Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

Santamaría‐Holek, I.; Reguera, David; Rubı́, J. M.

doi:10.1103/physreve.63.051106

Cited by 47 publications

(98 citation statements)

References 36 publications

(52 reference statements)

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“…(12) and (13), implies that the fluctuation-dissipation theorem (FDT) connecting the drift and diffusion terms of the Fokker-Planck equation is no longer valid due to the presence of the shear [7,15,16,22]. This important consequence following from Eq.…”

Section: Mesoscopic Entropy Production For the Dynamics Of A Suspmentioning

confidence: 99%

“…(7) and (10) assuming that the coefficients are symmetric tensors. Finally we introduced the friction tensor β ij leading to the relation [7] …”

Section: Mesoscopic Entropy Production For the Dynamics Of A Suspmentioning

confidence: 99%

“…In this article, we offer a general description of this shear-induced diffusion effect and the associated transition to irreversibility which is based on the application of the second law of thermodynamics, and on previous works devoted to analyze the dynamics of a suspension of Brownian particles in the presence of flows [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…One of these couplings is responsible for the dependence of the diffusion tensor on the imposed velocity gradient, even in the limit of small specific thermal energy: k B T /m → 0, with k B T the thermal energy and m the mass of a particle [7]. This dependence of the diffusion tensor on the velocity gradient leads to the shear-induced diffusion effect that depends crucially on hydrodynamic interactions [10,11,12,13,14], and the breaking of the fluctuation-dissipation relation (FDR) at mesoscopic level, [7,15,16,17,18,19,20,22].…”

Section: Introductionmentioning

confidence: 99%

“…We calculate the entropy production of the system in the phase space of the particles and find the corresponding Onsager couplings [7,8,9]. One of these couplings is responsible for the dependence of the diffusion tensor on the imposed velocity gradient, even in the limit of small specific thermal energy: k B T /m → 0, with k B T the thermal energy and m the mass of a particle [7].…”

Section: Introductionmentioning

confidence: 99%

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Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

2009

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We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated to the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction and use Lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.

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Section: Mesoscopic Entropy Production For the Dynamics Of A Suspmentioning

confidence: 99%

“…(7) and (10) assuming that the coefficients are symmetric tensors. Finally we introduced the friction tensor β ij leading to the relation [7] …”

Section: Mesoscopic Entropy Production For the Dynamics Of A Suspmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

2009

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Mixing, Ergodicity and the Fluctuation-Dissipation Theorem in Complex Systems

Vainstein

Costa

Oliveira

Jamming, Yielding, and Irreversible Deformation in Condensed Matter

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Complex systems such as glasses, gels, granular materials, and systems far from equilibrium exhibit violation of the ergodic hypothesis (EH) and of the fluctuation-dissipation theorem (FDT). Recent investigations in systems with memory [1] have established a hierarchical connection between mixing, the EH and the FDT. They have shown that a failure of the mixing condition (MC) will lead to the subsequent failures of the EH and of the FDT. Another important point is that such violations are not limited to complex systems: simple systems may also display this feature. Results from such systems are analytical and obviously easier to understand than those obtained in complex structures, where a large number of competing phenomena are present. In this work, we review some important requirements for the validity of the FDT and its connection with mixing, the EH and anomalous diffusion in one-dimensional systems. We show that when the FDT fails, an out-ofequilibrium system relaxes to an effective temperature different from that of the heat reservoir. This effective temperature is a signature of metastability found in many complex systems such as spin-glasses and granular materials.

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