The mass transfer resistances were analyzed by estimating the Biot number (Eq. (11)), which is a dimensionless number used in transient mass transfer

and consisting of the ratio www.selleckchem.com/products/PLX-4032.html between mass transfer resistances inside and at the surface of a particle. This parameter is used to estimate whether or not the mass inside a particle will vary significantly in space, from a mass gradient applied to its surface. Other parameter often used is the apparent Thiele modulus (Eq. (12)) that is the ratio between intrinsic chemical reaction rate in the absence of mass transfer limitation and the rate of diffusion through the particle. equation(11) Bi=ksRDef equation(12) ϕap=R29vobsDefC0where vobs=ΔCΔt The PSO version used in this study was based on the work of Schwaab, Biscaia, Monteiro, & Pinto (2008) which presents a detailed description of the algorithm. The PSO technique GW572016 was originally proposed by Kennedy & Eberhart (1995) based on the social behavior of collection of animals. Each individual of the swarm, called particle, remembers the best solution found by itself and by the whole swarm along the search trajectory. The particles

move along the search space and exchange information with others particles, in accordance with the following equations: equation(13) vp,dk+1=w·vp,dk+c1·r1(xp,dind−xp,dk)+c2·r2(xdglo−xp,dk) equation(14) xp,dk+1=xp,dk+vp,dk+1 In the Eqs. (13) and (14), p denotes the particle, d is the search direction, k represents the interaction number,

v is the velocity (or pseudo-velocity) of the particle and x is the position of particle, xind and xglob represent the regions of the search space where the objective function attains low (optimum) values, where xind is the best position found by the particle itself, while xglob is the best position found by whole swarm. In addition, r1 and r2 are two random numbers with uniform distribution in the range comprehended between 0 and 1. The parameters before w, c1 and c2 are search parameters, which there are called of inertial weight, the cognition and social parameters, respectively. The PSO was configured according previous works ( Burkert et al., 2011 and Moraes et al., 2009), using forty particles, and the inertial weight, cognition and social parameters were set at 0.7, 1.0, 1.0, respectively. Fig. 1 presents the kinetic of single component adsorption of glucose, fructose and sucrose on various cationic forms of X zeolite. It is observed that the equilibrium was reached within 60 min in all cases, which corroborates with Heper et al. (2007), which reported that the glucose adsorption reaches the steady state within 30 min. From the Fig. 1, it is seen that the NaX zeolite made it possible to adsorb about 200 g/L of the initial concentration of glucose and fructose after 60 min.