A magnetohydrodynamic chaotic stirrer

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. Comments Copyright Cambridge University Press. Reprinted from Journal of Fluid Mechanics, Volume 468, 2002, pages 153-177. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/58 J. Fluid Mech. (2002), vol. 468, pp. 153–177. c © 2002 Cambridge University Press DOI: 10.1017/S0022112002001635 Printed in the United Kingdom 153 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 AND H A I M H. B A U† Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA (Received 11 July 2001 and in revised form 8 May 2002) 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.