The use of an innovative inverse numerical modeling method for the evaluation and parameter estimation of barberry anthocyanins ultrasound assisted extraction

Abstract

There has been a significant interest to extract functional ingredients by novel methods such as ultrasound assisted extraction, recently, whereas limited engineering data are available in this regard. The aim of this study was to develop a precise and powerful technique based on inverse parameter estimation of finite volume model to estimate process coefficients of barberry anthocyanin compounds (ACs) ultrasound-assisted extraction (UAE). For this purpose, anthocyanin concentration over time was determined under different experimental conditions. Then, a new numerical model considering a complex system of dispersion, diffusion and degradation was developed and coupled with a parameter estimation code. Finally, parameters were estimated by minimizing differences between experimental and numerical data. UAE enhanced the extraction rate while degradation of the extracted barberry ACs was occurred. Therefore, it was necessary to understand the rate parameters of the process. The predicted coefficients of overall mass transfer, diffusion (De), dispersion (E), and degradation (kdeg) of the barberry ACs under different conditions were (1.375–2.731 × 10−7 m/s), (2.523–5.012 × 10-11 m2/s), (1.000 × 10−7–1.000 × 10-3 m2/s), and (1.000 × 10−7–5.637 × 10-5 1/s), respectively. A good agreement between the experimental and predicted data were obtained. Sonication was shown to affect both extraction rate and degradation rate. Higher De values were obtained at the presence of sonication while high duty cycles could increase degradation rates.