Development of a model for the simulation of Farinograph measurements
Abstract
Based upon kneading curves obtained from eight wheat flours using different cultivars, a mathematical model was developed to simulate the middle curve of Farinograph measurements. In the model the different states of the protein polymers during the kneading process are considered. All together five different states of protein polymer fractions are presumed: 1. non-hydrated, 2. unstretched, 3. stretched, 4. intermediate and 5. broken protein polymer fraction, which are represented by their corresponding state variables. The model consists of five connected ordinary differential equations with first and second order kinetics, which describe the dynamic behavior of the state variables using four kinetic parameters. Four state variables are used in a weighted sum (four parameters) to calculate the Farinograph middle curve. Using the dynamic process model the eight different Farinograph measurements are fitted individually by eight parameters in total. The system of differential equations was solved with an implicit finite difference method. Each step of the fit was done by a Quasi-Newton method. The overall fits were very good, with an average R2 of 0.996 ± 0.003 and an average sum of squared errors of 5,000 ± 3,000 BU2.
- Publication:
-
ESAFORM 2016
- Pub Date:
- October 2016
- DOI:
- 10.1063/1.4963609
- Bibcode:
- 2016AIPC.1769r0006H