A theoretical model to predict the amounts of sugar and water in a binary mixture and its experimental validation by time domain nuclear magnetic resonance

Abstract

Time-domain nuclear magnetic resonance (TD-NMR) enables quick, non-invasive, and cost-effective quantification of sugar in a solution. This study proposed a theoretical model to quantify the amounts of sugar and water in a binary sugar solution (a solution where a single type of sugar, either a monosaccharide or disaccharide, is dissolved in water) using TD-NMR. The mathematical model was developed by focusing on the mass balance equation and the acquisition signal (relating to the total hydrogen content) to predict the individual masses of sugar and water. To validate the model, a monosaccharide (fructose) and a disaccharide (saccharose) were used. In order to predict the individual masses of sugar and water, the experimental value of the total hydrogen content in the solution was a prerequisite, which depended on the conversion factor (k). The value of k was obtained using three methods: (a) varying the amount of water, (b) varying the amount of sugar in water, and (c) changing the source of hydrogen (replacing the hydrogen of water with the hydrogen of sugar). The k obtained solely from pure water were not feasible for quantifying sugar due to its high mean absolute relative error (MARE ≈ 30%). The model achieved a MARE of 2%–5% for both sugar solutions when k was sourced from the individual sugar solution. Furthermore, linear regression showed a strong fit (R2 ≥ 0.97) between the predicted and actual masses of sugar and water, indicating the model’s reliability and feasibility.