Topological mixing study of non-Newtonian duct flows

Speetjens, Mfm Michel; Metcalfe, Guy; Rudman, Murray

doi:10.1063/1.2359698

Cited by 41 publications

(77 citation statements)

References 22 publications

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“…Figure 1b shows three successive reorientations of Q = 2p/3 by superposing successive sets of streamlines. We will call this stirred potential flow the rotated potential mixing (RPM) flow, and we will find that it leads to chaotic advection and transport in the disc in a manner similar to that of previous work on reoriented flows Speetjens et al 2006;Lester et al , 2009. To see the route to chaos more clearly, consider the time-averaged Hamiltonian H of this periodically reoriented flow (PRF),…”

Section: A Periodically Reoriented Irrotational Flowmentioning

confidence: 99%

“…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).…”

Section: Theorymentioning

confidence: 99%

“…Points approach stable manifolds as they move forward in time and approach unstable manifolds as they move backward in time. Periodic elliptic points are important because they have disconnected (possibly large) island regions around them that sequester or hinder (through cantori) material transport and reaction activity (Ottino et al 1992;Speetjens et al 2006). Islands are regions of rotation without much deformation that have KAM surfaces separating them from the rest of the flow.…”

Section: Theorymentioning

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: A Periodically Reoriented Irrotational Flowmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

See 1 more Smart Citation

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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“…In fact, three-dimensional spatially periodic steady flows with one unidirectional component can be transformed into twodimensional time-periodic flows v . v. 22 Hence, the generic properties of the corresponding advective-diffusive scalar transport are in the remainder of this section exemplified in terms of two-dimensional time-periodic systems. These concepts are applied to both time-periodic and spatially periodic systems in Secs.…”

Section: B Systems With Two-dimensional Time-periodic or Three-dimenmentioning

confidence: 99%

“…͑5͒ these periodic points and structures emerge in the two-dimensional mapping between spatial levels ͓0,Z ,2Z ,...͔. 22 Incompressible flows admit two types of nondegenerate periodic points: ͑i͒ elliptic points, which form the center of persistent nonmixing regions ͑"elliptic islands"͒; ͑ii͒ hyperbolic points, the associated manifolds of which accomplish the exponential stretching and folding of fluid parcels that underlies chaotic advection. 29 Generic two-dimensional advection patterns associated with periodic systems following Eq.…”

Section: Properties Of the Asymptotic Advection Patternmentioning

confidence: 99%

Eigenmode analysis of scalar transport in distributive mixing

2009

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In this study, we explore the spectral properties of the distribution matrices of the mapping method and its relation to the distributive mixing of passive scalars. The spectral (or eigenvector-eigenvalue) decomposition of these matrices constitutes discrete approximations to the eigenmodes of the continuous advection operator in periodic flows. The eigenvalue spectrum always lies within the unit circle and due to mass conservation, always accommodates an eigenvalue equal to one with trivial (uniform) eigenvector. The asymptotic state of a fully chaotic mixing flow is dominated by the eigenmode corresponding with the eigenvalue closest to the unit circle (“dominant eigenmode”). This eigenvalue determines the decay rate; its eigenvector determines the asymptotic mixing pattern. The closer this eigenvalue value is to the origin, the faster is the homogenization by the chaotic mixing. Hence, its magnitude can be used as a quantitative mixing measure for comparison of different mixing protocols. In nonchaotic cases, the presence of islands results in eigenvalues on the unit circle and associated eigenvectors demarcating the location of these islands. Eigenvalues on the unit circle thus are qualitative indicators of inefficient mixing; the properties of its eigenvectors enable isolation of the nonmixing zones. Thus important fundamental aspects of mixing processes can be inferred from the eigenmode analysis of the mapping matrix. This is elaborated in the present paper and demonstrated by way of two different prototypical mixing flows: the time-periodic sine flow and the spatially periodic partitioned-pipe mixer.

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Optimizing the rotated arc mixer

et al. 2008

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in Wiley InterScience (www.interscience.wiley.com).Using the mapping method an efficient methodology is developed for mixing analysis in the rotated arc mixer (RAM). The large parameter space of the RAM leads to numerous situations to be analyzed to achieve best mixing, and hence, it is indeed a challenging task to fully optimize the RAM. Two flow models are used to study mixing: one based on the full three-dimensional (3-D) flow field, and a second one based on a simplified 2.5-D model, where an analytical solution is used for transverse velocity components in combination with a Poiseuille profile for the axial velocity component. Detailed 3-D velocity field analyses reveal locally significant deviations from the Poiseuille profile e.g., presence of back-flow, but only minimal differences in mixing performance is found using both flow models (3-and 2.5-D) in the RAM designs that are candidates for accomplishing chaotic mixing. Despite the computational advantage of the 2.5-D approach over the 3-D approach, it is still cumbersome to analyze mixing for large number of designs using techniques based on particle tracking, e.g., Poincareś ections, dye traces, stretching distributions. Therefore, in this respect the mapping method provides an engineering tool able to tackle this optimization problem in an efficient way. On the basis of mixing evaluations, both in qualitative and quantitative sense, for the whole range of parameter space, the optimum set of design and kinematical parameters in the RAM is obtained to accomplish the best mixing.

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Topological mixing study of non-Newtonian duct flows

Cited by 41 publications

References 22 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

Eigenmode analysis of scalar transport in distributive mixing

Optimizing the rotated arc mixer

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