From Reynolds’s stretching and folding to mixing studies using horseshoe maps

Ottino, Julio M.; Jana, Sadhan; Chakravarthy, V. Srinivasa

doi:10.1063/1.868308

Cited by 51 publications

(47 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…with corresponding symmetry axis I 1 = S 2 I 1 the reflection of I 1 about I 2 (Ottino et al 1994;Speetjens et al 2004). Figure 6 gives the symmetry axes I 1 (red), I 1 (green), I 2 (blue) corresponding with the set of time-reversal symmetries (S 1 , S 1 , S 2 ) for the Poincaré sections at Θ = 3π/4 and T step = 0.2.…”

Section: Symmetry Within Sampling Levelsmentioning

confidence: 99%

“…Hence, said symmetries are key to shape and arrangement of the islands and thus play an essential role in the entrapment of production fluid. Moreover, the co-existence of multiple time-reversal symmetries implies periodic points Φ(x) = x at intersections of their symmetry axes (Ottino et al 1994). Thus the elliptic point upon which the predominant island is centred, e.g.…”

Section: Symmetry Within Sampling Levelsmentioning

confidence: 99%

“…Symmetries in the stroboscopic map are key organizing mechanisms in the Poincaré sections and thus vital to the "route to chaos" (Ottino et al 1994;Speetjens et al 2006;Lester et al 2009). The symmetry analysis of the isotropic case expands on that following Lester et al (2009).…”

Section: Symmetriesmentioning

confidence: 99%

See 2 more Smart Citations

Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems

2017

View full text Add to dashboard Cite

Enhanced geothermal systems (EGSs) are a promising concept to make geothermal power generation available in many regions worldwide. However, in current EGSs generally only a fraction of the geothermal reservoir is effectively accessed by the production fluid, resulting in suboptimal performance. Recent studies in the literature on a two-dimensional Darcy flow in a circular reservoir driven by reoriented injector-producer wells demonstrated that well configurations and pumping schemes designed on the basis of chaos theory enable efficient distribution of the production fluids throughout the entire reservoir. Key to this is accomplishment of chaotic advection, i.e. the rapid dispersion and stretching of material fluid regions, by a "proper" flow forcing. However, these studies concern isotropic reservoirs, while geothermal reservoirs typically are highly anisotropic. Our theoretical/computational study expands on said studies by investigating the impact of anisotropy on fundamental aspects of the Lagrangian transport of production fluids. This reveals that anisotropy generically eliminates key organizing mechanisms in the Lagrangian transport, viz. symmetries, and thus tends to promote disorder and, inherently, chaotic advection. However, symmetries are partially preserved-and thus order and coherence partially restored-in non-generic cases such as pumping schemes employing an even number of injector-producer wells and well configurations aligned with the anisotropy. Symmetry associated with well alignment in fact appears crucial to an intriguing "order within chaos" observed only in such cases: prolonged confinement of fluid to subregions of chaotic areas.

show abstract

Section: Symmetry Within Sampling Levelsmentioning

confidence: 99%

Section: Symmetry Within Sampling Levelsmentioning

confidence: 99%

See 1 more Smart Citation

Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems

2017

View full text Add to dashboard Cite

show abstract

“…Experiments with channels with complex surface topology including grooved walls have revealed that microscale mixing is enhanced by ''chaotic advection'', a process which was first reviewed by Aref (1984). He describes how mixing is still possible even at low Reynolds number by repeated stretching and folding of fluid elements (Ottino et al 1994). If properly applied, this mechanism causes the interfacial area between the fluids to increase exponentially, which can then lead to an enhanced intermaterial transport, hence mixing.…”

Section: Introductionmentioning

confidence: 99%

“…If properly applied, this mechanism causes the interfacial area between the fluids to increase exponentially, which can then lead to an enhanced intermaterial transport, hence mixing. A comprehensive mathematical description of the exponential growth of interfacial surfaces can be found in the book by Ottino (1989). Mixers, which utilize the principle of ''chaotic advection'', were designed in the following years (Kim 2007).…”

Section: Introductionmentioning

confidence: 99%

Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

Sarkar

Narváez

Harting

2012

Microfluid Nanofluid

View full text Add to dashboard Cite

Chaotic micromixers such as the staggered herringbone mixer developed by Stroock et al. allow efficient mixing of fluids even at low Reynolds number by repeated stretching and folding of the fluid interfaces. The ability of the fluid to mix well depends on the rate at which ''chaotic advection'' occurs in the mixer. An optimization of mixer geometries is a non-trivial task which is often performed by time consuming and expensive trial and error experiments. In this paper an algorithm is presented that applies the concept of finite-time Lyapunov exponents to obtain a quantitative measure of the chaotic advection of the flow and hence the performance of micromixers. By performing lattice Boltzmann simulations of the flow inside a mixer geometry, introducing massless and noninteracting tracer particles and following their trajectories the finite time Lyapunov exponents can be calculated. The applicability of the method is demonstrated by a comparison of the improved geometrical structure of the staggered herringbone mixer with available literature data.

show abstract

Chaotic advection and reaction during engineered injection and extraction in heterogeneous porous media

2014

View full text Add to dashboard Cite

During in situ remediation of contaminated groundwater, a treatment solution is often injected into the contaminated region to initiate reactions that degrade the contaminant. Degradation reactions only occur where the treatment solution and the contaminated groundwater are close enough that mixing will bring them together. Degradation is enhanced when the treatment solution is spread into the contaminated region, thereby increasing the spatial extent of mixing and degradation reactions. Spreading results from local velocity variations that emerge from aquifer heterogeneity and from spatial variations in the external forcings that drive flow. Certain patterns in external forcings have been shown to create chaotic advection, which is known to enhance spreading of solutes in groundwater flow and other laminar flows. This work uses numerical simulations of flow and reactive transport to investigate how aquifer heterogeneity changes the qualitative and quantitative aspects of chaotic advection in an aquifer, and the extent to which these changes enhance contaminant degradation. We generate chaotic advection using engineered injection and extraction (EIE), an approach that uses sequential injection and extraction of water in wells surrounding the contaminated region to create time-dependent flow fields that promote plume spreading. We demonstrate that as the degree of heterogeneity increases, both plume spreading and contaminant degradation increase; however, the increase in contaminant degradation is small relative to the increase in plume spreading. Our results show that the combined effects of EIE and heterogeneity produce substantially more stretching than either effect separately.

show abstract

From Reynolds’s stretching and folding to mixing studies using horseshoe maps

Cited by 51 publications

References 16 publications

Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems

Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems

Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

Chaotic advection and reaction during engineered injection and extraction in heterogeneous porous media

Contact Info

Product

Resources

About