Panel A is a depiction of the physical system and the concentration profile along the x-axis at time less than zero. The concentration is zero everywhere.
Panel B is a depection of the physical system and the concentration profile along the x-axis at time equal zero (like the Big Bang!). At x < 0, the concentration is suddenly raised to a value of Co everywhere to the left of the origin, x=0. This condition represents a step function input and is a suitable approximation of some upstream source zone that has a constant concentration. The concentration to the right of the origin (x > 0) is still zero.
Panel C is a depiction of the physical system and the concentration profile aling the x-axis at some time greater than zero. The source mass has moved to the right of the origin a distance determined by the species velocity and dispersed along the translational front proportional to the dispersivity in the system.
The analytical solution (Ogata-Banks) is
The solution is applicable for porous media flow, where the velocity (below) is the mean section velocity (seepage velocity divided by the porosity). The solution can also be used with streams and pipes (porosity = 1).
Detailed Explaination (Under Construction)