Magneto-hydrodynamics based microfluidics
Introduction
In recent years, there has been a growing interest in developing lab-on-a-chip (LOC) systems for bio-detection, biotechnology, chemical reactors, and medical, pharmaceutical, and environmental monitoring. LOC is a minute chemical processing plant that integrates common laboratory procedures ranging from filtration and mixing to separation and detection. The various operations are done automatically within a single platform. To achieve these tasks, it is necessary to propel, stir, and control fluids. Since in many applications, one uses buffers and solutions that are electrically conductive, one can transmit electric currents through the solutions. In the presence of an external magnetic field, the interaction between the electric currents and magnetic fields results in Lorentz body forces, which, in turn, can be used to propel and manipulate fluids. This is the domain of magneto-hydrodynamics (MHD).
The application of MHD to pump, confine, and control liquid metals and ionized gases is well-known (Woodson and Melcher, 1969, Davidson, 2001). The application of MHD to weakly conductive electrolyte solutions is somewhat more complicated due to electrodes’ electrochemistry. Recently, various MHD-based microfluidic devices including micro-pumps (Jang and Lee, 2000, Lemoff and Lee, 2000, Huang et al., 2000, Bau, 2001, Sadler et al., 2001, Zhong et al., 2002, Bau et al., 2002, Bau et al., 2003, Sawaya et al., 2002, West et al., 2002, West et al., 2003, Ghaddar and Sawaya, 2003, Bao and Harrison, 2003a, Bao and Harrison, 2003b, Eijkel et al., 2004, Wang et al., 2004, Arumugam et al., 2005, Arumugam et al., 2006, Qian and Bau, 2005b, Homsy et al., 2005, Homsy et al., 2007, Affanni and Chiorboli, 2006, Aguilar et al., 2006, Kabbani et al., 2007, Patel and Kassegne, 2007, Duwairi and Abdullah, 2007, Ho, 2007), stirrers (Bau et al., 2001, Yi et al., 2002, Qian et al., 2002, Gleeson and West, 2002, Xiang and Bau, 2003, Gleeson et al., 2004, Qian and Bau, 2005a), networks (Bau et al., 2002, Bau et al., 2003), heat exchangers (Sviridov et al., 2003, Singhal et al., 2004, Duwairi and Abdullah, 2007), and analytical and biomedical devices (Leventis and Gao, 2001, West et al., 2002, West et al., 2003, Bao and Harrison, 2003a, Lemoff and Lee, 2003, Eijkel et al., 2004, Clark and Fritsch, 2004, Homsy et al., 2007, Gao et al., 2007, Panta et al., 2008) operating under either DC or AC electric fields have been designed, modeled, constructed, and tested. The DC operation is often adversely impacted by the electrodes’ electrochemistry leading to bubble formation and electrode corrosion. These problems are partially solved with the use of AC fields. AC operation requires, however, the use of electromagnets instead of the permanent magnets that are used in DC operation, which increases power consumption. Moreover, AC operation induces parasitic eddy currents that may lead to excessive heating. DC operation with RedOx species that undergo reversible electrochemical reactions alleviates many of the disadvantages of DC MHD (Qian and Bau, 2005b, Arumugam et al., 2006, Kabbani et al., 2007).
The advantage of MHD compared to electroosmosis is operation at relatively small electrode potentials, typically below 1 V, and much higher flow rates as long as the conduit’s dimensions are not too small. The disadvantage of MHD is that it is a volumetric body force which scales unfavorably as the conduit’s dimensions are reduced. Thus, MHD is appropriate mostly for moderate conduit sizes with characteristic dimensions on the order of 100 μm or larger.
In this paper, we review the basic theory of MHD as applied to low conductivity solutions and describe various applications of MHD such as pumps, integrated fluidic networks, stirrers, liquid chromatographs, thermal cyclers, and microcoolers.
Section snippets
Theory
We consider an incompressible, viscous fluid. The velocity vector u satisfies the continuity equationWe adopt here the notation that bold letters represent vectors. The momentum equation iswhere ρ and μ are, respectively, the liquid’s density and viscosity; t is time; J is the electric current flux; p is pressure; and B is the magnetic field intensity. In the above, we assume that the liquid’s magnetic permeability is sufficiently small so that the magnetic field
Practical considerations
Many of the difficulties encountered when using electrolyte-based MHD devices are associated with the electrodes’ chemistry. In a closed system, one must operate at sufficiently low potential differences between the electrodes, typically below ∼1.2 V, to avoid the electrolysis of water. The electrolysis of water would cause an accumulation of gas bubbles along the surface of the electrode. Such a gas blanket will shield the electrodes and prevent current transmission through the solution.
MHD-based micro-pumps
The best known application of MHD is fluid pumping. One possible embodiment of a MHD pump is depicted in Fig. 1. The device consists of a conduit with two electrodes deposited along its opposing walls. The conduit is filled with a conductive medium (either electrolyte solution or liquid metal). When a potential difference is applied across the two opposing electrodes, current flux J flows through the solution. In the presence of a magnetic field B, the electric current J interacts with the
Conclusions
In many microfluidic applications, it is necessary to propel fluids from one part of the device to another, control fluid motion, stir, and separate fluids. However, due to the small size of the devices and the desire to carry out a large number of operations, these tasks are far from trivial. MHD offers an elegant, inexpensive, flexible, customizable means of performing some of these functions.
The flow in MHD-based microfluidics is induced through the interaction between an external magnetic
Acknowledgement
This work is supported, in part, by NIH STTR Grant 545817 to Vegrandis (HHB).
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