Analytical Formulation of the Electric Field Induced by Electrode Arrays: Towards Automated Dielectrophoretic Cell Sorting
Abstract
:1. Introduction
2. Electric Field Produced by an Electrode Array
2.1. Cell Sorting Using Parallel Electrode Arrays
2.2. Generic Solution of the Electric Potential Produced by an Electrode Array Expressed as a Fourier Series
- the spatial variables can be separated:
- the dependence along the axis can be expressed as a Fourier series:
3. Analytical Formulation of the Electric Potential Produced by One Plane of Electrode Array
3.1. Boundary Conditions of the Electric Potential
- the electric potential on the nth electrode is , ,
- the electric potential between two electrodes is linear, ,
- the electric potential is symmetrical across lateral boundaries, , , …, ,
- the potential is grounded at height h,
3.2. Analytical Formulation of the Fourier Coefficients Satisfying the Boundary Conditions
4. Generalization to the Analytical Formulation of the Electric Potential and the Dielectrophoretic Force Produced by Two Planes of Electrode Arrays
4.1. Generalization of the Electric Potential to the Case of Two Parallel Planar Arrays of Electrodes
4.2. Dielectrophoretic Force Formulation
5. Results and Discussion
5.1. Comparison between the Analytical Model and a Numerical Simulation
5.2. Influence of the Length of the Fourier Series
5.3. Computing Time of the Fourier Series
5.4. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
DEP | dielectrophoresis |
FEM | finite element method |
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N = 5 | N = 7 | N = 9 | N = 11 | N = 13 | N = 15 | |
---|---|---|---|---|---|---|
56.9° | 44.8° | 39.3° | 35.0° | 32.4° | 31.1° | |
42.2° | 32.6° | 28.7° | 25.2° | 24.0° | 23.9° | |
43.0° | 32.3° | 28.6° | 25.4° | 24.1° | 23.8° | |
41.5° | 32.1° | 28.2° | 25.4° | 24.2° | 24.1° |
N = 5 | N = 7 | N = 9 | N = 11 | N = 13 | N = 15 | |
---|---|---|---|---|---|---|
t | 0.214 | 0.208 | 0.209 | 0.217 | 0.218 | 0.221 |
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Gauthier, V.; Bolopion, A.; Gauthier, M. Analytical Formulation of the Electric Field Induced by Electrode Arrays: Towards Automated Dielectrophoretic Cell Sorting. Micromachines 2017, 8, 253. https://doi.org/10.3390/mi8080253
Gauthier V, Bolopion A, Gauthier M. Analytical Formulation of the Electric Field Induced by Electrode Arrays: Towards Automated Dielectrophoretic Cell Sorting. Micromachines. 2017; 8(8):253. https://doi.org/10.3390/mi8080253
Chicago/Turabian StyleGauthier, Vladimir, Aude Bolopion, and Michaël Gauthier. 2017. "Analytical Formulation of the Electric Field Induced by Electrode Arrays: Towards Automated Dielectrophoretic Cell Sorting" Micromachines 8, no. 8: 253. https://doi.org/10.3390/mi8080253