. A model differential equation for chemical reaction dynamics is given as kC x C D x C u t C −   =   +   2 2 where u is the velocity, D is the diffusion coefficient, k is a reaction rate, and C is the (dimensionless) concentration of a given chemical species.

(a) Determine the appropriate dimensions of D and k.

(b) Using a characteristic length scale L and average velocity V as parameters, rewrite this equation in dimensionless form and comment on any non-dimensional group appearing.