Application of genetic algorithm for determination of the effective diffusivity of andrographolide in plant materials

The effective diffusivity of natural medicinal components is an important property for a detailed pharmaceutical extraction study and a proper design of the extraction process and unit. A mass transfer mathematical model for solvent extraction of andrographolide was developed and numerically solved taking into account particle geometries, solvent concentration, mass fraction of two different geometries of plant materials, external mass transfer resistance and solid–liquid equilibrium concentration. Using inverse simulation approach with genetic algorithm, unknown four key parameters in the developed model, effective diffusivity, partition coefficient, average particle size and mass fraction of leaf particles were determined at different extraction temperatures and solvent concentrations. The simulated data through the genetic algorithm-numerical model (GA-NM) and experimental data showed a good agreement (r2 > 0.97 and MSE < 0.0016) indicating that the scheme with genetic algorithm can be effectively used for determination of the effective diffusivity of andrographolide in plant materials.