Introduction to Microelectromechanical Systems Engineering

Microfluidics for Biological Applications 171

capillary into a larger container of sample, or addition of liquid to a well at the
mouth of a channel on a chip, liquid is drawn into the channel without the applica-
tion of additional pressure.
Electrophoretic flow can be induced only in liquids or gels with ionized parti-
cles. The application of a voltage across the ends of the channel produces an electric
field along the channel that drives positive ions through the liquid toward the nega-
tive terminal and the negative ions to the positive terminal [see Figure 6.1(b)]. Neu-
tral particles in the channel are not directly affected by the field. The velocity of the
ions is proportional to the electric field and charge and inversely related to their size
[2]. In liquids, velocity is also inversely related to the viscosity, while in gels the
velocity depends on porosity.
Electroosmotic flow occurs because channels in glasses and plastics tend to have
a fixed charge on their surfaces. In glasses, silanol (SiOH) groups at the walls are
deprotonated in solution (they lose the hydrogen as a positive ion), leaving the sur-
face with a negative charge [3]. These negative ions then attract a diffuse layer of
positive ions, forming a double layer in the liquid [see Figure 6.1(c)]. The layer of
positive ions is not tightly bound and can move under an applied electric field.
When this sheath of ions moves, it drags the rest of the channel volume along with
it, creating electroosmotic flow. In contrast to pressure-driven flow, the velocity at
the center of the channel is about the same or slightly less, giving the fluid a flat
velocity profile. This plug flow is advantageous in many situations in biological
analysis where the spreading of a short-length sample into neighboring regions of a
channel is not desired. Electroosmotic pumping works best with small-dimension
channels. Flow velocities can range from a few micrometers per second to many mil-
limeters per second.
Electrophoretic flow and electroosmotic flow can be grouped together under
the heading of electrokinetic flow; indeed, both occur simultaneously in ionic solu-
tions with an applied electric field. The one that dominates depends on the details of
the solution and walls. Manufacturers of analysis equipment employing electroki-
netic flow generally design the system so that only one dominates. For example in
gel electrophoresis, the solution is a porous gelatinous medium, which cannot move
as a liquid would in electroosmosis. Instead, the charges percolate electrophoreti-
cally under the effect of the electric field through the porous gel. Alternatively, a liq-
uid buffer solution can be used in microchannels. Electroosmosis can dominate,
pushing the bulk of the flow in one direction. Positive ions within this bulk flow
move even faster relative to the bulk solution, while negative ions move in the oppo-
site direction with respect to the bulk solution, giving them a slower net velocity [3].

Mixing in Microfluidics
Volumetric flow rates in microscale channels are of course much lower than in mac-
roscopic channels, such as the water pipes in a building. The Reynolds number is
useful for comparing flows of different fluids in channels of dimensions that vary
over orders of magnitude. The Reynolds number is a dimensionless number related
to the ratio of kinetic energy in the fluid to the rate of loss of energy to friction. It is
given by ρ•ν•D/µ, where ρ is the fluid density, ν is the average velocity, D is the
diameter or equivalent “hydraulic diameter” of the channel, and ρ is the absolute
viscosity. For Reynolds numbers below about 2,300 for a tube with circular cross