PHYSICS

6.2.5. Stokes' Law
When a sphere of radius R moves with velocity V through a
stationary fluid and if the motion is nonturbulent, then the
viscous drag (F) on the sphere is given by Stokes' law:
F s=61r1]RV
(6.12)
where TJ is the viscosity of the fluid.
6.2.6. Erythrocyte Sedimentation Rate
The coefficient of viscosity (TJ) depends on temperature; the
approximate viscosity-temperature relation is:
b
1]=a.eT (6.13)
where a and b are constants and T is the absolute temperature.
The erythrocyte sedimentation rate (ESR) measures the distance
red blood cells will fall along the length of a vertical tube
over a given time period (e.g., I hour).
Sedimentation is normally accelerated as the temperature rises
and the viscosity decreases [see equation (6.13)]:
I
V==- (6.14)
1]
Sedimentation of red cells depends on the forces resisting
sedimentation (e.g. negative charges on the red cells surface, the
opposite stream of plasma, rigidity of the red cells) and the
forces accelerating sedimentation (e.g. anemia, plasma proteins).
Changes ESR values are associated with changes in plasma
proteins with can be caused with various diseases (e.g. rheumatoid
arthritis, temporal arteritis, polymyalgia rheumatica, tuberculosis
and Hodgkin's).
6.2.7. PoiseuiIle's Law of Flow
The French physicist Poiseuille showed experimentally that the
volume (Q) of liquid flowing through a tube of length I is directly
proportional to the pressure difference (p J - p) driving the liquid, and
proportional to the fourth power of the tube radius (R). The laminar
flow of liquids in pi pes is described by Poiseuille's Law 0/Flow:
54
I 1r·R 4
Q =--;]'8T'(PI - pz)· (6.15)
Poiseuille's law of flow can be used to quantitative measure
the viscosity (TJ) of liquids.
6.2.8. Sedimentation
When a sphere falls in a viscous medium, it reaches a terminal
velocity when the retarding forces, viscosity (F, = 6·1r·TJ·R· V) and
buoyancy (FA =pm-V· g =~ .n.R 3 p m·g) equal the weight (m- g =
=~ .n.R 3 p s p
• g) of the sphere:
f.n . R 3 • Psp • g = ~ . tt . R 3 • Pm' g + 6 . n . 1] . R . V (6.16)
where m is the mass of sphere, R = ~ -
the radius of sphere, P sp
and Pm - the density of the sphere and medium, and TJ - the
viscosity of the medium.
2· g . R Z • t . (p - P )
Hence. · 1] - Sp m (6 • 17)
9·/
and the terminal velocity (also called sedimentation velocity) can
be determined as:
V = g. P sp -
Pm
2. R Z
1] 9
6.2.9. Physical Principles of Ultracentrifugation
(6.18)
The movement of spherical particles in a centrifuge tube
(fig. 6.8) eventually reach a terminal velocity determined
by the frictional force (F; = 6·n·TJ·R· V), centripetal force
mmV 2 2 V 2 )
( Fcp = .---- = m 11/UJ r = Pm UJ r
r
55