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Galliero G.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

Using nonequilibrium molecular dynamics simulations on simple Lennard-Jones binary mixtures, we have studied the behavior of planar fluid-fluid interfaces undergoing shear flow. When the miscibility is low enough, a slip together with a partial depletion have been noticed at the interface between the two fluid phases. The slip length can reach a value equal to some molecular diameters and the corresponding interfacial viscosity can be two times smaller than the value in the bulk. It is shown how the omission of this slip may lead to flow-rate misevaluation when dealing with a multiphase flow in a nanoporous medium even for non polymer fluids. In addition, using the simulation results, a simple relation between interfacial tension and interfacial viscosity is proposed for the monoatomic systems studied in this work. Finally, it is shown that the interfacial viscosity cannot be fully accounted for by estimating the local viscosity deduced from the local thermodynamic properties of the interface. © 2010 The American Physical Society.

Nichita D.V.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids
Fluid Phase Equilibria | Year: 2016

The phase stability analysis problem is highly important in phase equilibrium calculations. The stability test limit locus (STLL) is an important underlying property of multi-component system phase diagrams, because in its vicinity the number of iterations for phase stability testing dramatically increases and divergence may occur. The cause of convergence problems in phase stability calculations, as well as of the existence of a discontinuity of the TPD function in the single-phase state, is the topology of the TPD surface. At the STLL, the stationary point of the TPD function is a saddle point (the Hessian is indefinite), and for pressures just above the STLL the Hessian matrix is ill-conditioned in a domain of the hyperspace that must be "crossed" by iterates starting from one of the initial guesses. This makes stability testing in the vicinity of the STLL really challenging, and any algorithm will experience difficulties in this (fortunately tiny in most cases) region. A change of variables would not eliminate this problem, since the TPD function in the new hyperspace inherits certain properties from the original one. In this work we propose a modified objective function which exhibits multiple global minima corresponding to the stationary points of the original (TPD) function. The highly desirable feature of the modified objective functions is that the Hessian matrix is positive definite in the vicinity of the STLL (the nature of the singularity is changed). One additional derivative level is required for minimizing the new objective function, but a normal termination of the iterative sequence in a reasonable number of iterations is worth this effort. The minimization is performed by a quasi-Newton BFGS method with line search, using a suitable change of variables which avoids improper scaling, as well as by Newton iterations. Criteria to switch from the original TPD formulation to the new one are required, since the use of the more complex formulation is justified only near the STLL. Results show how application of the proposed stability testing method for a number of typical extremely difficult situations ensures convergence within tens of iterations, while all other iterative methods for minimizing the TPD function are extremely slow, unstable or even divergent. © 2016 Elsevier B.V.

Hastie W.W.,University of KwaZulu - Natal | Watkeys M.K.,University of KwaZulu - Natal | Aubourg C.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids
Gondwana Research | Year: 2014

The ~. 183. Ma old Karoo Large Igneous Province extends across southern Africa and is related to magmatism in Antarctica (west Dronning Maud Land and Transantarctic Mountains) and parts of Australasia. Intrusive events, including the emplacement of at least ten dyke swarms, occurred between ~. 183. Ma and ~. 174. Ma. We review here the field evidence, structure and geochronology of the dyke swarms and related magmatism as it relates to melt sources and the mantle plume hypothesis for the Karoo LIP. Specifically, the magma flow-related fabric(s) in 90 dykes from five of these swarms is reviewed, paying particular attention to those that converge on triple junctions in southern Africa and Antarctica. The northern Lebombo and Rooi Rand dyke swarms form an integral part of the Lebombo monocline, which converges upon the Karoo triple junction at Mwenezi, southern Zimbabwe. Dykes of the Northern Lebombo dyke swarm (182-178. Ma) appear to have initially intruded vertically, followed later by lateral flow in the youngest dykes. In dykes of the Okavango dyke swarm (178. Ma) there is evidence of steep magma flow proximal to the triple junction, and lateral flow from the southeast to the northwest in the distal regions. This is consistent with the Karoo triple junction and the shallow mantle being a viable magma source for both these dyke swarms. In the Rooi Rand dyke swarm (174. Ma) there is also evidence of vertical and inclined magma flow from north to south. This flow direction cannot be reconciled with the Karoo triple junction, as the northern termination of the Rooi Rand dyke swarm is in east-central Swaziland. The Jutulrøra and Straumsvola dyke swarms of Dronning Maud Land display evidence of sub-vertical magma flow in the north and lateral flow further south. The regional pattern of magma flow is therefore not compatible with direction expected from the Weddell Sea triple junction. The overall flow pattern in Karoo dykes is consistent with the triple junction being an important magma source. However, the Limpopo Belt and Kaapvaal Craton have significantly controlled the structure and distribution of the Lebombo and Save-Limpopo monoclines and the Okavango dyke swarm. The locus of magma flow in dykes of Dronning Maud Land is at least 500. km from the Karoo triple junction, as is the apparent locus for the Rooi Rand dyke swarm. In comparison with recent modelling of continental assembly, the structure and flow of the dyke swarms, linked with geochronology and geochemistry, suggests that thermal incubation during Gondwana assembly led to Karoo magmatism. A plate tectonic, rather than a fluid dynamic plume explanation, is most reasonably applicable to the development of the Karoo LIP which does not bear evidence of a deep-seated, plume source. © 2013 International Association for Gondwana Research.

Hoang H.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids | Galliero G.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids
Journal of Physics Condensed Matter | Year: 2013

This work aims at providing a tractable approach to model the local shear viscosity of strongly inhomogeneous dense fluids composed of spherical molecules, in which the density variations occur on molecular distance. The proposed scheme, which relies on the local density average model, has been applied to the quasi-hard-sphere, the Week-Chandler-Andersen and the Lennard-Jones fluids. A weight function has been developed to deal with the hard-sphere fluid given the specificities of momentum exchange. To extend the approach to the smoothly repulsive potential, we have taken into account that the non-local contributions to the viscosity due to the interactions of particles separated by a given distance are temperature dependent. Then, using a simple perturbation scheme, the approach is extended to the Lennard-Jones fluids. It is shown that the viscosity profiles of inhomogeneous dense fluids deduced from this approach are consistent with those directly computed by non-equilibrium molecular dynamics simulations. © 2013 IOP Publishing Ltd.

Hoang H.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids | Galliero G.,CNRS Laboratory of Thermodynamics and Energetics of Complex Fluids
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

In this paper, molecular dynamics simulations of a simple Lennard-Jones fluid confined in narrow slit pores and undergoing shear have been performed. The aim is to investigate the effects of density inhomogeneities at the fluid-solid interfaces on the shear viscosity profiles. It has been found that the local viscosity was varying strongly with the distance from the solid walls for both dilute and dense fluid states with oscillations correlated to the density ones. To describe the computed viscosity profiles, we propose a scheme that uses the local average density model, combined with an adequate weight function, for the configurational viscosity and a semiempirical model for the translational viscosity. It is shown that the proposed approach is able to provide viscosity profiles in good agreement with those coming from simulations for different pore widths and for different fluid states (dilute to dense). © 2012 American Physical Society.

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