The effluent from a wastewater treatment plant is discharged to a river.
The plant fails to remove a trace organic contaminant of concern (A) that is originally absent from
the river, and the discharge rate is such that, at the point of discharge (z = 0, where z is
longitudinal distance along the river in the direction of motion), the cross - sectional average
concentration of contaminant is 0 . The contaminant sorbs to the sediments at the bottom of the
river via a first - order process and is subsequently biode - graded. The convection–dispersion
equation is
+ = D 2 − k t z z e z2 e A
where the effective diffusivity, De, the effective first - order rate constant, ke, and the water average
velocity, , are known.

Find (z) at steady state both upstream (z < 0) and downstream (z > 0) of the discharge point.