APPLICATION OF THE BOSANQUET APPROXIMATION FOR MODELING MOISTURE TRANSPORT IN POROUS HUMIDITY SENSORS

Abstract

Water vapor transport properties in porous dielectric structures are significantly influencing the performances of porous humidity sensors. Knowledge of diffusion paths that control the movement of moisture will be crucial in developing faster sensor response, sensitivity, and long-term stability. In porous materials, moisture transport is via a combination of bulk molecular transport and Knudsen transport depending on the ratio of pore size to the mean free path of water molecules. Multi-scale porous structures that require both diffusion and transport are often best described using traditional diffusion models. The Bosanquet approximation is a convenient method for including molecular and Knudsen diffusion together in a single effective diffusion coefficient. In this paper, a complete theoretical review of the Bosanquet approximation and moisture transport modelling in porous humidity sensors using the Bosanquet approximation is presented. The fundamentals of molecular diffusion and Knudsen diffusion are described and the Bosanquet equation is derived and discussed with respect to the applicability of the equation in the transition diffusion regimes. Theoretical calculations show the effect of the pore size on the diffusion behavior and the performance of the sensor. The review sets the basis for the current Bosanquet approximation, which is a useful analysis tool for moisture transfer through state-of-the-art porous dielectric materials, and for future coupled diffusion–adsorption modeling methods.