Chapter 6 – Forces  207

and will elute first from the bottom of the column. This enables separation of hydrophobic

and hydrophilic biomolecules.

6.2.2  CENTRIFUGATION TOOLS

Sedimentation methods can be used to purify and characterize different components in in

vitro biological samples. They rely on the formation of a sedimented pellet when it is spun in

a centrifuge, depending on the frictional viscous drag of the sample and its mass. Quantitative

measurements may be made using analytical ultracentrifugation, which generates centri­

petal forces ~300,000 times that of gravity and also have controlled cooling to avoid localized

heating in the sample, which may be damaging in the case of biological material. By estimating

the sedimentation speed, we can infer details of the size and shape of biological molecules

and large complexes of molecules, as well as their molecular mass. Balancing the centripetal

force on a particle of mass m being spun at angular velocity ω at a radius r from the axis of

rotation with the buoyancy force from the displacement of the solvent by the particle and the

viscous drag force due to moving through the solution with sedimentation speed v leads to a

relation for the sedimentation coefficient s:

(6.1)

s

v

r

m

solvent

particle

=

=

−

(

)

ω

ρ

ρ

γ

2

1

/

where

ρ is the density

γ is the frictional drag coefficient

Diffusion causes the shape of the sedimenting boundary of the spun solution to spread with

time. This can be monitored using either optical absorption or interference techniques,

allowing both the sedimentation coefficient and the translation diffusion coefficient D to be

determined. The Stokes–​Einstein relationship (see Chapter 2) is then used to determine γ

from D, which can be used to estimate the molecular mass.

A mix of different biological molecules (e.g., several different enzymes) may sometimes

be separated on the basis of sedimentation rates in a standard centrifugation device, and a

density gradient of suitable material (sucrose and cesium chloride are two commonly used

agents) is created, such that there is a higher density of that substance toward the bottom

of a centrifuge tube. By centrifuging the mix into such a gradient, the different chemicals

may separate out as bands at different heights in the tube and subsequently be extracted as

appropriate.

Field flow fractionation is a hydrodynamic separation technique that involves forward

flow of a suspension of particles in a sample flow cell plus an additional hydrodynamic force

applied normal to the direction of this flow. This perpendicular force is typically provided

by centrifugation of the whole sample flow cell. Particles with a higher sedimentation coef­

ficient will drift toward the edge of the flow cell due to this perpendicular force more rap­

idly than particles with a lower sedimentation coefficient. Under nonturbulent laminar flow

conditions, known as “Poiseuille flow” (see Chapter 7) in a typical cylindrical-​shaped pipe

containing the sample, the speed profile of the fluid normal to the pipe long axis is parabolic

(i.e., maximum in the center of the pipe, zero at the edges); thus, the particles with higher

sedimentation coefficients are shifted more from the fastest on-​axis flow lines on the pipe

and will have a smaller drift speed through the flow cell. This therefore enables particles to

be separated on the basis of sedimentation coefficient—​put simply, to separate larger from

smaller particles.

Microfluidics can use these principles to separate out different biological components on

the basis of flow properties. Here, flow channels are engineered to have typical widths on the