In this study, the solvent-swelling processes of coal particles of Zao Zhuang coal and Taiheiyo
coal were investigated using a novel orthogonal microscopy image analysis technique proposed
recently by our laboratory. The overshoot swelling and slow-climbing swelling are characteristic
of Zao Zhuang coal and Taiheiyo coal particles in pyridine at ambient temperature, respectively.
Super-Case II diffusion is dominant in Zao Zhuang coal particles and anomalous diffusion in
Taiheiyo coal. The present study shows that the slow-climbing-type solvent-swelling processes
of Taiheiyo coal particles can be described using the semiempirical model proposed by Ritger
and Peppas. However, overall solvent-swelling processes with an overshoot feature in many coals
could not be simulated well by the model. In addition, we observed that both the diffusion
mechanism exponent n and proportionality constant k in the model for the two coals have
characteristic statistical distributions. The distributions of n and k for Zao Zhuang coal are normal,
and those of Taiheiyo coal are doubly exponential. On the basis of these observations, the
connotation of the parameters, k and n, in the Ritger and Peppas model was expanded in view
of a statistical distribution. On the other hand, based on the analysis of swelling features of Zao
Zhuang coal particles in pyridine at ambient temperature, a series of new phenomenological
models, a second-order system with a unit-step forcing function in nature, was used to describe
the solvent-swelling processes of Zao Zhuang coal particles with or without overshoot features.
The simulated overall processes of the coal particles using the new models agree very well with
the measured ones and suggest that the viscoelastic properties of pyridine-dilated Zao Zhuang
coal, the main features of solvent-swelling and/or solvent transport of the coal particles, can be
well characterized by second-order system with the denominator τ2
s
2 + 2ζτs + 1 and a unit-step
forcing function (1/s).