Mixing in Stokes flow in an annular wedge cavity

Krasnopol’skaya, T. S.; Meleshko, V. V.; Peters, Gwm Gerrit; Meijer, Heh Han

doi:10.1016/s0997-7546(99)00119-3

Cited by 57 publications

(40 citation statements)

References 37 publications

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“…Computational methods for demarcating the manifold pairs (W u,s 1D , W s,u 2D ) of a given periodic point are following Ref. 38. Note that, for reasons of computational efficiency, 2D manifolds W 2D are approximated by curves W 2D emanating from the vector n = n 2 + n 3 , with n 2,3 the eigenvectors of the deformation tensor associated with W 2D .…”

Section: Barriers or (Ii) Accomplishing Chaotic Advection Through Tramentioning

confidence: 99%

Three-dimensional Lagrangian transport phenomena in unsteady laminar flows driven by a rotating sphere

et al. 2013

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Magnetic actuation of microscopic beads is a promising technique for enhancement and manipulation of scalar transport in micro-fluidic systems. This implies laminar and essentially three-dimensional (3D) unsteady flow conditions. The present study addresses fundamental transport phenomena in such configurations in terms of 3D coherent structures formed by the Lagrangian fluid trajectories in a 3D time-periodic flow driven by a rotating sphere. The flow field is represented by an exact Stokes solution superimposed by a nonlinear closed-form perturbation. This facilitates systematic “activation” and exploration of two fundamental states: (i) invariant spheroidal surfaces accommodating essentially 2D Hamiltonian dynamics; (ii) formation of intricate 3D coherent structures (spheroidal shells interconnected by tubes) and onset to 3D dynamics upon weak perturbation of the former state. Key to the latter state is emergence of isolated periodic points and the particular foliation and interaction of the associated manifolds, which relates intimately to coherent structures of the unperturbed state. The occurrence of such fundamental states and corresponding dynamics is (qualitative) similar to findings on a realistic 3D lid-driven flow subject to weak fluid inertia. This implies, first, a universal response scenario to weak perturbations and, second, an adequate representation of physical effects by the in essence artificial perturbation. The study thus offers important new insights into a class of flow configurations with great practical potential.

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Section: Barriers or (Ii) Accomplishing Chaotic Advection Through Tramentioning

confidence: 99%

Three-dimensional Lagrangian transport phenomena in unsteady laminar flows driven by a rotating sphere

et al. 2013

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“…In tracking the exponentially growing dye-streak, we have used the dynamic particle insertion algorithm of Krasnopolskaya et al (1999) to ensure that it remains well resolved. There is close agreement between λ theory and λ num .…”

Section: Numerical Simulations Of Dye Advectionmentioning

confidence: 99%

Topological chaos in inviscid and viscous mixers

2003

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Topological chaos may be used to generate highly effective laminar mixing in a simple batch stirring device. Boyland, Aref & Stremler (2000) have computed a material stretch rate that holds in a chaotic flow, provided it has appropriate topological properties, irrespective of the details of the flow. Their theoretical approach, while widely applicable, cannot predict the size of the region in which this stretch rate is achieved. Here, we present numerical simulations to support the observation of Boyland et al. that the region of high stretch is comparable with that through which the stirring elements move during operation of the device. We describe a fast technique for computing the velocity field for either inviscid, irrotational or highly viscous flow, which enables accurate numerical simulation of dye advection. We calculate material stretch rates, and find close agreement with those of Boyland et al., irrespective of whether the fluid is modelled as inviscid or viscous, even though there are significant differences between the flow fields generated in the two cases. IntroductionStatic and dynamic mixing devices are important in many industries, e. ) have demonstrated, in an unusual blend of ad hoc experimentation and abstract mathematics, that flows with the topology of certain braids achieve a material stretch rate which can be determined quantitatively, given only the topology of the flow. However, a key feature not predicted by their theoretical considerations is the size of the domain in which this stretch rate is attained. Indeed, according to the theory, this domain may have measure zero, and if this were the case then the theory would have little practical impact. Here we provide numerical results that support the observations of Boyland et al., that the chaotic region is in fact commensurate with the region of fluid through which the stirring elements move during operation of the device. We should make clear at the outset that we use the terminology 'topological chaos' in the same sense as Boyland et al. (2000), to

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“…For = / 2, the fluid strip is stretched exponentially in time-an indication of chaotic mixing. 46,47 This demonstrates that the multiple microactuator configuration can indeed be used to perform efficient mixing. In order to identify the optimal for the present configuration, the whole space from 0 to was explored; =3 / 2 gave approximately the same length stretch evolution as = /2, so space is assumed to be symmetric about = .…”

Section: -9mentioning

confidence: 89%

Active micromixer based on artificial cilia

et al. 2007

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We propose a design for an active micromixer that is inspired by the motion of ciliated micro-organisms occurring in nature. The conceptual design consists of an array of individually addressable artificial cilia in the form of microactuators covering the channel wall. The microactuators can be set into motion by an external stimulus such as an electric or a magnetic field, inducing either a primary or secondary motion in the surrounding fluid. To validate the concept and to help to design the precise mixer configuration, we developed a computational fluid-structure model. This model is based on a fictitious domain method that couples the microactuator motion to the concomitant fluid flow, fully capturing the mutual fluid-structure interactions. The simulated flow patterns resulting from the motion of single and multiple actuated elements ͑in a microchannel filled with a Newtonian fluid͒ under the action of a time-periodic forcing function are analyzed using dynamical systems theory to quantify the mixing efficiency. The results show that with a proper actuation scheme, two microactuators placed on the same wall of a microchannel can indeed induce effective mixing by chaotic advection; their distance should be small, but collisions should be avoided, and they can be actuated in a rather broad regime around 90°out of phase. Placing actuators on opposite walls also induces exponential stretching in the fluid, but if their length is relatively small, of the order of 20% of the channel height, mixing effectiveness is higher when they are arranged on the same wall.

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Mixing in Stokes flow in an annular wedge cavity

Cited by 57 publications

References 37 publications

Three-dimensional Lagrangian transport phenomena in unsteady laminar flows driven by a rotating sphere

Three-dimensional Lagrangian transport phenomena in unsteady laminar flows driven by a rotating sphere

Topological chaos in inviscid and viscous mixers

Active micromixer based on artificial cilia

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