Electrokinetics Models for Micro- and Nano-Fluidic Impedance Sensors

August 1, 2022

Army Research, Development and Engineering Command, Redstone Arsenal, Alabama

Exposure to toxic industrial chemicals (TICs) and pathogens has been acknowledged to pose a significant risk to mission capability and warfighter health. Due to their salient fieldability, microfluidics- and nanofluidics-based impedance sensors are increasingly finding favor in the biodetection and biodefense arena. However, their efficient modeling and design continues to be a challenge.

Analytical models describe the electric field distribution around the sense electrodes without consideration of the electrokinetic transport. Traditional equivalent circuit models, constructed by sets of primitive Differential-Algebraic Equations (DAEs), used to process and interpret the experimentally measured electrical impedance data are less useful for sensor design, in particular for nano-fluidic sensors that can feature overlapped electric double layers (EDLs). Numerical analysis approaches (e.g., finite element and finite difference) have also been utilized for high-fidelity analysis, design, and interpretation of impedance sensors with the focus on a single suspension cell.

In this context, high-fidelity models were used to resolve the electrokinetic transport process at the micro- and nano-scale and to interrogate the sensor performance subject to the variations in design parameters (such as medium concentration and conductivity, microchannel feature sizes, and fluidic manipulation). The models were verified by experimental data and can be used for fast, accurate analysis and design of micro- and nano-impedance sensors. The modeling framework presented here can be utilized to guide sensor design and protocol development of biodetection technologies, and also to interpret the experimental data/ observations for technological refinement.

The accompanying figure illustrates the principle of impedance-based molecular detection. The solution containing the analytes of interest is introduced into a microfluidic or nanofluidic environment (a). A pair of electrodes is energized with an AC field (characterized by a voltage and frequency). The induced current is related to the applied voltage and impedance of the system, which in turn is dependent on the composition of the solution (presence or absence of target agents).

In an analogy to electrical circuit theory, we can consider impedance in the solution as a combination of resistance and capacitance, with the solution acting as a resistor (R_sol), while the Electric Double Layer (E_DL) at the electrode surface and the solution in the channel act as capacitors (C_DL and C_sol). The equivalent electrical circuit and resistor-capacity connection is illustrated in Figure (c). The concentrations of analytes and electrolytes impact the impedance in two ways: (1) Resistivity (or resistance) of the solution is a function of its electrical conductivity and, hence, depends on electrolyte and analyte concentrations; (2) E_DL capacitance is a function of double layer thickness (which in turn is a function of electrolyte concentration) and surface charges at the electrode. Therefore, when a sample with different ionic compositions is flowed through the system, it changes both the E_DL capacitance and the solution resistance. The changes are reflected in the form of a disturbance (called “differential current”) to the induced base current.

This work was done by Yi Wang, Hongjun Song, Ketan Bhatt, and Kapil Pant of CFD Research Corporation; Monserrate C. Roman of NASA Marshal Space Flight Center; and Eric Webster, William Diffey, and Paul Ashley for the Army Research, Development and Engineering Command. For more information, download the Technical Support Package (free white paper) here under the DAQ, Testing & Sensors category. ARDEC-0008

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Electrokinetics Models for Micro and Nano Fluidic Impedance Sensors

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