Impact of chaos and Brownian diffusion on irreversibility in Stokes flows

Sundararajan, Pavithra; Kirtland, Joseph D.; Koch, Donald L.; Stroock, Abraham D.

doi:10.1103/physreve.86.046203

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…This interpretation is further supported by an elegant numerical model of the original experiment, which was shown to undergo a second-order nonequilibrium phase transition [4]. However, an alternative explanation was also proposed [14][15][16][17][18][19], which relies on the chaotic nature of trajectories in dynamical systems. In this view, a phase transition is not needed to explain the relatively sharp onset of irreversilibity observed in the experiments.…”

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confidence: 86%

Hyperuniform Density Fluctuations and Diverging Dynamic Correlations in Periodically Driven Colloidal Suspensions

2015

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The emergence of particle irreversibility in periodically driven colloidal suspensions has been interpreted as resulting either from a nonequilibrium phase transition to an absorbing state or from the chaotic nature of particle trajectories. Using a simple model of a driven suspension, we show that a nonequilibrium phase transition is accompanied by hyperuniform static density fluctuations in the vicinity of the transition, where we also observe strong dynamic heterogeneities reminiscent of dynamics in glassy materials. We find that single particle dynamics becomes intermittent and strongly non-Fickian, and that collective dynamics becomes spatially correlated over diverging length scales. Our results suggest that the two theoretical scenarii can be experimentally discriminated using particle-resolved measurements of standard static and dynamic observables.

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mentioning

confidence: 86%

Hyperuniform Density Fluctuations and Diverging Dynamic Correlations in Periodically Driven Colloidal Suspensions

2015

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“…(Long range hydrodynamic interactions were shown to play little role [15,16].) However, it has also been suggested by several authors [7,[17][18][19][20] that the onset of irreversibility could be due to chaotic motion of the particles rather than a nonequilibrium phase transition. In other words, macroscopic irreversibility could arise when the Lyapunov exponent is larger than some threshold without any diverging lengthscales or timescales.…”

Section: Introductionmentioning

confidence: 98%

Criticality and correlated dynamics at the irreversibility transition in periodically driven colloidal suspensions

Tjhung¹

2016

J. Stat. Mech.

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One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving force. We consider a simple numerical model for driven suspensions which allows us to characterize in great detail a large body of physical observables that can be experimentally determined to assess the existence and universality class of such a non-equilibrium phase transition. Characterizing the behaviour of static and dynamic correlation functions both in real and Fourier space we determine in particular several critical exponents for our model, which take values that are in good agreement with the universality class of directed percolation. We also provide a detailed analysis of single-particle and collective dynamics of the system near the phase transition, which appear intermittent and spatially correlated over diverging timescales and lengthscales, and provide clear signatures of the underlying criticality.

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“…Reversibility of transport in creeping Couette flow has experimentally been demonstrated by Heller (1960), and the impact of diffusion on the reversibility of transport in such systems has been analyzed by Sundararajan et al. (2012), among others. In the present study, we analyze to which extent second central spatial moments of solute plumes in heterogeneous porous media decrease upon reversal of the flow field.…”

Section: Introductionmentioning

confidence: 99%

Linear Stochastic Analysis of the Partial Reversibility of Ensemble and Effective Dispersion in Heterogeneous Porous Media

Stettler

Dentz

Cirpka

2023

Water Resources Research

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Solute transport in the subsurface is strongly affected by the heterogeneity of the porous medium at all scales. In this context, (macro)dispersion denotes the process of a solute cloud expanding its spatial extent upon transport (e.g., Dagan et al., 2003;Gelhar et al., 1979). In heterogeneous porous media, there are two contributions to dispersion: advective spreading, which is the volume-preserving distortion of the plume due to the non-uniform flow field, and diffusive mixing, which is the dilution of the plume by Brownian motion (Dentz et al., 2011).Spreading is deterministically caused by the geometry of the porous medium and the distribution of hydraulic conductivity. It leads to an increase of the plume surface while the plume volume remains constant. By contrast, mixing increases the volume over which the plume is distributed, implying a reduction of concentration in the plume center (Kapoor & Kitanidis, 1996). With the increased surface area of the plume and steepening of concentration gradients due to contraction of fluid elements perpendicular to the direction of their stretching (Dentz et al., 2011;Le Borgne et al., 2015), advective spreading in heterogeneous media fosters enhanced diffusive mixing. However, over very long periods of time, spreading increases much faster than mixing, so that applying parameterizations that are good for advective spreading to solute mixing leads to a strong overestimation of mixing.Only mixing facilitates chemical reactions of reactants that are initially separated. Therefore it is of vital interest to separate the contributions of spreading and mixing to overall dispersion. Mixing is an irreversible process, whereas the deformation of a solute plume due to spatially variable advection is perfectly reversible. In thermodynamics, irreversibility implies an increase of entropy. Along these lines, Kitanidis (1994) introduced the dilution index as metric of solute mixing. The dilution index is defined as the exponent of the Shannon entropy of the spatial concentration distribution. With the exception of very simple cases, such as a truly Gaussian plume in a homogeneous flow field, the dilution index cannot be computed analytically. In heterogeneous aquifers with

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Impact of chaos and Brownian diffusion on irreversibility in Stokes flows

Abstract: We study a reversal process in Stokes flows in the presence of weak diffusion in order to clarify show that this universality breaks down due to the distribution of strain rates. In the limit of 13 infinitesimal diffusivity, we predict qualitatively distinct behavior in the chaotic case.

Cited by 5 publications

References 16 publications

Hyperuniform Density Fluctuations and Diverging Dynamic Correlations in Periodically Driven Colloidal Suspensions

Hyperuniform Density Fluctuations and Diverging Dynamic Correlations in Periodically Driven Colloidal Suspensions

Criticality and correlated dynamics at the irreversibility transition in periodically driven colloidal suspensions

Linear Stochastic Analysis of the Partial Reversibility of Ensemble and Effective Dispersion in Heterogeneous Porous Media

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