Diffusion in a single phase homogeneous system

At the beginning of diffusion, time t = 0 and the total amount of color having mass m is located at position x = 0. Because of the theoretically infinitely thin layer 5x of the color source, the initial concentration there is infinite and the concentrations at all other positions of the bar are zero. The solution of the diffusion equation (7-12) is immediately given as  

The values for A resulting from Eq. (7-21) are used in obtains the solution Eq. (7-18) and then one 

In the above case, half of the substance diffuses in the positive direction and the other half in the negative direction of the x-axis. 

If an absolute barrier is now assumed to exist at position x = 0 so that diffusion can occur only in the direction x 0 then the half of m diffusing in the x 0 is reflected by the barrier and overlaps the other half diffusing in the x 0 direction (Fig. 7-5a). Because the symmetry of the curve (7-22) with respect to the source at the position x = 0, one obtains a solution for diffusion in a half open media that is double the value of Eq. (7-22)  

The requirement of a barrier layer at x = 0 is expressed mathematically by the boundary condition of dcldx = 0 at x = 0. 

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