Effects of thermodynamically coupled reaction diffusion in microalgae growth and lipid accumulation: Model development and stability analysis

• Modified microalgal growth rate model is proposed.
• Non-stirred chemostat and LNET are used to derive dimensionless equations.
• Four different cases have been discussed for microalgal physiology in open system.
• Spatiotemporal linear stability analysis of the model is presented.

This study investigates and presents the effects of thermodynamically coupled nonisothermal reaction-diffusion processes on microalgae growth, substrate consumption and neutral lipid production in a pond or wastewater treatment plant. The non-stirred chemostat hypothesis and linear nonequilibrium thermodynamics theory are applied to formulate the model equations that account the bulk phase compositions and temperature, resistances to the heat and mass transfers, and cross effects due to the thermodynamic coupling of heat and mass flow in the presence of chemical reaction. Nondimensional forms of the model equations are numerically solved. Bulk phase concentrations and temperatures, external resistances to heat and substrate transfers, and thermodynamic coupling may generate substantial number of new parameters that control the evolution and stability in microalgal growth and lipid production that are important for biofuels. Instabilities due to perturbations in nutrient concentrations may lead to spatial structures where the wavenumber plays important role in reaction diffusion systems.