Comparison of Domain and Similarity Models for Characterizing Moisture Sorption Equilibria of Paper Siddharth G. Chatterjee* Empire State Paper Research Institute, Faculty of Paper Science and Engineering, SUNY College of Environmental Science and Forestry, 1 Forestry Drive, Syracuse, New York 13210 Everett’s domain and Mualem’s capillary-radii similarity models of hysteresis were used to characterize the moisture sorption equilibria of a bleached kraft paperboard of mean basis weight 230 g/m 2 . The models predicted the experimental equilibrium moisture content (EMC) of the paperboard for the case of desorption scanning (similarity model only), adsorption scanning, spiral, and loop trajectories inside the main sorption hysteretic loop with good precision. Over an RH range of 15-90%, the root-mean-square deviation between the predicted and experimental EMCs was 0.11-0.83% (domain model) and 0.21-0.64% (similarity model). However, the similarity model is easier to use and requires data of only the two boundary isotherms that envelop the main hysteretic loop. The similarity method obviates the need of taking additional labor-intensive and time-consuming scanning curve data that is necessary to develop the moisture distribution function of the domain model and predicts higher-order EMC trajectories that lie inside the main hysteretic loop in a consistent fashion. Introduction The moisture content of paper is a key parameter that affects its mechanical properties. There is a loss in strength of paper products when they are subjected to a changing relative humidity (RH) of the surrounding environment. Recent research suggests that the phe- nomenon of accelerated creep of paper under cyclic humidity conditions can be understood as resulting from the interaction of tensile loading and moisture gradients in the paper. 1 Such transient moisture gradients are believed to result in localized load cycling, leading to accelerated creep. To describe moisture gradients in paper or paperboard under transient humidity condi- tions, it is necessary to develop a moisture transport model that has two aspects: (1) moisture sorption equilibria and (2) moisture transport characteristics of the paper under consideration. 2-4 It is the objective of this work to address the first aspect, specifically, the mathematical characterization of moisture sorption equilibria, which, in the case of paper, is complicated by the phenomenon of hysteresis. The theoretical de- scription of moisture sorption equilibria of paper will allow a more precise prediction of its equilibrium moisture content (EMC) as a function of its RH history and, thus, will also benefit personnel in paper testing laboratories in developing more informed conditioning procedures for their paper samples. In a previous publication, we reported a detailed experimental investigation of the moisture sorption equilibria of a machine-made bleached kraft paperboard (free of fillers and additives) with special attention focused on the interior of the main sorption hysteretic loop. 5 Utilizing the domain model of hysteresis devel- oped by Everett, 6 a moisture distribution function (MDF) was constructed from experimental boundary adsorption, boundary desorption, and desorption scan- ning isotherms. The MDF completely characterizes the interior of the main hysteretic loop at a given temper- ature and can, in principle, predict the EMC of a paper sample (based on its oven-dry weight) given its past arbitrary RH history. Predictions of two adsorption scanning isotherms and two spiral EMC-RH trajecto- ries inside the main hysteretic loop were made by using the MDF and were found to be in good agreement with experimental observations. The experimental determination of the MDF of the domain model is time-consuming and laborious, as it requires data from the boundary adsorption and de- sorption isotherms and a family of either desorption scanning or adsorption scanning isotherms. Under the hypothesis that the domain or moisture distribution function was mathematically self-similar, Mualem 7,8 developed two similarity methods (direct and capillary- radii) to describe the hysteresis of the wetting and drying processes in porous media. These methods require information only from the experimental bound- ary isotherms that envelop the main hysteretic loop and provide analytical expressions for all paths within the main hysteretic loop in a consistent fashion. Recently, Peralta and Bangi 9,10 used these methods to model the EMC-RH hysteresis of yellow poplar wood at 30 °C. They found good agreement of the theoretical EMC predictions with the experimental desorption scanning isotherms of yellow poplar wood that Peralta had reported earlier. 11 The objectives of the present work, which is a con- tinuation of our earlier work, 5 are the following: (a) to present a geometrical interpretation of Mualem’s capil- lary-radii similarity model; (b) to compare the capillary- radii similarity model of hysteresis, 8,10 which is math- ematically simpler and easier to use than the direct- similarity approach, 7,9 with Everett’s domain model of hysteresis; and (c) to test the models against a variety of experimental EMC-RH trajectories (desorption scan- ning, adsorption scanning, spiral, and loop) obtained with the bleached kraft paperboard whose sorption equilibria were reported earlier. 5 * Phone: (315) 470-6517. Fax: (315) 470-6945. 188 Ind. Eng. Chem. Res. 2001, 40, 188-194 10.1021/ie000437f CCC: $20.00 © 2001 American Chemical Society Published on Web 12/07/2000