Background
Actuation of ferrofluids using only external magnetic fields offers the possibility of compact, reliable and simple fluid manipulation schemes both in macro and micro scales. However, most of these schemes have so far focused on magnetic forces acting on the free ferrofluid surface and on utilizing these forces to pump a secondary, non-magnetic fluid (as shown in Fig. 1). As a result, application potential of these schemes as compact and integrated pumps are limited by practical considerations, such as the compatibility and mixing potential of the two fluids and the surface properties of the channel walls, or the need for external moving permanent magnets.
Source: G. S. Park and S. H. Park, IEEE Trans.
Mag., vol. 35, no. 55, Sept. 1999.
Source: A. Hatch, et al., J.MEMS, vol.10, no.2, June 2001.
Fig. 1. Some existing pumping schemes using ferrofluids.
Fig. 1. Schematic drawing of nanoparticles in ferrofluid suspension. (Source: FerroTec Corp.)
What is needed is an approach that allows pumping ferrofluids themselves in closed-loop geometries at multiple scales, enabling various applications ranging from integrated cooling systems to implantable drug delivery and cellular manipulation devices. In this fashion, ferrofluid chemistry and composition can be engineered for the specific application at hand, and the same actuation scheme can be employed for virtually all types of ferrofluids.
Ferrohydrodynamics and Traveling Magnetic Fields
There are two mechanisms by which the magnetization of a magnetic nanoparticle can relax after the applied field has been changed. In the first mechanism, the relaxation occurs by particle rotation in the liquid (Brownian relaxation). In the second mechanism, the relaxation is due to rotation of the magnetic moment within the particle (Neel relaxation). Given the magnetic material, the viscosity and the temperature of the carrier liquid, the particle size determines which relaxation mechanism dominates. As depicted in Fig. 2 below, particles smaller than a certain size relax via the Neel mechanism, while Brownian relaxation dominates for larger ones.
Fig. 2. Magnetite particles larger than about 10 nm relax via the Brownian mechanism, while in those smaller than about 8 nm, Neel mechanism dominates.
In a ferrofluid comprised of magnetite nanoparticles larger than 10 nm in diameter, a rotating magnetic field externally applied on the ferrofluid will cause the particles to rotate as well. There is an optimum rotation frequency for maximum angular momentum transfer to the particles -- go too fast and the particles cannot catch up with the rotation. The average Brownian time constant of a ferrofluid determines that optimum frequency.
If the rotating magnetic field has an intensity gradient, not all the magnetic nanoparticles in the ferrofluid will rotate at the same speed. Consequently, a gradient in angular momentum can be formed within the ferrofluid, which, within a confined channel, could be translated into linear ferrofluid motion. A traveling magnetic field can create such an excitation in the vicinity of a ferrofluid within a flow channel.
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Actuation using traveling waves involves magnetic body forces and torque on the magnetic moment of the nanoparticles, both of which affect the overall pumping.
The animation on the right illustrates how a traveling magnetic field looks like on a planar substrate. The wave itself is generated by sinusoidal currents running through electrodes in quadrature. In the most ideal case, we assume that the ferrofluid is mono-disperse (a single particle size) and magnetically linear. In order to describe what happens to the ferrofluid in the presence of a traveling wave, governing equations, including magnetization constitutive law and coupled linear and angular momentum conservation equations are solved numerically (Fig. 3). The result is the magnetic field strength inside the ferrofluid, as well as the flow and spin velocities of the magnetic particles. |
The magnetization relaxation equation (MRE) for a ferrofluid is:
Coupled Navier-Stokes Equations, both for linear and angular velocity:
Iterative Solution Approach:
Fig. 3. The magnetic relaxation equation for a monodisperse, ideal ferrofluid; the coupled Navier-Stokes equations that describe the ferrohydrodynamics; the iterative solution approach used to solve the equations.
Simulation results suggest that the flow velocity is strongly dependent on the traveling wave period. Maximum flow velocity is achieved when the product of the excitation wave number and radius of the ferrofluid cylinder approaches unity (Fig. 4) . Once geometric dimensions are chosen, the flow velocity can be precisely controlled by the applied magnetic field frequency. Interestingly, as the height of the channel is chosen smaller, maximum pumping peak shifts to lower frequencies. The same findings apply to both cylindrical and Cartesian geometries.
 
Fig. 4. Maximum flow velocity is achieved when the product of the excitation wave number and the height of the channel containing the ferrofluid approaches unity.
Micro-scale Device Fabrication
In experiments designed based on ferrohydrodynamic models, we have demonstrated that it is possible to pump ferrofluids directly via traveling magnetic fields, both at the macro and micro scales. Macro-scale pumping experiments are relatively straightforward to set up (requiring a trip to the local plumbing store); micro devices (incorporating micro-electro-mechanical systems, or MEMS) necessitate microfabrication and construction of microfluidic channels. Fig. 5 below illustrates the basic steps involved in creating a microfluidic channel network over an electrode pattern over a special substrate.
Fig. 5. Microfabrication process for the micro-scale ferrohydrodynamics testing device [REF].
The microfluidic channel is fabricated using soft lithography [1]. The electrodes can either be etched, or electroplated in place; Fig. 5 depicts the former process. Pressure sensors at the ends of the channel detect pressure changes associated with ferrohydrodynamic pumping. Alternatively, a closed-loop channel may be formed and flow rate could be monitored directly. A pressure reading obtained using such a microfabricated device is depicted in Fig. 6 below.
Fig. 6. Ferrohydrodynamic pumping data obtained from a device fabricated as depicted in Fig. 5.
Why study ferrofluid pumping on microfabricated devices? Well, for starters, being able to manipulate a liquid medium at the micro-scale without any mechanically moving components paves the way to fully integrated and more robust cellular sorting schemes (in the context of lab-on-a-chip devices), as well as tissue and whole organ generation on artificial media for lower risk implants. What is more, studying ferrohydrodynamics at the micro-scale is significant in the context of developing effective, rapid, sensitive and disposable pathogen detector chips.
Pathogen Detection via Ferrohydrodynamics
The dependence of the optimal pumping peak on the Brownian relaxation time constant suggests an effective scheme for pathogen detection. When target molecules or pathogens bind to the surface of a functionalized magnetic nanoparticle within a ferrofluid, the particle’s overall hydrodynamic volume increases, causing a corresponding rise in its Brownian relaxation time constant. Consequently, with enough particles bound to antigens, the optimum pumping frequency will shift towards a lower value. A quick sweep of pumping pressure versus excitation frequency, conducted both before and after the binding, will reveal the peak shift and signal the presence of the antigen.
The approach outlined above is relatively straightforward; however, it does not account for temperature and viscosity changes that may take place when a ferrofluid with functionalized nanoparticles is mixed with a sample liquid. Such temperature or viscosity changes may also shift the pumping peak, creating false positives.
Our solution: a ferrofluid with non-functionalized magnetic particles (e.g., 10 nm average overall hydrodynamic diameter) may be divided into two parts. The magnetic particles in one of them may be coated with the specific receptors (e.g., typical 10-20 nm antibodies), the effective hydrodynamic diameter of the coated nanoparticles will then be 20-30 nm. The ferrofluid produced by mixing these two parts will have equal amounts of 10 nm and 30 nm (assuming 20 nm antibodies are used) effective hydrodynamic diameter particles, which corresponds to two different pumping peaks (Fig. 7). Inevitably, there are smaller diameter particles (< 10 nm) which relax through the Neel mechanism. One can carefully engineer the ferrofluids (e.g., change the viscosity, change the mean particle diameter, etc.) so that the great majority of the magnetic particles are Brownian particles and the observed effect only comes from the Brownian relaxation mechanism.
Fig. 7. Microfabrication process for the micro-scale ferrohydrodynamics testing device [REF].
Ferrohydrodynamic pumping scales favorably down to smaller geometries. A batch fabricated pathogen detector chip the size of a postage stamp and containing a few microliters of a functionalized ferrofluid offers the convenience of a rapid, disposable assay with low cost and reliability, much like a pregnancy test kit. Prescreening incoming patients at hospitals for highly contagious diseases with such devices could bring significant time and cost savings by preventing unnecessary spread of infections, let alone save lives. Using these sensor chips in the field could also boost the readiness levels of doctors, public health officials and Homeland Security personnel for a potential biological threat.
This material is based upon work supported by the National Science Foundation under Grant No. EECS-0449264 and EECS-0529190. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and researchers, and do not necessarily reflect the views of the National Science Foundation.
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