Magnetic separation, manipulation and assembly of solid phase in fluids
Introduction
Separation and manipulation of suspended components is a problem faced in a variety of applications. Over the last three decades, magnetic separation technology has emerged as one of the most promising solutions. In this method, colloidal particles are manipulated by mismatches in their magnetization. Magnetic force can also be used to separate particles with differing non-magnetic properties such as size, shape, density, or even the degree to which a certain molecule is expressed on their surface. In the 1970s and 1980s, the majority of work was focused on wastewater treatment [1], [2], [3], [4], petroleum processing [5] and separation of biological entities including mammalian cells and bacteria [6], [7], [8]. Initial work was accompanied by advances in materials [9] and instrumentation [10], [11], [12] for separating weakly magnetic and ultrafine magnetic particles [13], [14], [15], [16], [17], [18] from fluid suspension. Representative work from this era is summarized in several review articles [19], [20]. In the 1990s and the current decade, magnetic separation techniques have been adopted in several life science diagnostic devices [21], [22], [23], [24], [25] and in drug delivery applications [26], [27], [28], [29], [30], [31]. Emerging applications have revitalized interest in the design and manufacture of high gradient magnetic separation systems [32], [33], [34], [35], [36], [37] and magnetic particle carriers [38], [39], [40], [41].
Most notably, recent advances in photolithography have allowed for production of structures with gradients exceeding 105 Teslas per meter, through the use of current lines [42], [43], domain walls in garnet films [44], [45] and arrays of small magnets patterned on fluid contacting surfaces [46], [47], [48], [49], [50], [51], [52], [53], [54], [55]. The small size of these structures and their exceedingly strong field gradients have made them useful not only in separation, but also in performing finer operations on particles in the fluid, including controlled transport [55], [56], [57], [58], [59] and micro-assembly [60], [61], [62] of particles above surfaces. Controlled transport of colloidal particles is commonly employed in lab-on-a-chip technology [63]. Directed assembly of colloidal particles has also shown promise for the future fabrication of photonic crystals and in the micro-arrangement of precious biological components, including cells and/or molecules, into desired configurations on a surface [64], [65]. The nimbleness of magnetic manipulation techniques have been on display in recent work on transport and assembly of magnetic [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54] as well as non-magnetic particles [55], [66], [67], [68], [69].
The objective of this paper is to review previous research and help systematize the theoretical framework of magnetic separation techniques. The paper will be organized as follows. Scaling principles in magnetic systems in the context of Brownian motion of colloidal particles will be reviewed in Section 2. Magnetic force will be compared with gravity and electrical forces in Section 3. The incorporation of hydrodynamics in models of magnetic separation will be discussed in Section 4. Limitations of this paper and some open questions will be discussed in Section 5.
Section snippets
Magnetic force scaling and Brownian motion
Two main classes of magnetic fluid models exist: continuum and particle models. In continuum models, the magnetic particles are considered to be inseparable from the fluid. The presence of the magnetic phase is accounted for implicitly by adding magnetization parameters to the usual degrees of freedom of the bulk fluid (i.e. velocity, density, temperature, and so on). This approach is usually employed in problems dealing with movement of the entire fluid, rather than separate fluid components.
Comparison of magnetic force with gravity and electrical forces
In addition to randomizing effects of thermal fluctuation one has to consider other influences on particle separation and manipulation phenomena. Gravity is one possible influence. Gravitational settling in colloidal systems is a well-known and widely discussed issue. For this reason, no detailed analysis will be presented here except for the comparison of gravitational and magnetic forces in the vicinity of gradient producing magnetic elements such as a magnetized sphere. To be specific the
Hydrodynamics in models of magnetic separation and manipulation
While fluid motion can, in general, be quite complex, this review will consider only relatively simple cases of low Reynolds number flow. The Navier–Stokes equation (see Ref. [71], for example) simplifies in this case to the following linear Stokes equation for the fluid velocity:where ρ is the fluid density, p is the pressure field, η is the fluid viscosity, and is the applied force field (in the case of magnetic manipulation dominated by magnetic
Conclusions and open questions
This paper attempted to provide an overview of applications and theoretical models for magnetic separation, manipulation and assembly. This overview was motivated by the desire to summarize past efforts in the vast area of magnetic separation and manipulation in light of recent interest in miniaturization of such systems. The paper focused on issues related to scaling of magnetic forces with sizes of particles and of gradient producing structures. It briefly reviewed literature related to
Acknowledgement
The authors are thankful for the financial support from the US National Science Foundation under the ECS-0304453 grant.
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