*3.2. The E*ff*ect of Particle Size*

Particle size is a physical property that affects the surface area of contact between a sorbent and the liquid phase, thus playing a key role in biosorption [30,31]. When the particle size is reduced, the area of contact is amplified, and the sites of sorption are more accessible, generating a better capacity, efficiency, and velocity of biosorption and a decrease in the time to reach equilibrium (Figure 1b). The present results are in agreement with previous reports of an enhanced biosorption capacity as the particle size diminishes, considering particles from 0.3 to 2.0 mm (Table 3).

**Table 3.** Kinetic parameters of the biosorption of Co2<sup>+</sup> by *PLEM*, using different particle sizes (*Cini* = 100 mg L−<sup>1</sup> , pH = 7.0).


The biosorption of Co2<sup>+</sup> was not significantly different (*p* > 0.05) between the size intervals of 0.3–0.5 mm and 0.5–0.8 mm. Therefore, a kinetic study was carried out to remove Co2<sup>+</sup> by *PLEM* at a particle size of 0.3–0.8 mm. The statistical analysis with two-way ANOVA and Tukey's test indicated the lack of significant difference (*p* > 0.05) between the equilibrium biosorption capacity *qeq* values of the samples with the following three particle sizes: 0.3–0.5, 0.5–0.8 mm, and 0.3–0.8 mm. The Co2<sup>+</sup> biosorption rate was slightly faster (as expected) at the smaller particle size range (0.3–0.5 mm), reaching equilibrium at 0.5 h. The particle size range of 0.5–0.8 mm achieved equilibrium in a longer period of time (0.75 h), probably due to the greater surface area available with a smaller particle size, leading to faster binding of Co2<sup>+</sup> ions to the surface of the biosorbent. With a particle size range of 0.3–0.8 mm, the time required to reach equilibrium (*teq*) of Co2<sup>+</sup> biosorption by PLEM was 0.5 h, similar to the time found for the smallest particles tested (0.3–0.5 mm).

One advantage of employing a particle size of 0.3–0.8 mm is that it is possible to utilize fixed-bed columns packed with the material. Volesky [32] suggested using a particle size of 0.4–0.7 mm, since smaller sizes could obstruct the bed and provoke a drop in pressure. Additionally, particles of 0.3–0.8 mm (but not smaller) allow for the application of more biosorbent material. If the particle size range is under 0.3 mm, pretreatment is more difficult. Hence, a particle size of 0.3–0.8 mm was chosen for the rest of the experiments. The experimental results of the Co2<sup>+</sup> removal capacity at equilibrium (*qeq*) were compared to the parameters of the kinetic models assayed (Table 3). As can be appreciated, the equation of the pseudo-second-order model shows a higher correlation coefficient (*R* 2 ) and lower error functions (*ASE*, *Sy.x*, and *AICc*) than the other two models.
