Numerical Simulation Noise and Its Significant Impact on the Dielectrophoretic Motion of Particles Near the Electrode Edges

Dielectrophoresis (DEP) has been extensively researched over the years for filtration, separation, detection, and collection of micro/nano/bioparticles. Numerical models have historically been employed to predict particle trajectories in three-dimensional (3D) DEP systems, but a common issue arises due to inherent noise near the edges of electrodes due to electric potential discontinuity, specifically when calculating electric field and gradient of electric field-squared, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:mrow><mml:mo>∇</mml:mo> <mml:mo>|</mml:mo> <mml:mi>E</mml:mi></mml:mrow> <mml:msup><mml:mo>|</mml:mo> <mml:mn>2</mml:mn></mml:msup> </mml:mrow> <mml:annotation>$\nabla |E{|^2}$</mml:annotation></mml:semantics> </mml:math> . This noise can be reduced to a certain extent with a finer mesh density but results near the electrode edge still have significant error. Realizing the importance of particle-electrode edge interactions prevalent in positive DEP systems, analytical solutions given by Sun et al. was incorporated to demonstrate an improved 3D model of interdigitated electrodes. The results of electric field and gradient of electric field-squared of the numerical model and the improved analytical 3D model were compared, within a simulation space of 50 µm height, 10 µm width, and 50 µm length with interdigitated electrodes of the same width and gap of 10 µm. The DEP particle trajectory error due to the noise was quantified for different particle sizes at various heights above the electrode edge. For example, at 5 V_rms, a trapped 500 nm particles exhibited a velocity error of 10⁴ µm/s (it should have been zero).