Diffusion with convection
The transport of particles arising from the motion of a streaming fluid is called convection. If for the moment we ignore diffusion, then the flux of particles through an area Ain an interval ∆t when the fluid is flowing at a velocity can be calculated in the way we have used several times before (by counting the particles within a distance v ∆t), and is
J=
This J is called the convective flux. The rate of change of concentration in a slab of thickness l and area Ais, by the same argument as before and assuming that the velo city does not depend on the position,
When both diffusion and convection occur, the total change of concentration in a region is the sum of the two effects, and the generalized diffusion equation is
A further refinement, which is important in chemistry, is the possibility that the concentrations of particles may change as a result of reaction. When reactions are included in eqn 21.71 (Section 24.2), we get a powerful differential equation for discussing the properties of reacting, diffusing, convecting systems and which is the basis of reactor design in chemical industry and of the utilization of resources in living cells.
