However, in order to derive a characteristic length scale of a particle, it is necessary to make assumption about its geometric shape. Currently, we assume that all particles are spherical. Accordingly, the representative diameter of a class j particle can be written as

(6–4)

The sphere-equivalent surface area of a class j particle is then given as

(6–5)

In the above equations,

(6–6)

and

(6–7)

are respectively the "unit" diameter and the "unit" surface area of the bulk species in particle core.