New trends in modelling of breakthrough curves to remove pollutants using adsorption on advanced monoliths geometries.

This work proposes a rigorous mathematical model capable of reproducing the adsorption process in dynamic regime on advanced monoliths geometries. For this, four bed geometries with axisymmetric distribution of channels and similar solid mass were proposed. In each geometry a different distribution of channels was suggested, maintaining constant the bed dimensions of 15 cm high and 5 cm radius. The mathematical modeling includes mass and momentum transfer phenomena, and it was solved with the COMSOL Multiphysics software using mass transfer parameters published in the literature. The overall performance of the column was evaluated in terms of breakthrough (CA/CA0 = 0.1) and saturation times (CA/CA0 = 0.9). The mass and velocity distributions obtained from the proposed model show good physical consistency with what is expected in real systems. In addition, the model proved to be easy to solve given the short convergence times required (2-4 h). Modifications were made to the bed geometry to achieve a better use of the adsorbent material which reached up to 80%. The proposed bed geometries allow obtaining different mixing distributions, in such a way that inside the bed a thinning of the boundary layer is caused, thus reducing diffusive effects at the adsorbent solid-fluid interface, given dissipation rates of about 323 × 10-11 m2/s3. The bed geometry composed of intersecting rings deployed the best performance in terms of usage of the material adsorbent, and acceptable hydrodynamical behavior inside the channels (maximum fluid velocity = 35.4 × 10-5 m/s and drop pressure = 0.19 Pa). Based on these results, it was found that it is possible to reduce diffusional effects and delimit the mass transfer zone inside the monoliths, thus increasing the efficiency of adsorbent fixed beds.

The spreading of Covid-19 in Mexico: A diffusional approach.

In this work, we analyze the spreading of Covid-19 in Mexico using the spatial SEIRD epidemiologic model. We use the information of the 32 regions (States) that conform the country, such as population density, verified infected cases, and deaths in each State. We extend the SEIRD compartmental epidemiologic with diffusion mechanisms in the exposed and susceptible populations. We use the Fickian law with the diffusion coefficient proportional to the population density to encompass the diffusion effects. The numerical results suggest that the epidemiologic model demands time-dependent parameters to incorporate non-monotonous behavior in the actual data in the global dynamic. The diffusional model proposed in this work has great potential in predicting the virus spreading on different scales, i.e., local, national, and between countries, since the complete reduction in people mobility is impossible.

Self-similar Turing patterns: An anomalous diffusion consequence.

In this work, we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and it is modeled through a space-dependent diffusion coefficient with a power-law functional form.

Effect of two viscosity models on lethality estimation in sterilization of liquid canned foods.

A numerical study on 2D natural convection in cylindrical cavities during the sterilization of liquid foods was performed. The mathematical model was established on momentum and energy balances and predicts both the heating dynamics of the slowest heating zone (SHZ) and the lethal rate achieved in homogeneous liquid canned foods. Two sophistication levels were proposed in viscosity modelling: 1) considering average viscosity and 2) using an Arrhenius-type model to include the effect of temperature on viscosity. The remaining thermodynamic properties were kept constant. The governing equations were spatially discretized via orthogonal collocation (OC) with mesh size of 25 × 25. Computational simulations were performed using proximate and thermodynamic data for carrot-orange soup, broccoli-cheddar soup, tomato puree, and cream-style corn. Flow patterns, isothermals, heating dynamics of the SHZ, and the sterilization rate achieved for the cases studied were compared for both viscosity models. The dynamics of coldest point and the lethal rate F0 in all food fluids studied were approximately equal in both cases, although the second sophistication level is closer to physical behavior. The model accuracy was compared favorably with reported sterilization time for cream-style corn packed at 303 × 406 can size, predicting 66 min versus an experimental time of 68 min at retort temperature of 121.1 ℃.

A theoretical study of the dissociation of the sI methane hydrate induced by an external electric field.

Molecular dynamics simulations in the equilibrium isobaric-isothermal (NPT) ensemble were used to examine the strength of an external electric field required to dissociate the methane hydrate sI structure. The water molecules were modeled using the four-site TIP4P/Ice analytical potential and methane was described as a simple Lennard-Jones interaction site. A series of simulations were performed at T = 260 K with P = 80 bars and at T = 285 K with P = 400 bars with an applied electric field ranging from 1.0 V nm(-1) to 5.0 V nm(-1). For both (T,P) conditions, applying a field greater than 1.5 V nm(-1) resulted in the orientation of the water molecules such that an ice Ih-type structure was formed, from which the methane was segregated. When the simulations were continued without the external field, the ice-like structures became disordered, resulting in two separate phases: gas methane and liquid water.

Fractal continuum model for tracer transport in a porous medium.

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

Transport in fractal media: an effective scale-invariant approach.

In this paper an advective-dispersion equation with scale-dependent coefficients is proposed for describing transport through fractals. This equation is obtained by imposing scale invariance and assuming that the porosity, the dispersion coefficient, and the velocity follow fractional power laws on the scale. The model incorporates the empirically found trends in highly heterogeneous media, regarding the dependence of the dispersivity on the scale and the dispersion coefficient on the velocity. We conclude that the presence of nontrivial fractal parameters produces anomalous dispersion, as expected, and that the presence of convective processes induces a reescalation in the concentration and shifts the tracer velocity to different values with respect to the nonfractal case.