Mantanis-model

Mantanis’s model - A prediction model for the maximum swelling of wood in organic liquids
The swelling of wood is a distinctive phenomenon of all elastic materials but differs to some extent for different types of materials. According to Nageli (1854), a solid is said to swell when it takes up a liquid and simultaneously realizes three (3) conditions: i) its dimensions are increased with an following thermal change as a consequence of the taking up of another phase, ii) it maintains its homogeneity in a microscopic sense, iii) its cohesion is reduced but not eliminated thus becoming soft and flexible.
It is known in the literature that the phenomenon of swelling of wood in water and organic liquids is a complex process influenced by several parameters; none of which can independently predict the maximum extent of the wood swelling. During the doctorate research work of Mr. George Mantanis at the University of Wisconsin-Madison (1991-1994), a new prediction model was created. The statistical analysis of this work allowed the assessment of the statistical significance of each of the parameters involved on the wood swelling. A regression equation model, named Mantanis’s model, was subsequently made.
The model allows the prediction of the wood swelling based on liquid and wood parameters such as solvent basicity (donor number), molar volume of solvent, air-dry density of wood, hydrogen bonding capability parameter, and molecular weight of solvent (Mantanis 1994, Mantanis et al. 1995). This model can be of helpfulness to researchers and practitioners in several wood processes including chemical pulping, wood preservation, removal of extractives, dimensional stabilization and chemical modification of wood. After a thorough statistical analysis, it was found that the best predictive model for the maximum (tangential) swelling of wood in organic liquids is the following:
S = 2.27 + 0.316 SB - 0.0426 MV + 4.92 WD
(1.25) (0.016) (0.0068) (1.94)
Where,
S: the maximum tangential swelling of wood,
SB: the solvent basicity,
MV: the solvent molecular volume,
WD: the density of wood species
Note: Numbers in parentheses are the standard deviations
The R-square value of the regression model was 0.826, and the standard deviation was 2.1%. The typical plot of the residuals versus fitted values showed a reasonable fit. At last, it should be noted that the addition of the hydrogen bonding parameter (HD) into this statistical model seemed not to improve the fit (R-square = 0.828).
References
Nageli C.V. (1854). Die starkenkorner. Morphologische Physiologische, Chemisch-Physikalische und Systematisch-Botanische Nomographie, Zurich, Switzerland
Mantanis G.I., Young R.A. and R.M. Rowell (1995). Swelling of wood. Part IV. A statistical model for prediction of maximum swelling of wood in organic liquids. Wood and Fiber Science 27(1): 22-24.
Mantanis G.I. (1994). Swelling of lignocellulosic materials in water and organic liquids. PhD thesis, Dept. of Forestry, University of Wisconsin-Madison, Madison, Wisconsin, USA.
Article written in March 2014

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