Kinetic equations for reactions with diffusion

Note that ignoring the effects associated with diffusion of substances reacting in solution requires substantiation, since the contact of reagent molecules is achieved due to stirring and diffusion. 

Consider a diffusionless equation describing an evolution of concentration of two substances X, Y, [X] = x, [Y] = y with time  

Let us assume that a reaction is carried out in a reactor shaped as a thin, long pipe. 

Let us now allow the possibility of diffusion of the molecules X, Y along the reactor axis (the diffusion in lateral directions may be neglected). The variables x, y, functions of time t, also become dependent on the distance r from one of the reactor walls, measured along its axis. The terms representing transport of the substances X, Y due to diffusion should be introduced into equations (4.30). Recall that the non-dimensional diffusion equation is of the form  

to account for diffusion in equations (4.29), they should be modified as follows  

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