Electrical Impedance Spectroscopy Study of Bubble-Associated Interfacial Changes in Physiological Saline Solution Under DC Excitation ^†

Abstract

Gas bubble evolution at electrified electrode–electrolyte interfaces and concurrent Faradaic processes change the electroactive area and the local current-density distribution and thereby the measured electrical impedance. This study investigated interfacial changes via electrical impedance spectroscopy (EIS) in a transparent parallel-plate chamber with physiological saline (0.9% NaCl) under direct-current (DC) excitation (2 V, 4 V and 8 V, 5 s, 10 s and 20 s, $n=3$). Paired EIS measurements from 40 Hz to 1 MHz revealed a dual-mechanism spectral signature: at 40 Hz, the estimated interfacial impedance contribution ($\mathrm{\Delta }{Z}_{int}={\left|Z\right|}_{40Hz}-R_{HF}$) decreased from $-4.13\%$ to $-41.48\%$, while phase shifted toward less negative values ($\mathrm{\Delta }\varphi$ from $+1.80°$ to $+17.41°$, from $-33.4°$ to $-16.0°$), consistent with electrode-surface Faradaic activation and increased interfacial conductance. At high frequencies (>$100\mathrm{kHz}$), solution resistance increased on average ($\mathrm{\Delta }{R}_{HF}=+0.53\%$ to $+5.04\%$), without resolved dose dependence ($p\ge 0.10$), placing the volumetric gas fraction between 0.4% and 3.2% by Bruggeman’s effective medium theory as an order-of-magnitude estimate. These estimates were compared with the 2D projected optical coverage (8.25% to 27.12% at 20 s) from a Python computer-vision algorithm. The spectral transition was consistent with a zero-crossing band ($f_{cross}\approx 0.27\mathrm{kHz} \mathrm{to} 12.6\mathrm{kHz}$) and with the absence of magnitude sensitivity at 1 kHz ($p=0.43$). Together, the EIS, optical, and numerical results indicate that post-DC impedance shifts reflect low-frequency interfacial Faradaic activation coupled with high-frequency geometric screening by bubbles.

1. Introduction

Gas bubbles nucleate at electrified electrode–electrolyte interfaces during electrolysis. Their growth reduces the effective wetted area, redistributes the local current-density distribution, and introduces additional electrical impedance contributions that are absent from the undisturbed cell [1,2,3,4]. In electrical impedance spectroscopy (EIS), these interfacial effects concentrate at low frequencies, where electrical double-layer charging, interfacial polarization, and charge-transfer mechanisms dominate the measured response [5,6,7,8]. In physiological saline media this creates an attribution problem: interfacial gas accumulation may be read as a bulk solution change if boundary phenomena are not isolated and analyzed explicitly.

Electrical impedance is a complex, frequency-dependent quantity whose interpretation in conductive electrolyte fluids and electrochemical systems requires separating bulk conductivity contributions from electrochemical surface phenomena and dielectric dispersions [5,9,10,11,12,13,14]. In electrochemical and biomedical applications involving electrical stimulation and electroporation, dielectric dispersion modulation, finite-element field modeling, and boundary reactions affect impedance-based monitoring [12,15,16,17,18]. The present study addresses that separation directly. It isolates the electrode–electrolyte interface in a transparent parallel-plate chamber filled with physiological saline solution (0.9% NaCl) subjected to DC excitation and evaluates the resulting impedance modifications over a multi-voltage (2 V to 8 V) and multi-duration (5 s to 20 s) experimental matrix. By coupling paired Before/After broadband EIS sweeps with optical documentation and 3D finite-element modeling in COMSOL Multiphysics, this work presents an experimental and numerical analysis of bubble-associated interfacial electrical impedance changes.

2. Materials and Methods

2.1. Experimental Setup and Electrical Protocol

The experimental apparatus consisted of a transparent parallel-plate chamber assembled inside a 100 mm × 20 mm borosilicate glass Petri dish, as schematically shown in Figure 1a. Two planar metallic electrodes (E1 and E2, each 15 mm × 25 mm × 1 mm) were mounted onto a 26 mm × 76 mm glass slide with a nominal interelectrode gap $g=5\mathrm{mm}$. The upper electrode surfaces were electrically insulated so that only the internal vertical faces bounding the gap remained electrochemically active within the 5 mm electrolyte layer. The electrolyte was commercial 0.9% NaCl physiological saline solution (Equiplex Medicamentos dos Sertões Ltda., Aparecida de Goiânia, GO, Brazil; nominal conductivity ${\sigma }_{el}\approx 1.5 \mathrm{S}/\mathrm{m}$) at room temperature (20.8 °C), replaced with a fresh aliquot for each test condition.

Figure 1. Experimental apparatus and numerical model: (a) top view of the chamber assembled in a Petri dish with slide carrier and planar parallel electrodes ($g=5\mathrm{mm}$); (b) verticalized optical observation configuration for inspecting interfacial bubbles, where white circles represent adhered gas bubbles; and (c) 3D finite-element model in COMSOL Multiphysics showing the electric potential distribution ($\mathrm{\Phi }$) in the chamber under DC excitation.

An adjustable regulated direct-current (DC) power supply (Minipa do Brasil Ltda., São Paulo, SP, Brazil) applied continuous excitation across a factorial matrix of three voltages (2 V, 4 V and 8 V, nominal fields $E_{nom}=V/g$ of 0.4 V/mm, 0.8 V/mm and 1.6 V/mm) and three exposure times (5 s, 10 s and 20 s) in triplicate ($n=3$, yielding 27 paired tests with post-DC latency below 5 s). The electrodes comprised planar AISI 304 stainless-steel plates with an active wetted geometric area of 15 mm × 5 mm ($A_{geom}=75{\mathrm{mm}}^2$). Electrical impedance spectroscopy (EIS) sweeps were acquired before and immediately after DC application (${\mathrm{EIS}}_{before}\to \mathrm{DC}(V,t)\to {\mathrm{EIS}}_{after}$) using a 4294A Precision Impedance Analyzer (Keysight Technologies, Santa Rosa, CA, USA; $V_{ac}=500\mathrm{mV}$, 801 logarithmic points from 40 Hz to 1 MHz) [6,19]. Electrolyte temperature was continuously tracked using a 10 kΩ negative temperature coefficient (NTC) thermistor (Epcos/TDK Electronics AG, Munich, Germany).

2.2. Optical Documentation and Python Bubble Detection Pipeline

Optical video recordings were acquired normal to the transparent chamber bottom (Figure 1b) over background graph paper (2.5 mm grid). Final frames were extracted at 20 s for 2 V, 4 V and 8 V using OpenCV 5.0.0.93 (cv2.VideoCapture). Morphometric quantification was implemented in Python 3.12/Streamlit 1.39.0 (Bubble ROI Tool) across three steps: (1) Scale-Invariant Spatial Calibration, with pixel-to-millimeter conversion $s=g_{\mathrm{mm}}/g_{\mathrm{px}}$ calibrated against the physical gap $g=5\mathrm{mm}$ ($g_{\mathrm{px}}\approx 34\mathrm{to}38\mathrm{px}$, $s\approx 0.13\mathrm{to}0.15\mathrm{mm}/\mathrm{px}$); (2) Native-Resolution Invariance, inversely remapping vector annotations to native camera resolution; and (3) Boolean Matrix Rasterization, converting regions of interest (ROI) and gas masks into boolean arrays to compute the projected 2D bubble coverage fraction ($F_{\mathrm{coverage}}$) via Equation (1):

$$F_{\mathrm{coverage}}={\displaystyle \frac{N_{\mathrm{bubble}}\cap N_{\mathrm{ROI}}}{N_{\mathrm{ROI}}}}\times 100={\displaystyle \frac{A_{\mathrm{bubble},\mathrm{proj}}}{A_{\mathrm{ROI}}}}\times 100,$$

(1)

where $N_{\mathrm{bubble}}$ and $N_{\mathrm{ROI}}$ are the pixel counts of bubble and ROI masks, and $A_{\mathrm{bubble},\mathrm{proj}}$ and $A_{\mathrm{ROI}}$ are the projected bubble area and total ROI area (${\mathrm{mm}}^2$), respectively. This formulation quantifies projected 2D occlusion over the active faces, overcoming stochastic 3D counting limitations caused by microbubble coalescence. Qualitative thermal imaging with an infrared FLIR camera (FLIR Systems, Inc., Wilsonville, OR, USA) was used to inspect potential surface films and redox deposits.

2.3. Numerical Modeling, Effective Medium Theory, and Post-Processing

A 3D finite-element model was implemented in COMSOL Multiphysics v5.1 (COMSOL AB, Stockholm, Sweden; AC/DC Module) (Figure 1c) representing the chamber, bulk electrolyte, and 14 discrete spherical bubbles attached laterally to electrode edges (radii 0.35 mm to 0.90 mm). The geometric core impedance $Z_{core}\left(f\right)=V_{ac}/I_{ac,E1}\left(f\right)$ was computed in the frequency domain across excitation frequency f. To reproduce instrumental and interfacial dispersion, the measurement-equivalent lumped formulation expressed in Equation (2) was coupled [5]:

$$Z_{sim}\left(f\right)={\left[{\left(Z_{core}\left(f\right)+R_s+j2\pi f{L}_w+{\displaystyle \sum _{k=1}^2}{\displaystyle \frac{R_{pol,k}}{1+j2\pi f{R}_{pol,k}{C}_{pol,k}}}\right)}^{-1}+j2\pi f{C}_p\right]}^{-1},$$

(2)

where $R_s=12.5 \mathrm{\Omega }$ is effective series resistance, $L_w$ is residual wiring inductance, $C_p$ is parallel parasitic capacitance, $j=\sqrt{-1}$ is the imaginary unit, and $R_{pol,k},C_{pol,k}$ ($k=1,2$) represent low-frequency interfacial polarization branches.

Interfacial impedance was isolated via $Z_{int}={\left|Z\right|}_{40Hz}-R_{HF}$ (with $R_{HF}$ measured in the resistive plateau at 200 kHz to 800 kHz). The volumetric gas fraction ($ϵ$) in the high-frequency conductive path was estimated using Bruggeman’s effective medium theory in Equation (3):

$${\displaystyle \frac{R_{HF,after}}{R_{HF,before}}}={(1-ϵ)}^{-3/2}\Rightarrow ϵ=1-{\left({\displaystyle \frac{R_{HF,before}}{R_{HF,after}}}\right)}^{2/3},$$

(3)

where $R_{HF,before}$ and $R_{HF,after}$ represent high-frequency bulk electrolyte resistance before and after DC excitation. Relative variations were expressed as $\mathrm{\Delta }\left|Z\right|(\%)={\left(\right|Z|}_{after}-{\left|Z\right|}_{before}{)/|Z|}_{before}\times 100$ and $\mathrm{\Delta }\varphi ={\varphi }_{after}-{\varphi }_{before}$. Simulation agreement was quantified by the logarithmic coefficient of determination ($R_{\log \left|Z\right|}^2$), symmetric mean absolute percentage error (sMAPE), and phase root mean square error (RMSE).

3. Results

3.1. Broadband Impedance Response and Numerical Model Validation

Figure 2 presents the complete overview of experimental Bode magnitude and phase spectra measured before and after DC excitation across all combinations of voltage (2 V, 4 V and 8 V) and exposure time (5 s, 10 s and 20 s) ($n=3$, mean ± standard deviation), overlaid with the simulated numerical model responses from COMSOL Multiphysics. Post-DC modifications concentrated predominantly in the low-frequency range (40 Hz to 100 Hz), where impedance magnitude $\left|Z\right|$ decreased systematically and phase angle $\varphi$ shifted toward less negative values (toward zero, $\mathrm{\Delta }\varphi >0$). At frequencies above 100 kHz, all curves converged to the predominantly resistive bulk electrolyte response (≈$42 \mathrm{\Omega } \mathrm{to} 45 \mathrm{\Omega }$), exhibiting an average positive shift ($\mathrm{\Delta }{R}_{HF}=+0.53\%$ to $+5.04\%$, condition means) associated with the physical presence of insulating gas bubbles.

Figure 2. Overview of broadband Bode magnitude (left axis) and phase (right axis) spectra for all combinations of voltage (2 V, 4 V and 8 V) and DC excitation time (5 s, 10 s and 20 s). Experimental curves show replicate means ($n=3$) with shaded $\pm \mathrm{SD}$ bands (Before in blue, After in orange); black dotted/dash-dotted lines represent the measurement-equivalent COMSOL Multiphysics numerical model.

The numerical model reproduced the experimental spectral dispersion across all nine tested conditions, achieving an overall mean $R_{\log \left|Z\right|}^2=0.980$, a mean magnitude sMAPE of 3.94%, and a mean phase RMSE of 2.67° (Table 1). This semi-quantitative agreement indicates that a 3D conductive electrolyte core with attached bubbles and lumped polarization terms can reproduce the instrument-observed response.

Table 1. Consolidated experimental variations at 40 Hz (mean ± SD, $n=3$), numerical model agreement metrics, and optical projected bubble coverage at 20 s.

Voltage	Time	${\mathit{\Delta }\left|\mathit{Z}\right|}_{40\mathbf{Hz}}$	$\mathit{\Delta }{\mathit{\varphi }}_{40\mathbf{Hz}}$	${\mathit{R}}_{\log \left|\mathit{Z}\right|}^2$	sMAPE	Coverage
(V)	(s)	(%)	(°)	–	(%)	(%)
2	5	$-3.06\pm 3.05$	$+1.80\pm 1.03$	0.993	2.72	–
2	10	$-11.40\pm 1.88$	$+4.45\pm 0.75$	0.993	2.64	–
2	20	$-12.88\pm 0.02$	$+4.69\pm 0.70$	0.992	2.86	8.25
4	5	$-13.08\pm 0.23$	$+4.97\pm 0.24$	0.987	3.45	–
4	10	$-14.46\pm 3.95$	$+5.08\pm 1.12$	0.983	4.05	–
4	20	$-18.78\pm 2.54$	$+8.55\pm 3.04$	0.977	5.06	25.39
8	5	$-19.68\pm 4.57$	$+12.95\pm 2.29$	0.971	4.59	–
8	10	$-22.93\pm 3.51$	$+13.85\pm 1.00$	0.970	4.94	–
8	20	$-31.49\pm 3.83$	$+17.41\pm 1.71$	0.955	5.16	27.12
Overall Mean		–	–	0.980	3.94	–

3.2. Low-Frequency Interfacial Dynamics (40 Hz) and Factorial Summary

At 40 Hz, raw relative impedance magnitude variation ($\mathrm{\Delta }\left|Z\right|$) exhibited dependence on both voltage and exposure duration, reaching $-31.49\pm 3.83\%$ at 8 V/ 20 s, accompanied by a phase shift toward less negative values ($\mathrm{\Delta }\varphi =+17.41\pm 1.71°$, from $-33.4°$ to $-16.0°$), reflecting reduced capacitive phase lag and enhanced interfacial Faradaic conductance. Estimating the interfacial impedance contribution ($\mathrm{\Delta }{Z}_{int}={\left|Z\right|}_{40Hz}-R_{HF}$) showed a progressive reduction with dose, spanning from $-4.13\pm 4.27\%$ (2 V/ 5 s) to $-41.48\pm 4.35\%$ (8 V/ 20 s). A two-way analysis of variance (ANOVA) on $\mathrm{\Delta }\left|Z\right|$ at 40 Hz confirmed statistically significant main effects for voltage ($F=60.12$, $p<0.001$) and exposure time ($F=20.31$, $p<0.001$). Voltage dependence for $\mathrm{\Delta }\varphi$ at 40 Hz was also statistically significant ($F=125.19$, $p<0.001$). In contrast, at intermediate frequencies such as 1 kHz, magnitude variation was small (between $-2.26\%$ and $+0.78\%$) and not statistically significant ($F=0.89$, $p=0.43$ for voltage; $F=0.78$, $p=0.47$ for time), whereas the low-frequency response retained dose sensitivity. For $\mathrm{\Delta }{R}_{HF}$, by contrast, neither voltage ($F=2.57$, $p=0.10$) nor time ($F=0.19$, $p=0.83$) was significant. Table 1 summarizes the factorial response across the $3\times 3$ matrix at 40 Hz alongside model agreement metrics and optical bubble coverage.

3.3. Optical Evidence of Interfacial Gas Evolution

Figure 3 displays representative optical frames captured after 20 s of excitation at 2 V, 4 V, and 8 V, with curated bubble masks highlighted in red. The visual records show accumulation of gas bubbles adhering preferentially to the active lateral edges of the electrodes. The projected bubble coverage within the near-electrode ROI increased progressively with applied voltage, from 8.25% at 2 V to 25.39% at 4 V and 27.12% at 8 V (Table 1).

Figure 3. Representative optical video frames after 20 s DC exposure at 2 V (left), 4 V (middle), and 8 V (right). Red overlays represent curated bubble-associated coverage masks near the active lateral electrode faces ($g=5\mathrm{mm}$).

4. Discussion

4.1. Physicochemical Mechanisms and Temporal Dispersion Dynamics

The broadband electrical impedance behavior following DC excitation (Figure 2) indicates that interfacial perturbations in conductive saline decouple two opposing physical regimes: at low frequencies (40 Hz to 100 Hz), electrochemical activation of the metallic interface dominates ($\mathrm{\Delta }{Z}_{int}<0$), whereas at high frequencies (>$100\mathrm{kHz}$), bulk geometric gas blockage emerges ($\mathrm{\Delta }{R}_{HF}>0$) [5,6]. Evolution across 5 s, 10 s and 20 s is consistent with increasing cumulative Faradaic charge transfer ($q=\int i_{\mathrm{dc}}dt$); however, because $i_{\mathrm{dc}}\left(t\right)$ was not recorded, exposure time is only a nominal dose proxy rather than a direct measurement of q.

At 40 Hz, the reduction in magnitude ($\mathrm{\Delta }\left|Z\right|=-31.49\pm 3.83\%$, with isolated $\mathrm{\Delta }{Z}_{int}$ dropping up to $-41.48\pm 4.35\%$) and phase advance toward less negative values ($\mathrm{\Delta }\varphi =+17.41\pm 1.71°$, from $-33.4°$ to $-16.0°$) stem from concurrent Faradaic water electrolysis and chloride oxidation ($2{\mathrm{Cl}}^{-}\to {\mathrm{Cl}}_2+2e^{-}$) in 0.9% NaCl [17,18]. These processes generate pH gradients and oxychlorinated species that promote depassivation and surface roughening of the AISI 304 electrodes (Figure 1), elevating double-layer capacitance ($C_{dl}$) and decreasing charge-transfer resistance ($R_{ct}\downarrow$) [7,9,10]. Although adherent microbubbles act as dielectric insulators (${\sigma }_{gas}\approx 0$) occluding 8.25% to 27.12% of the projected area (Figure 3), increased interfacial Faradaic conductance exceeds geometric gas constriction at low frequencies.

Conversely, above 100 kHz, the double layer acts as a capacitive short-circuit ($1/\omega C\to 0$), and impedance reflects solution resistance. Here, gas bubbles manifest as an average increase in bulk electrolyte resistance ($\mathrm{\Delta }{R}_{HF}=+0.53\%$ to $+5.04\%$, condition means). Applying Bruggeman’s effective medium theory ($R_{after}/R_{before}={(1-ϵ)}^{-3/2}$), this shift places $ϵ$ between 0.4% and 3.2%, as an order-of-magnitude estimate: $\mathrm{\Delta }{R}_{HF}$ shows no resolved dose dependence, and at 8 V $ϵ$ falls from 3.2% to 1.5% between 5 s and 20 s while optical coverage rises. Comparing it with projected 2D optical coverage (8.25% to 27.12%) indicates that edge-concentrated bubble clusters alter 2D visual projection without fully constricting the 3D current volume [1,2,8,20,21]. The coexistence of these two opposing mechanisms causes the differential spectrum to cross zero within a transition band $f_{cross}\approx 0.27\mathrm{kHz} \mathrm{to} 12.6\mathrm{kHz}$, explaining the magnitude null at 1 kHz ($F=0.89,p=0.43$), while phase preserves continuous dose sensitivity ($\mathrm{\Delta }\varphi$ from $-0.54°$ to $+2.03°$) [4].

4.2. Implications for Electroporation and Biomedical Sensing

This dual mechanism has direct implications for pulsed electric field (PEF) protocols, including irreversible electroporation (IRE), electrochemotherapy and gene electrotransfer [17,18]. Under high-voltage pulses, microbubbles along electrode edges distort the local field and generate current-density concentrations (edge effects) that compromise permeabilization homogeneity [17]. While clinical PEF protocols deliver energy in microsecond-to-millisecond pulses at $\mathrm{kV}/\mathrm{cm}$ field levels [18], the continuous DC regime investigated here ($E_{nom}=0.4 \mathrm{V}/\mathrm{mm} \mathrm{to} 1.6 \mathrm{V}/\mathrm{mm}$ for $5 \mathrm{s} \mathrm{to} 20 \mathrm{s}$) isolates steady-state bubble nucleation and Faradaic interface alterations without high-voltage transients. At the conductivity of the present medium, a standard electrochemotherapy train of eight 100 μs pulses near 1 kV/cm [22] deposits about 12 J mL⁻¹ at a peak power density of 15 kW mL⁻¹. The corresponding values here are 1.2 J mL⁻¹ to 77 J mL⁻¹ and 0.24 W mL⁻¹ to 3.8 W mL⁻¹. Thus, the cumulative energy density is comparable, but the peak power density is three to four orders of magnitude lower here, neglecting electrode overpotential. In real-time impedance-based monitoring [9,12], the low-frequency interfacial impedance drop from electrode Faradaic activation may be misattributed to cell membrane permeabilization, while high-frequency resistive bubble screening obscures intracellular ion release.

4.3. Limitations and Future Work

Limitations include the fixed-electrode geometry in a static chamber and triplicate testing ($n=3$, in 0.9% NaCl). Optical analysis assessed 2D projected coverage at 20 s without resolving millisecond-scale coalescence dynamics or 3D tomographic volumes. DC current and electrolyte temperature were not logged per condition, precluding direct calculation of $q=\int i_{dc}dt$; as conductivity rises about 2% per °C, Joule heating lowers $R_{HF}$, so the reported $\mathrm{\Delta }{R}_{HF}$ is a lower bound on geometric screening. Future work should incorporate real-time current and temperature logging, synchronized high-speed imaging, and distributed constant phase element (CPE) fitting to decouple charge-transfer kinetics from the stochastic evolution of the bubble layer.

5. Conclusions

This study established a coupled methodology integrating broadband electrical impedance spectroscopy, optical image analysis, and numerical modeling to evaluate interfacial gas bubble phenomena in physiological saline solution under DC excitation. Broadband EIS measurements showed that post-DC electrical modifications decouple two opposing physical regimes: low-frequency interfacial electrochemical activation (40 Hz to 100 Hz, where estimated interfacial $\mathrm{\Delta }{Z}_{int}$ dropped up to $-41.48\pm 4.35\%$ with phase advancing toward zero, $\mathrm{\Delta }\varphi =+17.41\pm 1.71°$) and high-frequency bulk resistive gas screening (>$100\mathrm{kHz}$, $\mathrm{\Delta }{R}_{HF}=+0.53\%$ to $+5.04\%$, without resolved dose dependence, giving an order-of-magnitude volumetric gas fraction of 0.4% to 3.2% via Bruggeman’s theory). The Python morphometric algorithm quantified gas accumulation along active electrode edges (2D projected coverage of 8.25% to 27.12% at 20 s), and 3D COMSOL Multiphysics modeling captured the experimental dispersion ($R_{\log \left|Z\right|}^2=0.980$). Identifying the mechanism-inversion crossover band ($f_{cross}\approx 0.27\mathrm{kHz} \mathrm{to} 12.6\mathrm{kHz}$) and decoupling interfacial impedance from bulk electrolyte resistance provide analytical guidelines to prevent misattributing electrode bubble artifacts to cellular permeabilization in electroporation procedures and electrical impedance sensing within conductive physiological media.