Volume flux density cylinder

Figure 9-12. Cylindrically symmetric flow of soil water toward a root (flow arrows indicated only for outermost cylinder). The volume flux density, Jv, at the surface of each concentric cylinder times the cylinder surface area (2jrr x /) is constant in the steady state, so Jv then depends inversely on r, the radial distance from the root axis.

Let the flux density --dl of particles A(i) decreases in collisions with particles B(j) only due to process 3. Since the I value is referred to unit surface and time, the decrease in the flux density during passing the dx distance is equal to the process rate W3 multiplied to the volume of a cylinder with the unit surflice area of the base and height dx, i.e.. 

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