The kinetics of adsorption of tetracycline on chitosan particles

Experiments to monitor and characterize the kinetics of adsorption of tetracycline on chitosan particles are reported in this work. The same pseudo-order kinetics that has been widely used for describing the adsorption in systems related to wastewater purification and drug loading was used to treat the present data. As some unexpected results came out from the experiments, it was necessary a detailed deduction for this sort of kinetics to be carried out, so that approximations related to short and long times were obtained. Firstly it was shown that an apparently linear t/q(t) versus t relationship did not imply a pseudo-second-order sorption kinetics, differently of what has been repeatedly reported in the literature. It was found that this misinterpretation could be avoided by using non-linear regression. Finally, the adsorption of tetracycline on chitosan particles was analyzed, using the insights obtained from theoretical analysis, and the parameters generated were used to analyze to adsorption kinetics and to propose an adsorption mechanism.     

Inapplicability of Asymptotic Results on the Minimal Spanning Tree in Statistical Testing

Penrose has given asymptotic results for the distribution of the longest edge of the minimal spanning tree and nearest neighbour graph for sets of multivariate uniformly or normally distributed points. We investigate the applicability of these results to samples of up to 100 points, in up to 10 dimensions. We conclude that the asymptotic results provide an acceptable approximation only in the uniform case. Their inaccuracy for the multivariate normal case means that they cannot be applied to improve Rohlf's gap test for an outlier in a set of multivariate data points, which depends on the longest edge of the minimal spanning tree of the set.     

Solute Concentration Statistics in Heterogeneous Aquifers for Finite Péclet Values

A Lagrangian framework is used for analysing the concentration fields associated with transport of nonreactive solutes in heterogeneous aquifers. This is related to two components: advection by the random velocity field v(x) and pore-scale dispersion, characterized by the dispersion tensor D _d; the relative effect of the two components is quantified by the Péclet number. The principal aim of this paper is to define the probability density function (pdf) of a nonreactive solute concentration and its relevant moments >C< and ² _c as sampled on finite detection volumes. This problem could be relevant in technical applications such as risk analysis, field monitoring and pollution control. A method to compute the concentration statistical moments and pdf is developed in the paper on the basis of the reverse formulation widely adopted to study solute dispersion in turbulent flows. The main advantages of this approach are: (i) a closed form solution for concentration mean and variance is attained, in case of small size of the sampling volume; (ii) a numerically efficient estimate of the concentration pdf can be derived. The relative effects of injection and sampling volume size and Péclet number on concentration statistics are assessed. The analysis points out that the concentration pdf can be reasonably fitted by the beta function. These results are suitable to be employed in practical applications, when the estimate of probability related to concentration thresholds is required.