ABSTRACT
Scholars studied chemostat model with variable yield coefficient and a growth rate in Monod expression for the existence of natural oscillations in a bioreactor. This article explores dynamical properties of a similar simple model, analytically and numerically, in which the growth rate is a modified Haldane expression. Study includes determination of analytic conditions for existence of steady-state washout and no washout solutions, optimization of the performance of the bioreactor when no washout solution occurs, stability of the optimized steady state solution, and the ranges of the parameter values for which natural oscillations (Hopf Bifurcation) take place. Investigation shows that it is possible to gain natural oscillations for much smaller values of the substrate concentration compared to Monod-based earlier works.
ABSTRACT
Spirulina platensis has been considered a promising source of food supplement to combat malnutrition worldwide. Numerous investigations have stated its immune activity, ability to absorb CO2 during the growth period, and antioxidant potential. Well-known theoretical biomass kinetic model sheds are capable of qualitative analysis of the fast microalgae growth. In this regard, we considered eight popular biomass models: Monod, Haldane, Andrews & Noack, Teissier, Hinshelwood, Yano & Koga, Webb and, Aiba model comprising analytical investigation within the numerical simulation. Besides, in this study, we establish a new mathematical biomass growth model by merging the well-known Hinshelwood and Yano & Koga models. We explored the most suitable Spirulina growth model to minimize the overstated and understated growth trends in the assorted eight biomass kinetic models. Our findings show microalgae biomass growth and substrate diminishes along with time, and these results were compared with available experimental data. Results present a high value of R2(0.9862), a low value of RSS (0.0813), AIC (-9.7277), and BIC (-8.2148) implied significantly fitted with the investigated data for the growth of Spirulina platensis compared with popular eight studied models.
