# Hybrid Bio-Mag-MEMS combining magnetophoresis and dielectrophoresis

G. Blaire, A. Masse, Luiz-Fernando Zanini, V. Gaude, S. Delshadi, T.

Honegger, D. Peyrade, M. Weidenhaupt, Frédéric Dumas-Bouchiat, F.

Bruckert, et al.

► To cite this version:

G. Blaire, A. Masse, Luiz-Fernando Zanini, V. Gaude, S. Delshadi, et al., Hybrid Bio-Mag-MEMS combining magnetophoresis and dielectrophoresis. The European Physical Journal B: Condensed Matter and Complex Systems, 2013, 86 (4), pp.165. 10.1140/epjb/e2013-30679-1. hal-00850011

HAL Id: hal-00850011

https://hal.science/hal-00850011v1

Submitted on 27 Mar 2025

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# Hybrid Bio-Mag-MEMS combining magnetophoresis and dielectrophoresis *

Guillaume Blaire¹,²,ª, Alain Masse¹, Luiz Fernando Zanini¹,³, Victor Gaude¹, Sarah Delshadi¹,
Thibault Honegger⁴, David Peyrade⁴, Marianne Weidenhaupt², Fr'ed'eric Dumas-Bouchiat³, Franz Bruckert²,
Orph'ee Cugat¹, and Gilbert Reyne¹

¹ G2Elab, CNRS UMR 5269 and Grenoble University, BP 46, 38402 St. Martin d'Hères, France

² LMGP, CNRS UMR 5628 and Grenoble-INP, BP 257, Grenoble, France

³ N'eel Institute, CNRS UPR 2940 and Joseph Fourier University, BP 166, 38042 Grenoble Cedex 9, France

⁴ LTM, CNRS UMR 5129 and CEA Grenoble, 38054 Grenoble, France

**Abstract.** The design of a new hybrid magnetic MEMS for biology (Bio-Mag-MEMS) is presented. It com-bines magnetophoresis, dielectrophoresis and microfluidics. These phenomena are used to sort magnetically tagged and non-tagged objects. Magnetic objects are trapped by the use of high gradient magnetophoresis. Thanks to dielectrophoresis these objects, once trapped, can be successfully released in a buffer. Efficient sorting is performed in this hybrid Bio-Mag-MEMS by using magnetic beads. A high sorting efficiency is demonstrated. Magnetic, Stokes and dielectrophoretic forces in the microfluidic channel are simulated with both analytical tools and the finite element method (FEM). The trajectories of magnetically tagged objects are simulated. Finally the fabrication and optimization of this device are detailed.

## 1 Introduction

Superparamagnetic (SPM) nanoparticles are becoming of widespread use in biology and medicine. Such particles are involved in various applications such as resonance imaging, drug delivery, hyperthermic tumour therapy [1], magnetofection [2] and manipulation of biological objects such proteins, cells [3] or DNA. The use of magnetic particles into lab-on-a-chip opens the way to magnetic cell sorting [4–6].

Sorting is fundamental both in biological research and in therapy. Presently, the most common cell sorters are based on the fluorescence effect. This tool has a high efficiency but presents also some drawbacks like: high cost of instrumentation and operation, the risk of cell damage at high flow rate and the required pre-treatment with fluorescent markers.

New methods have been developed to sort cells using magnetic particles. These particles can either be integrated into the cell by endocytosis or bound onto the cell surface by specific biological interactions.

Several magnetophoretic microsystems have been designed for cell sorting, based on various magnetic field sources: soft magnetic elements polarized by an external field [7], bulk permanent magnets [8], coils or electromagnets [9]. The magnetic field gradients, and therefore the

forces, obtained with permanent magnets can be greatly improved by reducing their size (see Sect. 3) [10]. The use of integrated micro-magnet arrays allows the production of magnetic gradients as high as 10⁶ T/m [11]. Thermo magnetic patterning (TMP) has been recently developed to produce high performance micro-magnets [12]. TMP is used to produce fine micro-patterned micro-magnets with magnetic properties equivalent to the best commercially available macro-magnets (remanence in the range [0.7–1.2 T], coercivity in the range [1.0–2.0 T]). Previous results have shown that magnetic beads can be attracted by, and trapped above, TMP magnet arrays [13]. Separation from non-magnetic beads was achieved with high separation efficiency [14]. In this work, magnetic trapping is coupled with dielectrophoresis to achieve more complex functions. This way, magnetic beads can be trapped by magnetophoresis and then released by dielectrophoresis. Thus, the quantity of magnetically tagged objects can be collected continuously and, therefore, greatly enhanced. Simulation, fabrication and results obtained with this new hybrid Bio-Mag-MEMS combining magnetophoresis and dielectrophoresis are detailed in Section 2.

## 2 Material and method

### 2.1 Description of the microsystem

The Bio-Mag-MEMS developed here combines a chessboard-like pattern of TMP micro-magnets with

<footnote>* Contribution to the Topical Issue "New Trends in Magnetism and Magnetic Materials", edited by Francesca Casoli, Massimo Solzi and Paola Tiberto.</footnote>

<footnote>ª e-mail: guillaume.blaire@g2elab.grenoble-inp.fr</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Description of the BioMagMEMS: exploded view showing the position of each element (magnets, channel, electrodes).</figcaption></figure>

a microfluidic channel, topped up with interdigitated indium tin oxide (ITO) electrodes (see Fig. 1). The polydimethylsiloxane (PDMS) microfluidic channel is sandwiched between the micro-magnet array (below), and a transparent glass wafer bearing the electrodes (above).

A magnetic layer is deposited onto a Si/SiO₂ wafer. The chessboard-like magnetic patterns used are 50 × 50 µm² squares, with thickness of ~1.3 µm. Two adjacent squares have opposite out of plane magnetizations in order to increase the magnetic field gradient locally, thus producing a high magnetic force on objects along the borders between squares. The micro-magnets are covered by a spin-coated PDMS layer. The thickness of this PDMS layer (a few µm) can be adjusted to control the magnetic latching force at the bottom of the channel.

The PDMS microfluidic channel has a rectangular section (38 µm high, 500 µm wide, 10 mm long). The ITO electrodes are interdigitated and placed on the top of the channel, perpendicular to the flow direction. The electrodes are 75 µm wide, spaced by 75 µm.

## 2.2 Microfluidic chip fabrication

Thick, hard magnetic films are produced by triode sputtering. Ta (100 nm)/NdFeB (5 µm)/Ta (100 nm) layers are deposited on a thermally oxidized (SiO₂) silicon substrate [15]. The remanence Bₘ of the films is about 1.2 T and their coercivity µ₀Hₘ is up to 2.3 T. Then, TMP is performed on 20 × 20 mm² films to obtain out of plane, up-down micro-magnetic patterns (generally chessboard arrays). A laser fluence of 300 mJ/cm² is used to heat the samples locally. Such fluence ensures a mean reversal depth of ~1.3 µm [11] without damaging the film surface. The electrodes are etched on a glass wafer, pre-coated with indium tin oxide (ITO) (Sigma Aldrich). A photoresist (AZ1512) mask is created via conventional lithography. Interdigitated electrodes are etched into the ITO using ion beam etching (argon plasma) [16,17].

Polydymethilsyloxane (Dow Corning, Sylgard 184) is spin-coated on the magnetic films in order to create a polymeric layer with thickness in the range [6–50 µm].

A commercially available sheet of dry film photoresist (DuPont Riston MultiMaster 540) with a thickness of 38 µm is applied on the PDMS layer. The microfluidic channel is patterned on this photoresist using conventional

lithography. PDMS is coated above, with mechanical pressure applied during polymerisation. The PDMS channel is obtained once the dry film is removed with acetone.

To bond the glass ITO electrode and PDMS channel, each surface (PDMS and glass) is exposed to oxygen plasma prior to direct contact. This method ensures a sealed and strong connection between the two parts.

# 3 Model and simulation

## 3.1 Governing equations

### 3.1.1 Magnetic forces

Once a magnetic field H is applied, the SPM nanobeads are submitted to a magnetic force Fₘ.

The “magnetic particles” widely used in high gradient magnetic separation (HGMS) are often polystyrene particles with embedded superparamagnetic nanoinclusions. In this case the magnetic force acting on the particle is calculated by summing the forces acting on each SPM inclusion:

$$F_m = \mu_0 \sum_{i=1}^{N} V_i M_i \nabla H \quad (1)$$

where µ₀ is the vacuum permeability and Vᵢ the volume of each of the n nanoparticles. The nanoparticle magnetization Mᵢ is induced, non linear, with a “saturation” rather low, typically around 10 to 100 mT. It is described by a Langevin-type function:

$$M_i = M_0 L(x) = M_0 \coth x - \frac{1}{x}, \quad (2)$$

M₀ being the 0 K magnetization of the particle and

$$x = \frac{\mu_0 V_i M_0 H}{k_B T} \quad (3)$$

where k_B is Boltzmann's constant and T the temperature.

### 3.1.2 Magnetic field and magnetic force mapping

Magnetic forces at each position in the channel, are computed by semi-analytical calculation, developed by Chigirinsky et al. [18]. The magnetic induction B is obtained by summing up the magnetic induction due to each magnet (see Fig. 4). The magnetic force acting on a SPM particle is proportional to its own magnetization and to the gradient of the magnetic induction.

Magnetization can be calculated thanks to equation (2). By this way a map of the magnetic force can be drawn (see Fig. 4). The magnetic volume force produced by the TMP magnets is strong (up to 10¹⁰ N/m³ near the magnet surface) and localized on the ridges between oppositely magnetized magnets. These strong magnetic forces allow the use of nanobeads to tag bigger objects.
<figure><img src="image_3.png" /><figcaption>Fig. 2. Microfabrication of the BioMagMEMS. Top: steps conducted to build the electrodes. Bottom: steps to build the microfluidic channel on the magnet.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Simulation results: (a) Z component of the magnetic field at 5 µm above the TMP magnets; (b) magnetic force at 5 µm above the TMP magnet; (c) evolution of the magnetic force with the elevation.</figcaption></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Volumic dielectrophoretic force in the channel. This force is produced by a voltage of 7 V at a frequency of 10 kHz.</figcaption></figure>

### 3.1.3 Dielectrophoretic force

Dielectrophoresis (DEP) is an electrical phenomenon which attracts (positive DEP) or repels (negative DEP) polarizable particles by applying a non-uniform AC electric field. The DEP force applied on a spherical particle can be expressed by [19]:

$$F_{DEP} = 2\pi r^3 \rho_m \alpha \nabla E_{RMS}^2 \quad (4)$$

where r is the radius of the particle, ρ is the effective dielectric permittivity of the medium, α is the real part of the Gauss-Mossotti factor [20] and E is the magnitude of the electric field around the particle.

Due to the high ratio between the electrodes width and the bead radius (typically 75 µm/1 µm) and considering the fact that the relevant parameter here is the force at the bottom of the channel (i.e., far away from the electrodes), the influence of the dielectric beads on the surrounding electric field can be neglected.

In our case, the only unknown parameter is E which can be calculated by solving the electrokinetic equation using COMSOL Multiphysics (Fig. 4).

### 3.1.4 Medium buoyancy forces

A spherical particle in a fluid is submitted to many different forces due to the medium: let us consider drag force $F_D$ and classical buoyancy $F_B$,

$$F_B = \frac{4}{3}\pi r^3 (\rho_{part} - \rho_{medium})g \quad (5)$$

where $v_{medium}$, $\rho_{medium}$ and $v_{part}$, $\rho_{part}$ are the velocities and mass densities of the medium and the particle, respectively, and g is the gravitational acceleration.

Computation of the drag force requires the fluid velocity to be known in each point of the microfluidic channel.

When inertia can be neglected compared to viscosity (i.e. Reynolds number ≪1) the Navier-Stokes equation can be simplified into the Stokes equation. This is general for most microfluidics.

The typical dimensions of the channel used present a high width-to-height ratio. Hence, an analytical solution of the Stokes equation can be found: the fluid follows a Poiseuille flow and the velocity of the fluid depends only of the z coordinate,

$$v_{medium}(z) = \frac{\Delta P}{2\eta L} (h - z)z. \quad (6)$$
In this case, the drag force on a sphere of radius $r$ can be expressed by:

$$F_D = 6\pi\eta r(v_{\text{medium}}(z) - v_{\text{part}}). \quad (7)$$

## 3.2 Microsystem modelling

### 3.2.1 Dielectrophoretic to Magnetic force ratio

Combination of magnetic and dielectrophoretic forces is only possible when dimensions (bead diameter, depth of the PDMS layer) and properties result in forces in the same order of magnitude. To optimize the microsystem's geometry, a typical case study is proposed. Objects of interest are complexes formed by a dielectric bead with a diameter of 1 µm (miming a biological object) tagged with SPM nanobeads with a diameter of 100 nm (see Fig. 7a). Simulations must take into account the technical constraints concerning the magnet, microfluidics and electrodes fabrication. The integrity of the electrodes must also be preserved and a voltage of 10 V on the electrodes is the maximal value.

Due to all these constraints, only two scalable parameters have been identified: the dielectrophoretic force (via the voltage) and the thickness of PDMS layer over the magnet (see Fig. 1). The natural variability in the formation of the complexes must also be taken into account. Typically the number of SPM nanobeads plugged on one dielectric bead is between one and ten. This variability can be balanced by the operating range of the voltage.

Comparison of the values of the magnetic and dielectrophoretic forces at the bottom of the channel is a good figure of merit for the design of the microsystem. Plotting the magnetic force versus the distance of the magnets and comparing these values to the dielectrophoretic force at the bottom of the channel, is the proposed way to identify areas where dielectrophoresis or magnetophoresis can overlap.

This comparison allows optimising a geometry where both dielectrophoresis and magnetophoresis are possible. In the case presented in this publication, with a moderate number of SPM nanobeads per dielectric bead, a PDMS thickness of 12.5 µm seems to be a good compromise (see Fig. 5) between DEP and magnetophoresis. With this geometry, all the complexes should be released by applying a voltage lower than 10 V.

### 3.2.2 Capture of magnetically tagged objects

During magnetic capture the electrodes are off. The only forces acting on the magnetically tagged object are $F_D$, $F_m$, and $F_B$. A low concentration ($c = 10^6$ beads/mL) of magnetically tagged objects in the medium is used. In this case the distance $s \sim c^{-1/3}$ (around 100 µm at this concentration) between two tagged objects is much higher than the radius of a magnetic particle so the dipole-dipole interaction can be neglected. The object of study is the association (see above) of one dielectric 1 µm bead bonded

<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison between the dielectrophoretic and the magnetic force in order to design the microsystem. The dielectrophoretic force is computed on a bead with a diameter of 1 µm at the bottom of the channel. Various voltages are simulated (2 V, 5 V, 10 V). The magnetic force is calculated on one or few SPM nanobeads (with a diameter of 100 nm). The evolution of these magnetic forces are studied in order to find a compromise between the DEP and the magnetic attraction. With a distance of 12.5 µm the two phenomena could be used.</figcaption></figure>

to a few 100 nm SPM particles. Some assumptions must be made:

- the dielectric beads are diamagnetic. Taking into account that the diamagnetic effect is ~$10^6$ lower than the superparamagnetic effect, the contribution of the dielectric bead in the calculation of the magnetic force is neglected;

- the 100 nm SPM particles are assumed to be much smaller than the 1 µm dielectric bead. As a consequence, the total force applied on the complex created by the dielectric bead and the SPM particles is the sum of the magnetic force on each SPM particle and of the drag force only on the dielectric bead;

- the complex does not deform;

- the variation of the magnetic field is negligible across the dielectric bead diameter.

With these assumptions the magnetic force can be calculated by using equation (1). The magnetic field is taken at the center of the dielectric bead and each SPM nanobeads give the same contribution. The total force applied on the complex can be expressed by: $F = NF_M + F_D$ where $N$ is the number of SPM nanobeads. Analytical calculations of the displacement and capture are performed with the same step-by-step approach as Zanini et al. [14]. Magnetic field, magnetic gradient and the various forces are calculated at each time step. Considering no rotation, the object can be considered to move at its limiting velocity. Given the position of the bead at a time $t$, its position at the time $t + dt$ is calculated with an explicit Euler method.

Simulations are performed for various numbers of SPM beads bound with the dielectric particles, in order to study the evolution of the trajectory with the number of SPM beads attached (see Fig. 6).
<figure><img src="image_8.png" /><figcaption>Fig. 6. Simulated trajectories of magnetically tagged objects, with various number of 100 nm SPM beads linked on the 1 µm dielectric bead, travelling through microfluidic channels above arrays of micro-magnets, starting from the top of the channel. Note that all the complexes are trapped in few mm.</figcaption></figure>

### 3.2.3 Release of the magnetically tagged objects

For the subsequent release, or second step, a buffer is pumped through the microfluidic system. At this point, no more magnetically tagged objects are introduced. The position of the captured objects on the micro-magnets is known due to the previous simulation. Once the electrodes are turned on, dielectrophoretic forces are applied to the complex objects. The dielectrophoretic force attracts the magnetically captured objects. When dielectrophoresis attraction overcomes magnetic latching, these objects are released.

The competition between the magnetic, the DEP and the drag forces must be regulated in order not to trap the magnetically tagged objects on the electrodes. To avoid this problem, we perform a low-frequency amplitude modulation (+/-0.5 V, 5 Hz) of the voltage around the critical voltage value. With this method, the magnetically tagged objects can escape from both the magnetic and dielectrophoretic potentials.

The critical voltage where the tagged objects can be released is determined once the magnetic and dielectrophoretic forces at the bottom of the channel are equal. As before, the magnetic force is calculated by summing up the contributions on each SPM nanobead. The dielectrophoretic force is computed by taking only the dielectric bead into account.

This critical value can be calculated (see Fig. 6) and gives very useful information. With the geometry previously chosen all the complexes must be released with a voltage lower than 10 V.

## 4 Experimentation

### 4.1 Principle of the sorting

The efficiency of the system for separating magnetically tagged objects and untagged objects is then studied with dielectric beads tagged to SPM nanobeads.

<figure><img src="image_9.png" /><figcaption>Fig. 7. Description of the protocol used to sort magnetically tagged objects. (a) Examples of construction created by a dielectric microbead and some SPM nanobeads. (b) These various complexes are introduced in the microfluidic channel with unlabelled objects. (c) When the electrodes are off magnetically tagged objects are trapped. (d) When electrodes are activated, the magnetically tagged objects are released.</figcaption></figure>

The dielectric beads chosen have a diameter of 1 µm. The SPM nanobeads (nano-screenMAG/G from Chemicell) used to tag are green fluorescent with a diameter of 100 nm. This gives a dimension ratio of 10 between the beads, resulting in a volume ratio of 1000. Both magnetic and dielectrophoretic forces are volume forces.

Dielectric-SPM nanobead complexes are formed by the use of the chemical link between two proteins: avidin and biotin. SPM nanobeads are functionalized with biotin while dielectric beads are functionalized with avidin. Due to the dissociation constant values, these links are assumed to be permanent during the experiment.

Then, SPM nanobeads and dielectric beads are mixed. An excess of dielectric beads prevents them to be covered with too many SPM nanobeads. Typically, 10⁶ dielectric beads are mixed with 10⁵ SPM nanobeads. To remove unconjugated beads, a first magnetic separation is performed.

The resulting solution is then mixed with a solution containing 10⁶ red fluorescent 1 µm non-magnetic beads and is injected in the microfluidics channel. Through the microsystem, the magnetically tagged objects in the solution are trapped by the micro-magnets array while non-labelled objects are collected at the output.

Finally, while a buffer is injected in the channel, electrodes are activated thus releasing the trapped objects.

Fluorescence intensity observations are used to measure the efficiency of the Bio-Mag-MEMS: green fluorescence characterizing the SPM nanobeads used to tag the non-magnetic objects, and red fluorescence for the non-labelled objects.

### 4.2 Experimental results

The experiment is realized with the protocol described above. Liquid solutions are collected at each step (capture
<figure><img src="image_10.png" /><figcaption>Fig. 8. Results of the fluorescence measures. Left: initial solution shows both untagged and tagged beads. Center: the solution which passes through the channel during the washing step shows less tagged beads. The trapping seems to be efficient. Right: the release solution shows more tagged beads.</figcaption></figure>

and release). The green and red fluorescence intensities of these two solutions are compared with those of the initial solutions.

Experiments are performed at the same flow rate of 15 µL/min. During the release, the voltage is progressively increased from 0 V to 11 V max in order to release all the complexes while preserving the integrity of the electrodes.

Results are plotted in Figure 8.

To quantify the various efficiencies, let us assume that the fluorescence intensity is proportional to the concentration of fluorochrome (this is correct as long as concentrations remain low).

The efficiency of capture is defined by

$$Q_{\text{trapping}} = \frac{[SPM]_{\text{initial}} - [SPM]_{\text{not-trapped}}}{[SPM]_{\text{initial}}} \times 100. \quad (8)$$

The efficiency of release is defined by

$$Q_{\text{release}} = 1 - Q_{\text{trapping}} - \frac{[SPM]_{\text{release}}}{[SPM]_{\text{initial}}} \times 100. \quad (9)$$

In this experiment, the Bio-Mag-MEMS presented in this publication achieved efficiency up to 95.0% for the trapping step, and up to 99.7% for the release step.

## 5 Conclusion and prospects

A new hybrid magnetic microfluidic microsystem for biology has been developed. Advantages of permanent magnets (high forces, autonomy, no Joule heating) and dielectrophoresis (variable forces) are combined.

The Bio-Mag-MEMS designed allows high efficiency sorting of magnetically-tagged objects and cells.

A better understanding of the coupling between magnetophoresis and dielectrophoresis should allow new

applications such as sorting cells with different dielectric permittivity or different magnetic tags.

Indeed, the voltage needed to release the magnetically tagged objects depends on various parameters:

- the ratio between the radius of the magnetic tags and the radius of the dielectric object;

- the dielectric permittivity of the tagged object;

- the number of magnetic beads bound.

With a fixed geometry, it will be possible to sort objects with various dielectric permittivities and various label. This function could be very useful in diagnostics to test the presence of several diseases for example.

The real challenge to perform this new kind of sorting is to take into account the dipole-dipole interaction between two SPM particles. Due to their magnetic moments M (induced and aligned with the magnetic field), two SPM nanobeads are attracted by a force given by:

$$F = \frac{\mu_0 M^2}{4\pi s^4} \quad (10)$$

where s is the distance between the two particles [21]. In most cases, the dipole strength is totally negligible compared to the magnetic force. But when complexes touch each other this force can become very significant. This may explain specific groupings or alignments of particles.

It is a real challenge to take into account these interactions between all the magnetic beads in the simulations, and future work should focus on these computations.

Another direction to go further is to test the same system with real biological objects such as cells or bacteria, and to compare this new approach with the conventional approach.

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