Page 31 - Introduction to Colloid and Surface Chemistry
P. 31
22 Kinetic properties
is attained, when the driving force on the particle and the resistance
of the liquid are equal:
m(l-vp)g=f (2 A)
where / is the frictional coefficient of the particle in the given
medium.
For spherical particles the frictional coefficient is given by Stokes'
law
/ = 67^ (2.2)
where i\ is the viscosity of the medium and a the radius of the particle.
Therefore, if p2 is the density of a spherical particle (in the
dissolved or dispersed state (i.e. P2 = 1/v)), then
4 3i \ *
1 m (P2 ~ P)g = faya —
dt
2
<** = 2a (p2 - p)g
or (2 3)
dt 9j l
The derivation of Stokes' law assumes that:
1. The motion of the spherical particle is extremely slow.
2. The liquid medium extends an infinite distance from the particle -
i.e. the solution or suspension is extremely dilute.
3. The liquid medium is continuous compared with the dimensions of
the particle. This assumption is valid for the motion of colloidal
particles, but not for that of small molecules or ions which are
comparable in size with the molecules constituting the liquid
medium.
For spherical colloidal particles undergoing sedimentation, diffusion
or electrophoresis, deviations from Stokes' law usually amount to
much less than 1 per cent and can be neglected.
