Analytical Formulation of the Electric Field Induced by Electrode Arrays: Towards Automated Dielectrophoretic Cell Sorting

Automatic trajectory control of single cells using dielectrophoresis based on visual feedback

This paper deals with the automatic control of the trajectory of T-lymphocytes using dielectrophoretic (DEP) actuation. Dielectrophoresis is a physical phenomenon induced by a non-uniform electric field enabling application of a force on a dielectric object. In most of the cases, it is used in a passive way. The electric field is in a steady state and the force applied on the cells depends on the cell's characteristics and position inside the channel. These systems are limited as cells with similar characteristics will undergo the same forces. To overcome this issue, active devices where the electric field changes over time were developed. However, the voltages that should be applied to generate the desired electric field are mostly computed offline using finite element methods. Thus, there is a low number of devices using automatic approaches with dielectrophoretic actuation where the electric field is computed and updated in real time based on the current position of the cell. We propose here an experimental bench used to study the automatic trajectory control of cells by dielectrophoresis. The computation of the dielectrophoretic force is done online with a model based on the Fourier series depending on the cell's characteristics, position and electric field. This model allows the use of a controller based on visual feedback running at 120 Hz to control the position of cells inside a microfluidic chip. As cells are sensitive to the electric field, the controller limits the norm of the electric field while maximizing the gradient to maximize the DEP force. Experiments have been performed and T-lymphocytes were successfully steered along several types of trajectories at a speed of five times their size per second. The mean error along those trajectories is below 2 μm. The viability of the cells has been checked after the experiments and confirms that this active DEP actuation does not harm the cells.

Numerical Solution of the Electric Field and Dielectrophoresis Force of Electrostatic Traveling Wave System

Electrostatic traveling wave (ETW) methods have shown promising performance in dust mitigation of solar panels, particle transport and separation in in situ space resource utilization, cell manipulation, and separation in biology. The ETW field distribution is required to analyze the forces applied to particles and to evaluate ETW design parameters. This study presents the numerical results of the ETW field distribution generated by a parallel electrode array using both the charge simulation method (CSM) and the boundary element method (BEM). A low accumulated error of the CSM is achieved by properly arranging the positions and numbers of contour points and fictitious charges. The BEM can avoid the inconvenience of the charge position required in the CSM. The numerical results show extremely close agreement between the CSM and BEM. For simplification, the method of images is introduced in the implementation of the CSM and BEM. Moreover, analytical formulas are obtained for the integral of Green's function along boundary elements. For further validation, the results are cross-checked using the finite element method (FEM). It is found that discrepancies occur at the ends of the electrode array. Finally, analyses are provided of the electric field and dielectrophoretic (DEP) components. Emphasis is given to the regions close to the electrode surfaces. These results provide guidance for the fabrication of ETW systems for various applications.

Dielectrophoresis Multipath Focusing of Microparticles through Perforated Electrodes in Microfluidic Channels

This paper presents focusing of microparticles in multiple paths within the direction of the flow using dielectrophoresis. The focusing of microparticles is realized through partially perforated electrodes within the microchannel. A continuous electrode on the top surface of the microchannel is considered, while the bottom side is made of a circular meshed perforated electrode. For the mathematical model of this microfluidic channel, inertia, buoyancy, drag and dielectrophoretic forces are brought up in the motion equation of the microparticles. The dielectrophoretic force is accounted for through a finite element discretization taking into account the perforated 3D geometry within the microchannel. An ordinary differential equation is solved to track the trajectories of the microparticles. For the case of continuous electrodes using the same mathematical model, the numerical simulation shows a very good agreement with the experiments, and this confirms the validation of focusing of microparticles within the proposed perforated electrode microchannel. Microparticles of silicon dioxide and polystyrene are used for this analysis. Their initial positions and radius, the Reynolds number, and the radius of the pore in perforated electrodes mainly conduct microparticles trajectories. Moreover, the radius of the pore of perforated electrode is the dominant factor in the steady state levitation height.

Control-oriented model of dielectrophoresis and electrorotation for arbitrarily shaped objects

The most popular modeling approach for dielectrophoresis (DEP) is the effective multipole (EM) method. It approximates the polarization-induced charge distribution in an object of interest by a set of multipolar moments. The Coulombic interaction of these moments with the external polarizing electric field then gives the DEP force and torque acting on the object. The multipolar moments for objects placed in arbitrary harmonic electric fields are, however, known only for spherical objects. This shape restriction significantly limits the use of the EM method. We present an approach for online (in real time) computation of multipolar moments for objects of arbitrary shapes having even arbitrary internal composition (inhomogeneous objects, more different materials, etc.). We exploit orthonormality of spherical harmonics to extract the multipolar moments from a numerical simulation of the polarized object. This can be done in advance (offline) for a set of external electric fields forming a basis so that the superposition principle can then be used for online operation. DEP force and torque can thus be computed in fractions of a second, which is needed, for example, in model-based control applications. We validate the proposed model against reference numerical solutions obtained using Maxwell stress tensor. We also analyze the importance of the higher-order multipolar moments using a sample case of a Tetris-shaped micro-object placed inside a quadrupolar microelectrode array and exposed to electrorotation. The implementation of the model in Matlab and Comsol is offered for free download.