p1u1 + p2u2 = 0 or k1ρ1u1 + k2ρ2u2 = 0 (3).
From (2) (3) we find by elementary algebra
u1/p2 = −u2/p1 = (u1 − u2)/(p1 + p2) = (u1 − u2)/P,
and therefore
p2u1 = −p2u2 = p1p2(u1 − u2)/P = k1k2ρ1ρ2(u1 − u2)/P
Hence equations (1) (2) gives
| dp1 | + | CP | (p1u1) = 0, and | dp2 | + | CP | (p2u2) = 0; |
| dx | k1k2 | dx | k1k2 |
whence also substituting p1 = k1ρ1, p2 = k2ρ2, and by transposing
| ρ1u1 = − | k1k2 | dρ1 | , and ρ2u2 = − | k1k2 | dρ2 | . |
| CP | dx | CP | dx |
We may now define the “coefficient of diffusion” of either gas as the ratio of the rate of flow of that gas to its density-gradient. With this definition, the coefficients of diffusion of both the gases in a mixture are equal, each being equal to k1k2/CP. The ratios of the fluxes of partial pressure to the corresponding pressure-gradients are also equal to the same coefficient. Calling this coefficient K, we also observe that the equations of continuity for the two gases are