Persona: Español Garrigos, José
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Español Garrigos
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Publicación Statistical mechanics of the GENERIC framework under external forcing(American Institute of Physics, 2023-07-10) Español Garrigos, JoséThe General Equation for Non-Equilibrium Reversible Irreversible Coupling (GENERIC) framework provides a thermodynamically consistent approach to describe the evolution of coarse-grained variables. This ramework states that Markovian dynamic equations governing the evolution of coarse-grained variables have a universal structure that ensures energy conservation (first law) and entropy increase (second law). However, the presence of external time-dependent forces can break the energy conservation law, requiring modifications to the framework’s structure. To address this issue, we start from a rigorous and exact transport equation for the average of a set of coarse-grained variables derived from a projection operator technique in the presence of external forces. Under the Markovian approximation, this approach provides the statistical mechanics underpinning of the GENERIC framework under external forcing conditions. By doing so, we can account for the effects of external forcing on the system’s evolution while ensuring thermodynamic consistency.Publicación Boundary conditions derived from a microscopic theory of hydrodynamics near solids(American Institute of Physics, 2019-04-08) Camargo-Trillos, Diego; Torre, J. A. de la; Delgado Buscalioni, Rafael; Chejne, Farid; Español Garrigos, JoséThe theory of nonlocal isothermal hydrodynamics near a solid object derived microscopically in the study by Camargo et al. [J. Chem. Phys. 148, 064107 (2018)] is considered under the conditions that the flow fields are of macroscopic character. We show that in the limit of macroscopic flows, a simple pillbox argument implies that the reversible and irreversible forces that the solid exerts on the fluid can be represented in terms of boundary conditions. In this way, boundary conditions are derived from the underlying microscopic dynamics of the fluid-solid system. These boundary conditions are the impenetrability condition and the Navier slip boundary condition. The Green-Kubo transport coefficients associated with the irreversible forces that the solid exert on the fluid appear naturally in the slip length. The microscopic expression for the slip length thus obtained is shown to coincide with the one provided originally by Bocquet and Barrat [Phys. Rev. E 49, 3079 (1994)].Publicación Microscopic Slip Boundary Conditions in Unsteady Fluid Flows(American Physical Society, 2019-12-31) Torre, J. A. de la; Duque Zumajo, Diego; Camargo-Trillos, Diego; Español Garrigos, JoséAn algebraic tail in the Green-Kubo integral for the solid-fluid friction coefficient hampers its use in the determination of the slip length. A simple theory for discrete nonlocal hydrodynamics near parallel solid walls with extended friction forces is given. We explain the origin of the algebraic tail and give a solution of the plateau problem in the Green-Kubo expressions. We derive the slip boundary condition with a microscopic expression for the slip length and the hydrodynamic wall position, and assess it through simulations of an unsteady plug flow.Publicación Solution to the plateau problem in the Green-Kubo formula(American Physical Society, 2019-02-19) Torre, J. A. de la; Duque Zumajo, Diego; Español Garrigos, JoséTransport coefficients appearing in Markovian dynamic equations for coarse-grained variables have microscopic expressions given by Green-Kubo formulas. These formulas may suffer from the well-known plateau problem. The problem arises because the Green-Kubo running integrals decay as the correlation of the coarse-grained variables themselves. The usual solution is to resort to an extreme timescale separation, for which the plateau problem is minor. Within the context of Mori projection operator formulation, we offer an alternative expression for the transport coefficients that is given by a corrected Green-Kubo expression that has no plateau problem by construction. The only assumption is that the Markovian approximation is valid in such a way that transport coefficients can be defined, even in the case that the separation of timescales is not extreme.Publicación The role of thermal fluctuations in the motion of a free body(ELSEVIER, 2024) Español Garrigos, José; Thachuk, Mark E.; Torre Rodríguez, Jaime Arturo de laThe motion of a rigid body is described in Classical Mechanics with the venerable Euler’s equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however, cannot satisfy this property, as a consequence of thermal fluctuations. We generalize Euler’s equations for a free body in order to describe dissipative and thermal fluctuation effects in a thermodynamically consistent way. The origin of these effects is internal, i.e. not due to an external thermal bath. The stochastic differential equations governing the orientation and central moments of the body are derived from first principles through the theory of coarse-graining. Within this theory, Euler’s equations emerge as the reversible part of the dynamics. For the irreversible part, we identify two distinct dissipative mechanisms; one associated with diffusion of the orientation, whose origin lies in the difference between the spin velocity and the angular velocity, and one associated with the damping of dilations, i.e. inelasticity. We show that a deformable body with zero angular momentum will explore uniformly, through thermal fluctuations, all possible orientations. When the body spins, the equations describe the evolution towards the alignment of the body’s major principal axis with the angular momentum vector. In this alignment process, the body increases its temperature. We demonstrate that the origin of the alignment process is not inelasticity but rather orientational diffusion. The theory also predicts the equilibrium shape of a spinning body.Publicación Non-local viscosity from the Green–Kubo formula(American Institute of Physics (AIP), 2020-05-07) Duque Zumajo, Diego; Torre, J.A. de la; Español Garrigos, José; https://orcid.org/0000-0001-7055-5835; https://orcid.org/0000-0002-1657-0820We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green–Kubo formula. However, the running Green–Kubo integral for the non-local shear viscosity does not have a plateau. By using a recently proposed correction for the Green–Kubo formula that eliminates the plateau problem [Español et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.Publicación Shear thickening of a non-colloidal suspension with a viscoelastic matrix(Cambridge University Press, 2019) Vázquez Quesada, Adolfo; Español Garrigos, José; Tanner, Roger I.; Ellero, Marco; https://orcid.org/0000-0003-1365-6052; https://orcid.org/0000-0001-8894-0395We study the rheology of a non-colloidal suspension of rigid spherical particles interacting with a viscoelastic matrix. Three-dimensional numerical simulations under shear flow are performed using the smoothed particle hydrodynamics method and compared with experimental data available in the literature using different constant-viscosity elastic Boger fluids. The rheological properties of the Boger matrices are matched in simulation under viscometric flow conditions. Suspension rheology under dilute to semi-concentrated conditions (i.e. up to solid volume fraction ϕ=0.3 ) is explored. It is found that at small Deborah numbers De (based on the macroscopic imposed shear rate), relative suspension viscosities ηr exhibit a plateau at every concentration investigated. By increasing De , shear thickening is observed, which is related to the extensional thickening of the underlying viscoelastic matrix. Under dilute conditions ( ϕ=0.05 ), numerical results for ηr agree quantitatively with experimental data in both the De and ϕ dependences. Even under dilute conditions, simulations of full many-particle systems with no a priori specification of their spatial distribution need to be considered to recover precisely experimental values. By increasing the solid volume fraction towards ϕ=0.3 , despite the fact that the trend is well captured, the agreement remains qualitative with discrepancies arising in the absolute values of ηr obtained from simulations and experiments but also with large deviations existing among different experiments. With regard to the specific mechanism of elastic thickening, the microstructural analysis shows that elastic thickening correlates well with the average viscoelastic dissipation function θelast , requiring a scaling as ⟨θelast⟩∼Deα with α⩾2 to take place. Locally, despite the fact that regions of large polymer stretching (and viscoelastic dissipation) can occur everywhere in the domain, flow regions uniquely responsible for the elastic thickening are well correlated to areas with significant extensional component.