A possible predictive mathematical model for the growth of a periphytic alga

Algae are photosynthetic organisms and have qualities that are very attractive for cultivation and industrial development for commercial purposes. When algal growth is analyzed for the production of biomass usually only the exponential phase of the growth curve is considered and the other phases are ignored. The objective of the work is to present a possible predictive mathematical model that allows a better understanding of the kinetic behavior of a periphytic microalgae by means of the use of the Smoluchowski discrete equation, with special emphasis on the lag phase. More specifically, unknown connection between the discrete Smoluchowski equation and the deterministic Baranyi model is shown in the present study. Analysis of this connection leads to a possible predictive mathematical model about of the kinetic behavior of a periphytic microalgae.