Mathematical and kinetic models are discussed for anaerobic solid‐state fermentation (SSF) in rotating‐drum bioreactors (RDBs). In this study, a simple approximate analytical expression pertaining to the concentration of substrate, biomass, and ethanol is derived in terms of all parameters. These analytical results were found to be in good agreement with numerical solutions (MATLAB/SCILAB) and experimental results.
In this paper, an approximate analytical method to solve the non-linear differential equations in an immobilized enzyme film is presented. Analytical expressions for concentrations of substrate and product have been derived for all values of dimensionless parameter. Dimensionless numbers that can be used to study the effects of enzyme loading, enzymatic gel thickness, and oxidation/ reduction kinetics at the electrode in biosensor/biofuel cell performance were identified. Using the dimensionless numbers identified in this paper, and the plots representing the effects of these dimensionless numbers on concentrations and current in biosensor/biofuel cell are discussed. Analytical results are compared with simulation results and satisfactory agreement is noted.
In this paper, mathematical model for cell growth and biofuel production under synthetic feedback loop is discussed. The nonlinear differential equations are solved analytically for the maximum production of biofuel under synthetic feedback. The closed-form of analytical expressions pertaining to the concentrations of cell density, repressor proteins, pump expressions, intracellular biofuel and extracellular biofuel are presented. The constant pump model is compared with feedback loop model analytically to know the biofuel production. The numerical solution of this problem is also reported using Scilab/Matlab program. Also, the analytical results are compared with previous published numerical results and found to be in good agreement.
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