Chemical and biological activity in open flows: A dynamical system approach

Tél, Tamás; Moura, Arnaldo Vieira; Grebogi, Celso; Károlyi, György

doi:10.1016/j.physrep.2005.01.005

Cited by 196 publications

(175 citation statements)

References 206 publications

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“…Closed advection is largely governed by the symmetries of the base flow and boundary conditions (Ottino et al 1992;Speetjens et al 2006). Open advection is largely governed by filamentary unstable manifolds (Tél et al 2005). As the RPM flow exhibits transport characteristics of both closed and open flows, we may call it a partially open flow.…”

Section: Theorymentioning

confidence: 99%

“…Points that do not exit after 10t ex are coloured black and correspond to an island. Tél et al (2005) A key theoretical concept is exit-time distributions from which one can derive exit rates. The orbits of points with the longest exit times can be followed to approximate the filamentary manifolds controlling transport in the chaotic scattering region.…”

Section: (C) Predictions: Island Existence Island Size and Residencementioning

confidence: 99%

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An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

Metcalfe

Lester

Ord

et al. 2010

Phil. Trans. R. Soc. A.

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The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31, 469-485 (doi:10.1063/1.866828)) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residencetime and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.

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Section: Theorymentioning

confidence: 99%

Section: (C) Predictions: Island Existence Island Size and Residencementioning

confidence: 99%

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

Metcalfe

Lester

Ord

et al. 2010

Phil. Trans. R. Soc. A.

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“…Mixing takes place at the fluid-fluid interface and is determined by the combined action of molecular diffusion, which acts to reduce the local concentration gradients, and advection, which controls the interface dynamics [16][17][18][19][20][21]. Understanding the interface dynamics between two miscible fluids is therefore crucial to explaining and predicting the rate of mixing.When a less viscous fluid displaces a more viscous one, their interface is deformed and stretched by a hydrodynamical instability known as viscous fingering [15,22,23], and this results in complex interface dynamics [16,17,24]. Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries.…”

mentioning

confidence: 99%

“…When a less viscous fluid displaces a more viscous one, their interface is deformed and stretched by a hydrodynamical instability known as viscous fingering [15,22,23], and this results in complex interface dynamics [16,17,24]. Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries.…”

mentioning

confidence: 99%

“…In such mixing-driven systems, the flow responsible for fluid displacement reflects the heterogeneity of the host medium structure [8][9][10][11] or the physical properties of the fluids, such as density [3,12,13] or viscosity [14,15]. Mixing takes place at the fluid-fluid interface and is determined by the combined action of molecular diffusion, which acts to reduce the local concentration gradients, and advection, which controls the interface dynamics [16][17][18][19][20][21]. Understanding the interface dynamics between two miscible fluids is therefore crucial to explaining and predicting the rate of mixing.…”

mentioning

confidence: 99%

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Interface evolution during radial miscible viscous fingering

2015

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We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t 1 2 , as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability. A large number of natural and industrial flow processes depend on both the degree and the rate of mixing between fluids, such as chemical reactions [1][2][3][4], combustion [5], microbial activity [6], and enhanced oil recovery [7]. In such mixing-driven systems, the flow responsible for fluid displacement reflects the heterogeneity of the host medium structure [8][9][10][11] or the physical properties of the fluids, such as density [3,12,13] or viscosity [14,15]. Mixing takes place at the fluid-fluid interface and is determined by the combined action of molecular diffusion, which acts to reduce the local concentration gradients, and advection, which controls the interface dynamics [16][17][18][19][20][21]. Understanding the interface dynamics between two miscible fluids is therefore crucial to explaining and predicting the rate of mixing.When a less viscous fluid displaces a more viscous one, their interface is deformed and stretched by a hydrodynamical instability known as viscous fingering [15,22,23], and this results in complex interface dynamics [16,17,24]. Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries. Other studies have also focused on the effects of anisotropic dispersion [31,33,36] [50], and flow configuration [51-55] on the viscous fingering instability. Despite the extensive work done, the effect of viscous fingering on mixing has only recently been investigated numerically for a rectilinear geometry [14,56]. While the dynamics of the interface between two miscible fluids is crucial to explain and predict the rate of mixing [1,16], a solid understanding of the temporal evolution of the viscously unstable fl...

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Impact of fluid deformation on mixing‐induced chemical reactions in heterogeneous flows

Borgne

Ginn

Dentz

2014

Geophysical Research Letters

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We develop an approach based on a lamellar representation of fluid mixing that provides a direct link between fluid deformation, the distribution of concentration gradients, and the upscaled reaction rates for fast reversible reactions. The temporal evolution of effective reaction rates is determined by the flow topology and the distribution of local velocity gradients. This leads to a significant increase of the reaction efficiency, which turns out to be orders of magnitude larger than in homogeneous flow. This approach allows for the systematic evaluation of the temporal evolution of equilibrium reaction rates and establishes a direct link between the reaction efficiency and the spatial characteristics of the underlying flow field as quantified by the deformation of material fluid elements.

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Chemical and biological activity in open flows: A dynamical system approach

Cited by 196 publications

References 206 publications

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

Interface evolution during radial miscible viscous fingering

Impact of fluid deformation on mixing‐induced chemical reactions in heterogeneous flows

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