Langmuir‐diffusion model: Its modification and further application to glutinous rice flour particles

Abstract

When the Langmuir‐diffusion model was applied to a continuous multistep dynamic vapor adsorption, an initial desorption of bound water was predicted for the relative humidity (RH) steps except the first. The desorption is physically meaningless. The model was modified with assuming probability ratio (β/γ) continuity between the boundary and field equations. The β/γ was calculated from the Park isotherm model. According to our modifying methodology, two parameter selection strategies exist while conducting parameter optimization: β as parameter while γ calculated using the β/γ ratio; γ as parameter while β calculated. These two strategies can result to almost identical total, free and bound water concentration evolution, nearly equal diffusivity, and qualitatively similar variation trends of both γ and β with free water concentration. Application of the modified model to the adsorption of glutinous rice flour revealed that the well‐documented bell‐like diffusivity vs RH curve did not hold for the free water. Practical Applications The Fickian law assumes that all water molecules diffuse equally. As we all know, at least two water populations with different mobilities coexist in most food materials. The Langmuir‐diffusion model assumes that the water molecules exist in free and bound states and that the free molecules may bond at certain sorption sites while diffusing. The modified version of the Langmuir‐diffusion model proposed here can be used to describe a continuous multistep vapor adsorption and deepen our understanding of moisture transfer mechanisms. This information can be applied in optimizing both the quality of food product and the economics of many food processes involving water transfer.

Extended dynamic vapor sorption of glutinous rice flour observed in logarithmic time scale and its modeling as a process with varying activation energy

“…The parallel exponential model (Tang, De Rooij, Van Duynhoven, & Van Breugel, 2008) and the triple exponential kinetic model (Glass et al, 2017) are the linearly superimposed results of two and three single exponential functions, respectively. The third theory‐based model couples the diffusion and the adsorption reactions, such as the dual mode diffusion model (Harley, Glascoe, & Maxwell, 2012; Zhao et al, 2019) and the Langmuir‐diffusion model (Guloglu, Hamidi, & Altan, 2017; Zhao et al, 2020). Even though extensive efforts have been made, it is still difficult to find a theoretical or phenomenological model which can give satisfactory prediction for each part of a water sorption kinetic curve from long time measurement (Nobile et al, 2004; Oliver & Meinders, 2011; Renzetti et al, 2012; Thybring et al, 2019).…”