Validation of a Method of Determination of Apparent Diffusivity Versus Composition in Solids

Abstract

A method is presented for computing the values of apparent diffusivity in solids with respect to the concentration of the diffusing substance (water or sodium chloride). This method does not require any assumption upon the mathematical relationship between diffusivity and concentration. It can be applied to experimental measurements of local concentration versus position within the solid (profiles) with relatively few measurements (circa 10) and a mathematical smoothing of the experimental data by using an artificial neural network model. The method was first validated on simulated data obtained by using a constant diffusivity value and on experimental profiles when the relation between diffusivity and concentration was given. It was then applied to original experimental moisture profiles obtained by putting gelatin gels with different initial moisture contents into contact for up to 14 days. The method was also successfully applied to five sets of experimental moisture and sodium chloride profiles taken from the literature and obtained from different food products. Apparent diffusivities calculated by our method were found in agreement with those obtained by authors using different numerical methods to compute the diffusivity values.

Keywords:

• Moisture diffusion
• Sodium chloride diffusion
• Boltzmann transformation
• Artificial neural network
• Food processing

Notes

*Pasta of cylindrical shape 15 × 3.2 cm, surface moisture content = 0.15 kg/kg dry matter.

**5 days experiments, pH = 5.3, saturated salt solution at 20 kg of salt/100 kg of water.

***8.1 days experiments, pH = 5.54, saturated salt solution at 20.5 kg of salt/100 kg of water.