arXiv subjects

Jorge Adrián Perera-Burgos

Publications and source records attributed to Jorge Adrián Perera-Burgos.

3 recordsLinked to original sources

arXiv2019

Analytical solutions from integral transforms for transient fluid flow in naturally fractured porous media with and without boundary flux

A kind of problems of radially symmetric transient fluid flow in a medium with a geometry similar to a hollow-disk can be addressed using the finite Hankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J. Engng. Sci., 3, 539 (1965)] works well only for homogeneous boundary conditions. We use the finite Hankel transform, together with the Laplace transform, to solve partial dfferential equations with inhomogeneous boundary conditions. With this aim, we propose a method to obtain an analytical solution of the problem of fluid flow in a finite naturally fractured reservoir with inner and outer boundaries having constant and time-dependent conditions, respectively. We assume that the reservoir has a producing well, with either constant terminal pressure or constant terminal rate, while the outer boundary has either an influx recharge or constant pressure. Using these case studies, we show that a part of the inverse transformation given by Cinelli can be expressed as closed formulas for long time solutions, at the same time that make it possible to capture the inhomogeneous condition and speed up the convergence of solutions. For Neumann-Neumann conditions, we show that the inverse expression of Cinelli is incomplete. In addition, an analysis of the flow characteristic curves in a reservoir with influx recharge is presented. The drawdown pressure curves are used to elucidate the statement that the pressure drop of a single-porosity reservoir with influx recharge resembles the flow behavior in a double-porosity closed reservoir, establishing a criteria to distinguish between both.

math.AP↗

arXiv2018

Glassy dynamics in asymmetric binary mixtures of hard-spheres

The binary hard-sphere mixture is one of the simplest representations of a many-body system with competing time and length scales. This model is relevant to fundamentally understand both the structural and dynamical properties of materials, such as metallic melts, colloids, polymers and bio-based composites. It also allows us to study how different scales influence the physical behavior of a multicomponent glass-forming liquid; a question that still awaits a unified description. In this contribution, we report on distinct dynamical arrest transitions in highly asymmetric binary colloidal mixtures, namely, a single glass of big particles, in which the small species remains ergodic, and a double glass with the simultaneous arrest of both components. When the mixture approaches any glass transition, the relaxation of the collective dynamics of both species becomes coupled. In the single glass domain, spatial modulations occur due to the structure of the large spheres, a feature not observed in the two-glass domain. The relaxation of the \emph{self} dynamics of small and large particles, in contrast, become decoupled at the boundaries of both transitions; the large species always displays dynamical arrest, whereas the small ones appear arrested only in the double glass. Thus, in order to obtain a complete picture of the distinct glassy states, one needs to take into account the dynamics of both species.

cond-mat.soft↗

arXiv2017

Self-consistent generalized Langevin equation theory of the dynamics of multicomponent atomic liquids

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid, and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.

cond-mat.soft↗