92168.pdf

Kinetic properties 27

The proportionality factor D is called the diffusion coefficient. It is

not strictly a constant, since it is slightly concentration-dependent.

Equations (2.4) and (2.5) can be derived using equation (2,8), as

follows.

Brownian displacement equation (2.4)

Consider a plane AB (Figure 2.2) passing through a dispersion and

separating regions of concentration Ci and c 2 , where c\ > c 2. Let the

average Brownian displacement of a given particle perpendicular to

AB be x in time t. For each particle, this displacement has equal

probability of being 'left to right' or 'right to left'. The net mass of

particles displaced from left to right across unit area of AB in time t

is, therefore given by

—2

m —

2x

„.. „

If x is small,

dc

Therefore,

1 dc_ 2

OT = X

2dx

(2.10)

From equation (2.8)

dc

m = -D—t

dx

(2.11)

1

q

x E

1

1

I x

Figure 2.2