Experimental study of Lagrangian turbulence in a Stokes flow

Chaiken, J.; Chevray, R.; Tabor, M.; Tan, Qinxue

doi:10.1098/rspa.1986.0115

Cited by 184 publications

(61 citation statements)

References 9 publications

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“…The connection to chaos comes through experiments on chaotic advection (Aref 1984, 2002, Ottino 1990). For instance, in their experiments on chaotic advection, Chaiken et al (1986) noted that if the dye passed through a chaotic region the recovery was less perfect, but they did not investigate this in detail. Since many of the typical flows can be realized experimentally, also the dynamics of the Gaussians discussed below should be experimentally accessible.…”

Section: Introductionmentioning

confidence: 99%

Echoes in classical dynamical systems

Eckhardt

2002

J. Phys. A: Math. Gen.

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Abstract. Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.

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Section: Introductionmentioning

confidence: 99%

Echoes in classical dynamical systems

Eckhardt

2002

J. Phys. A: Math. Gen.

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“…The discovery that simple, nonturbulent velocity fields can evolve into complicated motions through chaotic advection [1] has generated a great deal of interest in fluid mixing [2][3][4][5][6]. Previous research has been mainly restricted to Newtonian fluids, often in idealized model flows [2,5,6].…”

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confidence: 99%

Mixing of Non-Newtonian Fluids in Steadily Forced Systems

et al. 2005

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“…Our paper is also related to the studies of chaotic advection in two-dimensional, time-dependent Stokes flows induced by two rotating eccentric cylinders (i.e. Aref & Balachandar 1986;Chaiken et al 1986Chaiken et al , 1987. We provide here yet another practical example of chaotic advection in a simple flow system.…”

Section: Introductionmentioning

confidence: 99%

A magnetohydrodynamic chaotic stirrer

2002

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A magnetohydrodynamic (MHD) stirrer that exhibits chaotic advection is investigated experimentally and theoretically. The stirrer consists of a circular cavity with an electrode (C) deposited around its periphery. Two additional electrodes (A) and (B) are deposited eccentrically inside the cavity on the bottom. The cavity is positioned in a uniform magnetic field that is parallel to the cylinder's axis, and it is filled with a weak electrolyte solution. Fluid motion is induced in the cavity by applying a potential difference across a pair of electrodes. A closed-form, analytical solution is derived for the MHD creeping flow field in the gap between the two eccentric cylinders. A singular solution is obtained for the special case when the size of the inner electrode shrinks to a point. Subsequently, passive tracers' trajectories are computed when the electric potential differences are applied alternately across electrodes AC and BC with period T. At small periods T, the flow is regular and periodic in most of the cavity. As the period increases, so does the complexity of the motion. At relatively large periods, the passive tracer experiences global chaotic advection. Such a device can serve as an efficient stirrer. Since this device has no moving parts, it is especially suitable for microfluidic applications. This is yet another practical example of a modulated, two-dimensional Stokes flow that exhibits chaotic advection. A magnetohydrodynamic (MHD) stirrer that exhibits chaotic advection is investigated experimentally and theoretically. The stirrer consists of a circular cavity with an electrode (C) deposited around its periphery. Two additional electrodes (A) and (B) are deposited eccentrically inside the cavity on the bottom. The cavity is positioned in a uniform magnetic field that is parallel to the cylinder's axis, and it is filled with a weak electrolyte solution. Fluid motion is induced in the cavity by applying a potential difference across a pair of electrodes. A closed-form, analytical solution is derived for the MHD creeping flow field in the gap between the two eccentric cylinders. A singular solution is obtained for the special case when the size of the inner electrode shrinks to a point. Subsequently, passive tracers' trajectories are computed when the electric potential differences are applied alternately across electrodes AC and BC with period T . At small periods T , the flow is regular and periodic in most of the cavity. As the period increases, so does the complexity of the motion. At relatively large periods, the passive tracer experiences global chaotic advection. Such a device can serve as an efficient stirrer. Since this device has no moving parts, it is especially suitable for microfluidic applications. This is yet another practical example of a modulated, two-dimensional Stokes flow that exhibits chaotic advection. A magnetohydrodynamic chaotic stirrer By M I N G Q I A N G Y I , S H I Z H I Q I A N A N D H A I M H. B A U †

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Experimental study of Lagrangian turbulence in a Stokes flow

Cited by 184 publications

References 9 publications

Echoes in classical dynamical systems

Echoes in classical dynamical systems

Mixing of Non-Newtonian Fluids in Steadily Forced Systems

A magnetohydrodynamic chaotic stirrer

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