arXiv subjects

Maria Aguareles

Publications and source records attributed to Maria Aguareles.

6 recordsLinked to original sources

arXiv2025

Modelling hydrogen storage in metal hydrides

We develop a one-dimensional mathematical model for the loading process of hydrogen in a metal hydride tank. The model describes the evolution of the density and pressure of the hydrogen gas, the temperature of the tank, the averaged velocity of the gas through the porous metal structure, and the transformed fraction of metal into a metal hydride. The non-dimensionalisation of the model indicates a possible reduction of the system of equations and also shows that the density and the transformed metal fraction may be decoupled from the temperature equation. The reduced model is solved numerically. Introducing a spatial dependence into the kinetic reaction constant allows to explain unexpected temperature gradients observed in experiments.

cond-mat.mtrl-sci↗

arXiv2025

Assessment of averaged 1D models for column adsorption with 3D computational experiments

In the present manuscript, we formulate a 3D mathematical model describing the capture of a contaminant in an adsorption column. The novelty of our approach involves the description of mass transfer by adsorption via a nonlinear evolution equation defined on the surface of the porous media, while Stokes flow and an advection-diffusion equation describe the contaminant transport through the interstices. Simulations of 3D models with varying microstructures but identical porosity reveal a minimal impact of the microstructure on contaminant distribution within the column, particularly in the radial direction. Using homogenization theory and a periodic microstructure, we rigorously derive a 1D adsorption model that matches the standard form that is found in the literature, but contains two effective coefficients, the dispersion and the permeability, that explicitly incorporate microstructural details of the porous medium. The 1D model closely reproduces 3D results, the 1D concentration profiles closely match the cross-section averaged 3D profiles, and the outlet breakthrough curves are nearly identical. We also demonstrate how the 3D simulations converge to the solution of the 1D model as the microstructure is refined. Consequently, our model offers a theoretical foundation for the widely used 1D model, confirming its reliability for investigating, optimizing, and aiding in the design of column adsorption processes for practical applications.

physics.flu-dyn↗

arXiv2023

An analytical investigation into solute transport and sorption via intra-particle diffusion in the dual-porosity limit

We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damk\"ohler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against available experimental data for the removal of Mercury(II) and CO$_\text{2}$. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions.

cond-mat.other↗

arXiv2023

A rigorous derivation of the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation

In this work n-armed Archimedian spiral wave solutions of the complex Ginzburg-Landau equation are considered. These solutions are showed to depend on two characteristic parameters, the so called twist parameter and the asymptotic wavenumber. The existence and uniqueness of the value of the asymptotic wavenumber, depending on the twist parameter, for which n-armed Archimedian spiral wave solutions exist is a classical result, obtained back in the 80s by Kopell and Howard. In this work we deal with a different problem, that is, the asymptotic expression of the asymtptotic wavenumer for small values of the twist parameter. Since the eighties, different heuristic perturbation techniques, like formal asymptotic expansions, have conjectured an asymptotic expression of which is exponentially small with respect to the twist parameter. However, the validity of this expression has remained opened until now, despite of the fact that it has been widely used for more than 40 years. In this work, using a functional analysis approach, we finally prove the validity of the asymptotic formula, providing a rigorous bound for its relative error.

math.AP↗

arXiv2022

Modelling mass transfer from a packed bed by fluid extraction

A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between the solid and fluid. Two specific cases are analysed, the first where the extracted material has the same saturation solubility and rate of mass transfer throughout the process, the second where the solubility switches after a certain amount of erosion. In the first case there are only two model unknowns, the solubility and mass transfer coefficient, in the second there is a third unknown, the second solubility. Exploiting the fact that erosion is a slow process (relative to the flow rate) a perturbation solution based on the smallness of the amount removed is developed to describe the concentration and radius throughout the column. From this an analytical expression for the extracted fraction is obtained. The extracted fraction has a large linear section which results in a simple calculation to estimate the initial solubility from a very few or even a single data point. The remaining unknowns may also be easily calculated from the formula and later data points. A numerical solution, using finite differences, is developed to verify the perturbation solution. The analytical solution is also verified against experimental data for the removal of lanolin from wool fibres with a supercritical CO$_\text{2}$/ethanol solvent. Values for the mass transfer rate and two solubilities are obtained for different pressures and shown to provide excellent agreement with a series of experimental results for the extracted fraction.

cond-mat.other↗

arXiv2021

Mathematical modelling of fibre coating

In this report we formulate and analyse a mathematical model describing the evolution of a thin liquid film coating a wire via an extrusion process. We consider the Navier-Stokes equations for a 2D incompressible Newtonian fluid coupled to the standard equation relating the fluid surface tension with the curvature. Taking the lubrication theory approximation and assuming steady state, the problem is reduced to a single third-order differential equation for the thin film height. An approximate analytical solution for the final film height is derived and compared with a numerical solution obtained by means of a shooting scheme. Good agreement between the two solutions is obtained, resulting in a relative error of around 5\%. The approximate solution reveals that the key control parameters for the process are the initial film height, the fluid surface tension and viscosity, the wire velocity and the angle of exit at the extruder.

physics.flu-dyn↗