AC Dielectrophoresis Lab-on-Chip Devices

Synonyms

Dielectrophoretic force; DEP

Definition

Dielectrophoresis is the translational motion of a neutral particle by induced polarization in a nonuniform electric field. The magnitude and direction of the induced dielectrophoretic force are dependent on the characteristics of the applied electric field as well as the dielectric properties of the surrounding medium and of the particle itself.

Overview

Herbert Pohl was one of the first to study particle electrokinetics in the 1950s, particularly the manipulation of polarizable particles with nonuniform fields. He coined the term dielectrophoresis, and details of his investigations can be found in his classic text [1]. The advancement of microfabrication techniques and the demand of Lab-on-a-Chip technologies have led to the development of dielectrophoresis techniques for particulate, biological and pharmaceutical applications. Dielectrophoresis was initially used to manipulate particles and cells in the micrometer range ($\mathrm{1}$ $\mathrm{\mu m}$ to $\mathrm{1}$ $\mathrm{mm}$). Since the early 1990s, nanotechnology has incorporated dielectrophoresis for the manipulation of viruses, DNA, protein molecules and other nanoparticles (diameters of $\mathrm{1}$ $\mathrm{nm}$ to $\mathrm{1}$ $\mathrm{\mu m}$). This article provides a brief background of dielectrophoresis followed by its basic manipulation of particles using translation, rotation (electrorotation), orientation (electro-orientation) and traveling wave dielectrophoresis. This article approaches design considerations and modeling techniques for the micrometer length scale; it does not specifically address all dielectrophoresis complexities at the nanometer scale. The majority of this article deals with popular applications of dielectrophoresis including novel techniques to induce these forces; by no means does it cover all of the existing applications. For a more extensive explanation of dielectrophoresis the reader is referred to texts by Jones [2], Morgan and Green [3], and Hughes [4], the latter of which addresses techniques for nanometer-sized particles.

For most dielectrophoresis cases, the applied electric field is an alternating current (AC) signal, created with a common frequency generator. In typical experimentation, frequencies are generally greater than 100 kHz with magnitudes below 20 V peak-to-peak. The shape of the signal is typically sinusoidal, but pulse signals have also been used in dielectrophoresis applications. This signal is applied to electrode geometries, the micrometer-sized features of which can be created using simple microfabrication techniques. Electrodes are typically fabricated on the surface of silicon wafers or glass substrates, including microscope slides. For most biological applications it is recommended that the species of interest be visually observed by optical means, which leaves glass or other transparent materials as favorable substrates. In the case where the electrodes themselves hinder visual observation they are patterned out of indium tin oxide (ITO), a transparent conducting material. Microfluidic channels and other fabricated features can easily be incorporated into the system. It is possible to manipulate, separate or group targeted cells with novel electrode geometry design and fabrication. Due to its simplicity in fabrication and its susceptibility to visual observation and analysis, dielectrophoresis is a favorable technique for biological experimentation.

Dielectrophoretic forces, though, can be induced by means other than an applied electric signal through electrodes. Optical tools can be implemented to modify an applied electric field, making these methods more susceptible for dynamic as opposed to static manipulation of electric fields with surface electrodes. Dielectrophoresis applications are not limited to particulate manipulation either. With properly configured surface-electrode geometry, it is possible to induce fluid motion and create nanoliter-sized droplets. Additionally, dielectrophoretic forces can be utilized to manipulate particles to build micro- and nanostructures such as wires.

Basic Methodology

Before we can incorporate dielectrophoresis into Lab-on-a-Chip systems it is important to have a grasp of the theory behind dielectrophoresis. Basic theory, common experimental parameters, typical dielectrophoretic manipulation techniques, particle modeling considerations and dielectrophoresis-induced effects are discussed below.

Dielectrophoresis

Dielectrophoresis is the translational motion of a particle by induced polarization in a nonuniform electric field. When conductive, uncharged particles are exposed to an electric field they will polarize, inducing a dipole on the particle. The magnitude and charge orientation of the induced dipole are dependent on the permittivities and conductivities of the medium and of the particle. If the electric field is uniform the induced charges on both sides of the particle are equal, creating no net force on the particle. However, if the electric field is nonuniform (Fig. 1) there will be a net force greater than zero. The general expression for the dielectrophoretic force of a homogeneous sphere is expressed as

$$ F_{{\textrm{DEP}}}=2\pi\varepsilon _{{0}}\varepsilon _{{\textrm{m}}}r^{3}\textrm{Re}\big[{K(\omega)}\big]\nabla E^{2} $$

(1)

where $\varepsilon _{{0}}$ is the permittivity of free space, $\varepsilon _{{\textrm{m}}}$ is the relative permittivity of the medium, $r$ is the radius of the particle, $\textrm{Re}\left[{K(\omega)}\right]$ is the real part of the Clausius–Mossotti factor and $\nabla E^{2}$ is the gradient of the magnitude of the electric field squared. This equation assumes that the there is no applied phase gradients to the electric field. The Clausius–Mossotti factor is defined as

$$ K(\omega)=\frac{\varepsilon _{{\textrm{p}}}^{\ast}-\varepsilon _{{\textrm{m}}}^{\ast}}{\varepsilon _{{\textrm{p}}}^{\ast}+2\varepsilon _{{\textrm{m}}}^{\ast}} $$

(2)

where subscripts p and m are assigned to the particle and medium, respectively, and $\varepsilon$ ${}^{{\ast}}$ is called the complex permittivity. The complex permittivity is

$$ \varepsilon^{{\ast}}=\varepsilon _{{0}}\varepsilon _{{\textrm{r}}}-j\frac{\sigma}{\omega} $$

(3)

where $j$ is $\sqrt{-1}$, $\varepsilon$ ${}_{{\textrm{r}}}$ is the material's relative permittivity, $\sigma$ is the material's conductivity and $\omega=2\pi f$ (where $f$ is the applied frequency). The Clausius–Mossotti factor is a function of frequency and, depending on the dielectric properties of the medium and particle, this factor can be either positive or negative with a possible range of $+1.0$ to $-0.5$. If $\textrm{Re}\left[{K(\omega)}\right]$ is negative, the particle experiences negative dielectrophoresis (nDEP) and is repelled from gradients in the nonuniform electric field (Fig. 1). For a positive value of $\textrm{Re}\left[{K(\omega)}\right]$, the particle is attracted to high electric field gradients with positive dielectrophoresis (pDEP). With dielectrophoresis it is possible to manipulate particles using a variety of techniques and applications.

Figure 1

A polarizable particle in a nonuniform electric field

Particle Manipulation

Figure 2

Dielectrophoretic manipulation techniques: (a) electrorotation, (b) electro-orientation, (c) particle trapping and (d) traveling wave dielectrophoresis

The majority of dielectrophoretic manipulation of particles includes translating (dielectrophoresis), rotating (electrorotation), orienting (electro-orientation), trapping and using traveling wave dielectrophoresis. Figure 2 provides an illustrative representation of each technique. In electrorotation a torque is applied to a particle that is subjected to a rotating electric field (Fig. 2a). The induced dipole takes a finite amount of time to polarize in a neutral dielectric particle, which attempts to orient itself with the direction of the electric field. This dipole, though, lags behind the applied rotating electric field. The reorientation of the dipole with the electric field induces a torque on the particle, rotating it. Next, electro-orientation involves the alignment of a nonspherical particle in a uniform electric field (Fig. 2b). When an ellipsoidal particle polarizes, the dipole moment will align the particle with its longest nondispersed dipole parallel to the field lines. Its orientation is a function of the electric field frequency and the dielectric properties of the medium and particle.

Dielectrophoretic forces, though, can be used to not only rotate a particle, but trap it as well. There are two types of particle trapping, those that utilize pDEP or nDEP forces. For example, four electrodes can be positioned in a quadrupole arrangement and, when the appropriate electric field is applied, a particle or particles are trapped in the electric field null at its center (Fig. 2c). Particle trapping will be revisited later in this article. Traveling wave dielectrophoresis is the linear application of electrorotation (Fig. 2d). An AC electric wave is produced by applying an electric field that travels linearly along a series of electrodes. The particle will translate in the same or opposite direction as the traveling wave depending on the properties of the applied signal frequency and the dielectrics of the particle and medium.

Modeling and Dielectrophoretic Effects

When incorporating dielectrophoresis in Lab-on-a-Chip systems, additional modeling parameters and electro-physiological interactions need to be considered. Obviously, biological cells and some particulates are not all completely spherical nor are they homogeneous. Typically cells are modeled as multi-shelled particles with each shell having its own respective conductivity and permittivity. Additionally, nonspherical particles are modeled as ellipsoids. For each of these situations the Clausius–Mossotti factor is extended to include these geometrical and layered effects by applying polarization factors. These modifications are described in detail elsewhere [2,3,4]. The dielectric properties of some particles and cells are unknown; however, dielectric techniques can be applied to determine these characteristics. For example, when an induced particle changes from pDEP to nDEP, or vice versa, this is called its crossover frequency. Similarly, a particle in electrorotation that changes in rotational velocity or direction under different conditions will give insight into its dielectric properties. Many of the previously mentioned dielectrophoretic manipulation techniques can be applied to determine particle dielectric characteristics. By varying both the medium conductivity and the applied frequency, the changes in a particle's induced dielectrophoretic behavior can be visually observed.

The electric field can induce higher order poles, called multipoles, instead of the assumed dipole. This occurs when the electric field is highly nonuniform; for example, when the electrode geometry is on the same length scale as the particle or when a particle is in a field null. For most applications, though, the dipole assumption accurately depicts the behavior of the particle. However, multipoles can effect the particle's interaction with the electric field and will react differently from an induced dipole. The electric field can also induce some negative physiological effects to the cell by inducing cell heating and influencing transmembrane voltage. Transmembrane voltage can affect ion movement and damage voltage-sensitive proteins. The electric field itself can heat the surrounding medium in what is called Joule heating. Joule heating creates temperature gradients that can directly heat the cell or create localized convection currents. By working at the micrometer length scale some of these negative effects are minimized; however, they may still influence the system and cannot be ignored.

Key Research Findings

This dielectrophoresis background only serves as a brief overview; these technologies need to be explored in more detail before incorporating them into a Lab-on-a-Chip system. Lab-on-a-Chip systems integrate techniques of small fluid and sample handling with detection or process capabilities. Dielectrophoresis can be incorporated into these systems to manipulate, separate or trap cells as well as control small amounts of fluid. This technology can be used to trap cells for additional analysis, separate cell types based on dielectric properties, dispense picoliter droplets or used for similar manipulative applications. However, dielectrophoresis itself cannot be used as a sensor, except to determine dielectric properties of cells or detect such changes in response to stimuli. The integration of sensory technologies with dielectrophoresis is not discussed. Instead, specific novel dielectrophoresis applications are addressed in detail.

Trapping Particles

One of the more popular dielectrophoretic manipulation techniques involves the trapping of individual or groups of cells. Dielectrophoresis can be thought of as electrical tweezers that will grab onto and position cells. Trapping can be accomplished by means of novel electrode geometries that utilize pDEP or nDEP forces to selectively capture a particle or cell. Some electrode geometries induce both types of forces simultaneously; an example of such an arrangement involves interdigitated electrodes (Fig. 3). Planar electrode fingers, whose width and gap separation are a few times larger than the diameter of the particles of interest, have alternating applied voltages (either $\mathrm{180}$ ${}^{\circ}$ out of phase or alternating $+V$/ground). This geometry creates a strong pDEP force at the edges of the electrodes and a field null above the center of each electrode strip. This arrangement provides both trapping capabilities and the ability to determine unknown particle dielectric properties from visual observation. For example, at a particular frequency and medium conductivity a particle will experience a pDEP force. However, for a different applied frequency and/or a change in medium conductivity the same particle could undergo nDEP. The strength of the dielectrophoretic trapping force can be estimated with the hydrodynamic drag necessary to release the particle. Similarly, interdigitated electrodes can be used to separate two cells that experience opposite pDEP/nDEP forces due to their different dielectric characteristics. Interdigitated electrodes are one of the simpler electrode geometries, compared to other trapping arrangements.

Figure 3

Dielectrophoresis of particles with interdigitated electrodes (side view). Particles experiencing pDEP are attracted to the edges of the electrode while nDEP forces repel the particle to the middle of the electrode

Figure 4

Various electrode geometries for dielectrophoretic traps: (a) pDEN trap (side view), (b) nDEP planar trap (top view), and (c) nDEP octopolar trap

Other electrode geometries have been designed to capture individual cells using either pDEP or nDEP forces. A number of these geometries have been explored by Voldman and his research group [5] and will be discussed here. For pDEP, geometries are created that generate extreme electric field gradients in the trapping region. A geometry that creates such a field gradient is illustrated in Fig. 4a. An electrode smaller than the diameter of the particle has the signal applied through it to a larger, receiving electrode. The generated electric field would be similar to that illustrated in Fig. 1, with a high gradient in proximity to the smaller electrode. Electric field nulls have also been generated with electrode geometries for nDEP traps. Recall the quadrupole geometry in Fig. 2c. When an appropriate electric field is applied a field null is created in the center of the trap. The trapped particle is repelled from the surrounding regions of field gradients. Another nDEP trap is illustrated in Fig. 4b. The electric field is applied from the trapping electrode to the receiving electrode strip. A particle is trapped within the generated null inside the “boxed” electrode geometry. These previous geometries will trap a particle near the surface of the substrate. Electrodes, though, can be arranged three-dimensionally to create traps that capture particles and cells in suspension. One example is a nDEP trap using two stacked quadrupole geometries, resulting in an octopole trap (Fig. 4c). The electric field null is generated in the midplane between these two electrode substrates and thus a particle experiencing nDEP is captured in suspension. These are just a few examples of established trapping geometries, as others could be designed to suit a particular trapping application.

There are numerous trap geometries that exist for both pDEP and nDEP. These electrode arrangements and cell concentration can be varied to trap both single cells and groups of cells alike. However, there are dielectrophoretic interactions that cannot be ignored for trapping applications. Multipoles may need to be considered for single-particle traps since the generated field will have inhomogeneities on the scale of the particle itself. Also, particle–particle dielectrophoretic interactions will influence the capabilities of multi-particulate traps. Dielectrophoresis, therefore, needs to be accurately modeled and thoroughly investigated prior to use in a specific application.

Electrode-Based Systems

Microsystems have incorporated dielectrophoretic forces into microchannels to manipulate particles and cells with various electrode geometries. Electrodes can be used to align target cells or separate particulate cells from the rest of the sample, an example of which is illustrated in Fig. 5. These systems use a three-dimensional arrangement of electrodes, with mirrored electrode geometries aligned and separated by microfluidic structures. Thus the electrodes in Fig. 5 are on the top and bottom surfaces of the microchannel and do not significantly impede or manipulate the fluid flow. This system is optimized for a particular set of cells such that the applied signals generate the strongest dielectrophoretic forces; this system will operate with the maximum possible applied flow rate for more effective processing. The system, though, will be selective to a set of cells with the same or similar dielectric properties. This process is obviously advantageous for an application that selectively separates cells based on their dielectric properties. Additionally, this system can simultaneously separate and trap targeted cells for selective biological investigations. An example of a dielectrophoresis system and a description of its potential for biological analysis is explained in [6]. These dielectrophoresis techniques can be coupled with a variety of existing biological tools for innovative applications including fluorescence evaluation of cells in small populations, cell sorting, long-term investigations of single cells, cellular kinetics and other similar Lab-on-a-Chip analyses.

Figure 5

An illustration of a dielectrophoretic microsystem that can selectively sort particles (top view). Recall that the electrodes are on the top and bottom surfaces of the microchannel and to not mechanically manipulate the particles

Insulating Dielectrophoresis

Conventionally, the nonuniform electric fields for dielectrophoresis applications are produced directly with an arrangement of conductive electrodes. However, a nonuniform electric field can be generated in microchannels without direct interaction with electrodes. For example, Cummings generated nonuniform electric fields using remote electrodes placed at the inlet and outlet of the microchannel [7]. The electric field is applied across the channel and is deformed by the variations in the channel geometry or by insulating structures or posts within the microchannel. These mechanical structures within the channel will affect the generated electric field as well as dynamically change the flow field; these can be successfully coupled to produce an efficient particle concentrator within the channel. By using remote electrodes, electrochemical reactions and other unwanted dielectrophoretic effects will not occur within the section of particle collection or concentration. However, this technique relies on the application of higher voltages to produce the necessary electric field gradient, with magnitudes in the hundreds to thousands of volts (outside the range of conventional waveform generators).

The driving mechanism for fluid flow for these systems is electrokinetic in that it combines features of electroosmotic and electrophoretic flows. Insulating dielectrophoresis Lab-on-a-Chip systems use a coupled arrangement of electrokinetic and dielectrophoretic phenomena to separate or capture targeted particles. Consider such a dielectrophoresis system that has an array of insulating posts within a microchannel. At a low applied electric field there will be induced electrokinetic motion but minimal particle manipulation effects from dielectrophoresis. However, at higher magnitudes the influence of insulating posts becomes apparent, inducing dielectrophoretic forces on the particles. At a certain threshold in the applied electric field dielectrophoresis forces on the particles are greater than the electrokinetic forces, resulting in captured targeted particles at the insulating posts. Releasing these particles is just a simple decrease in signal magnitude. Structures other than posts have been successfully used to similarly manipulate and separate particles of different dielectric properties.

Optical Dielectrophoresis

An electrode-less approach to induce localized dielectrophoretic forces can be created by light illumination in optically induced dielectrophoresis. This technique utilizes low-power optical beams to manipulate particles and cells. Consider an AC electric signal applied across two parallel electrodes with a film of photoconductive layer in between. This generates a uniform electric field across the film; however, the photoconductive layers have higher conductivities under illumination, thus distorting the otherwise uniform electric field. An illustration of a simplified optically induced dielectrophoresis system is shown in Fig. 6. The illumination of the photoconductive layer produces a virtual electrode and locally induced dielectrophoretic forces. These forces can be used in pDEP or nDEP applications and have the distinct advantage of being temporary, as opposed to permanent microfabricated electrode features. For example, trapped particles can be moved with the translation of the illumination pattern and released by simply turning off the light.

Figure 6

An example for a simple setup for optically induced dielectrophoresis. The optical source is illuminated through the ITO/glass substrate onto the photoconductive layer, creating an electric field gradient in which particles experiencing pDEP are attracted

Figure 7

Liquid dielectrophoresis with a set of planar electrode fingers with an insulating layer (top view and side view). A signal is applied to manipulate the liquid to travel along the gap between the electrodes

These optical methods, though, have been developed to include image projectors to manipulate cells using larger, patterned illumination areas. For example, virtual structures can be used to direct cells or can be alternatively used to pattern trapped cells. An investigation of optically induced dielectrophoresis for cellular manipulation is found in detail elsewhere [8]. This investigation characterizes the controllability of these optical techniques. This technique, though, should not be confused with optical tweezers (also called optical traps), which manipulate cells with forces generated by a highly focused laser beam. Optical tweezers use high optical intensity that may cause damage to the cell or induce localized heating. In contrast, optically induced dielectrophoretic techniques have about 1000 times less optical intensity.

Liquid Manipulation

Outside of particle manipulation, dielectrophoresis has also been used to control small volumes of liquid [9]. Liquids themselves also polarize and will, therefore, respond to nonuniform electric fields by being attracted to high-field-intensity regions. Liquid dielectrophoresis influences hydrostatic equilibrium and does not directly manipulate the fluid using dynamic mechanisms typically associated with electro-osmotic flow, electroconvection or other electrohydrodynamic methods. As with all dielectrophoresis techniques, liquid dielectrophoretic forces become stronger at smaller length scales, typically the micrometer length scale. Simple applications of this technique require a fluid running between two closely spaced planar electrodes (Fig. 7). A signal is applied between these two electrodes inducing the collection of individual molecules to the area of highest field intensity, along the edges of the electrodes. The liquid will translate and fill the area along these electrode “fingers” until equilibrium is achieved.

When the signal is removed the liquid will retract and return to its original hydrostatic equilibrium form. This retraction can be coupled together with surface structures to generate nanoliter droplets. However, typical voltage magnitudes are in the hundreds of volts, resulting in Joule heating and electrolysis. Electrolysis can be easily avoided by coating the electrode surface with an insulating layer. Heating is typically insignificant when liquids are nonconductive; however, water and other highly conductive liquids will undergo Joule heating. To cope with these issues in present liquid dielectrophoresis systems, very short applications of voltage ($<{\mathrm{0.1}}{\mathrm{s}}$) are applied to avoid heating. Liquid dielectrophoresis involves a complex relationship between electrohydrodynamics, fluid dynamics, surface effects, Joule heating and dielectrophoresis but this technique provides a rapid actuation of liquid that can be utilized in Lab-on-a-Chip systems.

Molecular Dielectrophoresis

Dielectrophoresis has also been used to manipulate macromolecules such as DNA, viruses, proteins and carbon nanotubes. The term colloids will be used here to generally describe a particle between 1 nm and 1000 nm. At this scale we need to take into consideration additional parameters that will affect the efficiency and application of dielectrophoresis. The first is Brownian motion, or the random chaotic movement of molecules, which will introduce another destabilizing variable if we were to trap colloids. Second, electrostatic effects at the surface of colloids, created by the electrical double layer, will influence particle–particle interactions. Factors such as hydrodynamic drag, buoyancy, electrothermal effects and a particle's double layer interactions need to be considered when applying dielectrophoresis to colloids.

The importance of mechanically controlling these structures in Lab-on-a-Chip systems with dielectrophoretic techniques will aid in the understanding of their biological interactions with other subcellular entities. For example, miniature quadrupole traps can be used to determine the crossover frequency of specific proteins and viruses. Capturing viruses at a particular set of experimental parameters will give insight into their identification as well as provide a means to concentrate or separate these particles. The crossover frequency of a protein is not only a function of medium conductivity, but it is dependent on the pH as well. Thus, dielectrophoresis can be coupled with chemistry-oriented techniques in order to approach the experimentation of single molecules. DNA has also been manipulated using dielectrophoresis. In one study [10], DNA was uncoiled from its natural bundled condition and stretched between two electrodes, aligning itself along the field lines. It was shown that it took about one-third of one second to uncoil a 48,500 base-pair DNA to a length of 17 $\mu$m. The applications of DNA manipulation include electrical measurements between electrodes and positioning of DNA for structural purposes or modification. Carbon nanotubes have also been manipulated similarly. These manipulative techniques have contributed to the assembly of nanometer-sized structures.

Dielectrophoretic Assembly

Dielectrophoresis can be utilized in assembly procedures to induce particle–particle interactions or to use attractive forces between electrodes to position a component and complete a circuit. When two polarized particles come into close proximity to each other they will undergo an attractive force due to their dipole interactions. This is referred to as dipole–dipole interaction, mutual dielectrophoresis or pearl chaining because this phenomenon creates strings of particles. Recall that a particle's induced dipole aligns itself to the electric field and that like particles will always have the same dipole orientation. These particles will have an attractive force since their opposite charges are aligned facing each other. Additionally, these particle chain formations can also be attributed to the distorted electric field caused by the particle's induced dipole. These field disturbances can cause a localized dielectrophoretic force, increasing the strength of these particle–particle interactions. Pearl chains are typically observed near electrode edges where the strength of the electric field is the greatest.

Pearl chains of nanoparticles can be arranged and fused together to create a nanowire or other similar structures. However, other dielectrophoresis techniques can be utilized to assemble a variety of geometries. Dielectrophoretic traps and optical dielectrophoresis can assemble groups of like particles. Electro-orientation techniques have been used to align and connect nanowires between electrodes. Functionalized particles can be implemented with dielectrophoresis Lab-on-a-Chip systems to create biological sensory or assembly systems. Dielectrophoresis, therefore, is a very versatile engineering tool.

Future Directions for Research

As a nonmechanical and minimally invasive process, dielectrophoresis presents as a tool to be used in Lab-on-a-Chip systems to manipulate particles and cells. These techniques will continue to evolve as the size of microfabricated features continue to decrease past the nanometer scale. This miniaturization will give rise into more comprehensive, subcellular microsystems which need novel methods to manipulate specific entities to suit a biological, chemical or sensory purpose. Dielectrophoresis phenomena at these decreasing length scales will continue to be characterized, leading to newly developed dielectrophoresis phenomena and subsequent innovative manipulation techniques. The future of dielectrophoresis is with the continued investigation and development of novel applications of dielectrophoresis techniques. With the integration of these technologies, a complete dielectrophoresis-driven Lab-on-a-Chip diagnostics system is possible.

Cross References

AC Electro-Osmotic Flow

Dielectrophoresis

Dielectrophoretic Motion of Particles and Cells

Electrokinetic Motion of Cells and Nonpolarizable Particles

Electroosmotic Flow (DC)

Electrophoresis

Electrothermal Effects

Joule Heating in Electrokinetic Flow: Theoretical Models

Lab-on-a-Chip (General Philosophy)

Lab-on-a-Chip Devices for Particle and Cell Separation

Techniques for Manipulating Cells