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In this paper, a fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media is derived. The determined imbibition height and imbibition mass of capillary rise are in satisfying agreement with the existing models reported in the literature. It is found that the imbibition height and imbibition mass of capillary decreases with increasing relative roughness. Besides, it is observed that the equilibrium time in a single tortuous capillary with roughened surfaces decreases with an increase in relative roughness. In addition, it is seen that the imbibition height and imbibition mass of capillary rise increases with imbibition time. With the proposed fractal model, the physical mechanisms of capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media are better elucidated. One advantage of our fractal analytical model is that it contains no empirical constant, which is usually required in previous models.

A novel cellulose-based adsorbent (CGS) was synthesized by a facile, two-step modification route. It was characterized by the FTIR, XRD, and SEM technique. The adsorption characteristics of CGS were compared with those of native cellulose using crystal violet (CV) as an adsorbate in this work. The effects of contact time, temperature, pH, and initial concentration on the sorption were all investigated. The adsorption kinetics for both CGS and cellulose were found to follow a pseudo-second-order (P-S-O) kinetic model. The equilibrium data of CGS fitted well with the Langmuir isothermal model, and the maximum theoretical adsorption capacity of CGS for CV was 218.82 mg g–1 at 50 °C; the adsorption increased by 70.8% compared to that of native cellulose. A thermodynamics study was also performed. The comparative study confirmed that the structure of CGS is more conducive for the adsorption of CV than cellulose. Furthermore, adsorption/desorption experiments showed that CGS could be reused for at least eight cycles with stable sorption ability after being regenerated with 50% ethanol solution (pH 3.0).

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