Reaction and ultraslow diffusion on comb structures.

A two-dimensional (2D) comb model is proposed to characterize reaction-ultraslow diffusion of tracers both in backbones (x direction) and side branches (y direction) of the comblike structure with two memory kernels. The memory kernels include Dirac delta, power-law, and logarithmic and inverse Mittag-Leffler (ML) functions, which can also be considered as the structural functions in the time structural derivative. Based on the comb model, ultraslow diffusion on a fractal comb structure is also investigated by considering spatial fractal geometry of the backbone volume. The mean squared displacement (MSD) and the corresponding concentration of the tracers, i.e., the solution of the comb model, are derived for reactive and conservative tracers. For a fractal structure of backbones, the derived MSDs and corresponding solutions depend on the backbone's fractal dimension. The proposed 2D comb model with different kernel functions is feasible to describe ultraslow diffusion in both the backbone and side branches of the comblike structure.

Caffeine Adsorption onto Bentonite Clay in Suspension and Immobilized

Abstract This study describes the use of bentonite in suspension for the caffeine adsorption (pollutant of emerging concern) by taking different conditions of the pH, adsorbent mass, adsorbent calcination temperature and interferents into account. The results were compared with those obtained using bentonite immobilized in alginate beads. The acid medium has a greater efficiency for the caffeine adsorption and the adsorbent calcination temperature exerts, due to structural changes. Caffeine removal higher than 90% was obtained at optimized conditions. The Langmuir model indicated a better fit of the data and the adsorption capacity of caffeine onto bentonite. The bentonite immobilized led to a slower adsorption process in relation to the suspended.

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models.

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

On the equivalence between specific adsorption and kinetic equation descriptions of the admittance response in electrolytic cells.

The response of an electrolytic cell, in the shape of a slab, is analyzed in the framework of the Poisson-Nernst-Planck model in the limit of full dissociation. Two different types of boundary conditions on the electrodes are compared. One type describes the exchange of charges between the volume and the external circuit, in the form originally proposed by Chang and Jaffé and later extended to include specific adsorption, where the surface current density is proportional to the variation of the surface bulk density of ions with respect to the value of equilibrium. The other one describes the surface adsorption, in the limit of Langmuir. We show that in the simple case where the ions dissolved in the insulating liquid are identical in all the aspects, except for the sign of the charge, the two models are equivalent only if the phenomenological parameter entering the boundary condition of the Chang-Jaffé model, κ, is frequency dependent, and related to the adsorption coefficient, k(a), in the form κ = iωτ/(1 + iωτ)k(a), where τ is the desorption time and ω the circular frequency of the applied voltage, as proposed long ago by Macdonald.

Relaxation of the nematic deformation when the distorting field is removed.

We investigate the relaxation of the nematic deformation when the distorting field is switched off. We show that the usual analysis based on the diffusionlike equation does not allow a complete description of the phenomenon because it does not permit one to satisfy the initial boundary condition, at t=0 , on the first time derivative of the nematic tilt angle. An alternative approach to the problem, taking into account the inertial properties of the nematic molecules, allows one to satisfy the initial boundary conditions on the first-order time derivative of the tilt angle. In this framework the dynamical evolution of the nematic deformation, in the initial time, depends on the inertial properties of the nematic molecules. However, the typical relaxation time is so short that, for all practical effects, the first time derivative of the tilt angle is discontinuous at t=0 . A more realistic description involves the switching time of the distorting field. In this framework, the initial boundary condition of the first-order derivative is automatically satisfied. Our analysis shows that the description based on the diffusion equation works well when the switching time is very small with respect to the diffusion time.