In this paper we study the mathematical properties of a scaled nonlinear model for interaction of algae with light. The growth dynamics is modeled by a couple of nonlinear equations for the evolution of the concentration of algae and the light intensity, in a column of water. A diffusion model is derived applying formally the modified Chapman-Enskog expansion to the Boltzmann-like evolution system for a small parameter ϵ, proportional to the average time between successive photon-water collisions. Existence and uniqueness of a positive solution are proved, using semigroup perturbation theory.