Pore size optimisation of humidity sensor—a probabilistic approach

Moisture adsorption in ceramic sensors undergoes a series of different chemical and physical mechanisms with respect to humidity of the incident gas mixture. Pore size of the ceramic specimen is one of the major parameters which contribute significantly to the condensation. Since the free path of the incident water vapour molecules alters with the changes in the vapour content in the carrier gas, an optimum pore size that would be comparable to the free path of the wayward vapour molecules is always desirable under all humidity conditions. A probabilistic model has been presented in this paper for pore size optimisation of ceramic under simplified assumptions. Model results have been presented for a variety of carrier gases for which the Brownian motion gets restricted and the associated energy attains a minimum so that the vapour adsorption becomes most likely. The pore size works out in the nano range. The overall pore size equates 80.91 nm at normal pressure. Under increased pressure the experimentally determined pore size for ceramic samples tallies well with the pore size computed from the model. The probabilistic treatment of mean free path of vapour molecules in this study accommodates for the basic limitations of classical kinetic theory of gas.