Electric Field-Line Distortion in Electrochemistry: Turbulence and Resistance

How electrolyte flow and the presence of a gas phase alter current distribution, ohmic losses, and the interpretation of electrochemical measurements.

In an electrochemical cell, current does not flow through a metal wire between the two electrodes: it passes through a solution by means of ion motion. When the system becomes heterogeneous, the paths available to the current can change. One important example is the gas bubbles that form during electrolysis. As they interact with the liquid flow, they alter the local current distribution and may increase the ohmic potential drop.

For explanatory purposes, these effects can be described as a “disturbance of electric field lines.” In the scientific literature, however, it is more precise to speak of redistribution of current lines, distortion of the electric potential field, and an increase in effective ohmic resistance. Above all, one point needs to be made clear: turbulence in a homogeneous electrolyte does not, by itself, imply an increase in electrical resistance. The increase documented in numerous studies primarily concerns multiphase systems and spatial variations in conductivity. [1–3, 6]

Electric current lines are not liquid flow trajectories

As a first approximation, consider an electrolyte region in which ionic current is dominated by migration in an electric field. The current density j is related to the electric potential φ and the conductivity κ by:

j = −κ ∇φ

Under quasi-steady-state conditions, with no appreciable accumulation of charge in the bulk, ∇·j = 0 also holds. Combining the two expressions gives:

∇·(κ ∇φ) = 0

These simplified equations describe how the conductivity distribution and cell geometry determine the potential field and the paths followed by electric current. When κ is uniform, the shape of the field depends mainly on the geometry and boundary conditions. If κ varies from point to point, however, the current lines redistribute. In the presence of strong concentration gradients, more comprehensive ionic transport models are required, including diffusion and convection. [2, 5]

The fundamental distinction is that electric current lines do not coincide with liquid flow streamlines. A vortex in a single-phase electrolyte of constant composition and temperature does not force ions to follow a longer electrical path simply because the fluid is rotating. Fluid motion affects the electric field indirectly when it changes concentrations, temperature, bubble distribution, or other properties of the system.

Why gas bubbles increase ohmic resistance

During water electrolysis, as in many industrial processes, gases are generated at the electrode surfaces. Compared with the conductive solution, a gas bubble is an almost insulating region. Current must flow around it and becomes concentrated in the remaining liquid pathways.

This leads to three distinct effects:

• Obstruction of ionic pathways in the bulk electrolyte. Dispersed bubbles reduce the effective conductivity of the gas–liquid mixture and increase the ohmic potential drop at a given current.
• Shielding of the electrode surface. Adhering bubbles locally prevent contact between the electrode and the electrolyte and may concentrate current in the uncovered regions, also affecting the activation overpotential.
• Time-dependent fluctuations. Bubble nucleation, growth, coalescence, and detachment continuously alter the geometry of conductive pathways; the measured resistance may therefore vary even during a constant-current experiment.

This is more than a qualitative hypothesis. Bongenaar-Schlenter and colleagues measured both bubble and current distributions using a segmented nickel electrode, explicitly relating the gas void fraction to the cell’s ohmic resistance. Mandin and colleagues subsequently showed, through a coupled electrical and fluid-dynamic model, how nonuniform gas distributions can perturb the potential field and current density. [1, 2]

A simple model: effective conductivity

For an ideal single-phase cell with electrodes of area A separated by a distance L, the resistance can be approximated as RΩ = L/(κA). This expression provides a useful geometric reference, but it becomes insufficient when the medium contains two phases.

One approximation used in electrolyzer modeling is the Bruggeman relation:

κeff ≈ κliquid · (1 − ε)^(3/2)

Here, ε is the gas volume fraction, or gas void fraction. If the macroscopic geometry remains unchanged and the assumptions of the model apply, the ratio of the resistance of the two-phase medium to that of the bubble-free electrolyte is:

RΩ,eff / RΩ,0 ≈ (1 − ε)^(−3/2)

For example, with ε = 0.20, we obtain RΩ,eff / RΩ,0 ≈ 1.40, corresponding to a theoretical increase of about 40%. This is an illustrative calculation, not a universal prediction. Bubble size, shape, location, and spatial distribution—particularly near the electrodes—may require a more detailed description. [5]

It is also important to distinguish ohmic resistance RΩ, associated with ionic transport and the cell materials, from charge-transfer resistance Rct and mass-transport limitations. An increase in the voltage-to-current ratio alone does not prove that RΩ has increased.

What role does turbulence actually play?

Turbulence affects this phenomenon through the hydrodynamics of the system. It can detach bubbles from electrodes, carry them into the solution, break them up or change their distribution, and mix regions with different concentrations. The electrical outcome therefore depends on the balance between competing processes.

In a single-phase system, stronger convection generally improves the supply of reactants and the removal of products near the electrode, reducing mass-transport limitations. This does not mean that every component of the impedance necessarily decreases, but it does rule out treating “more turbulence = higher ohmic resistance” as a general law. Studies of current distribution in turbulent-flow cells show that geometric, kinetic, and transport effects must be distinguished. [4]

In gas–liquid systems, the situation is different. Flow may enhance mixing while simultaneously keeping bubbles suspended in the electrolyte or near an electrode, where they obstruct current pathways. Cao and colleagues examined this competition in microreactors operating under Taylor flow conditions: recirculation within the liquid improves mass transport, whereas the bubbles distort the electric field and adversely affect current distribution. [7]

Raman and colleagues observed an even subtler competition during the growth of individual hydrogen bubbles: a bubble may reduce the concentration overpotential by removing dissolved gas near the electrode while simultaneously increasing the ohmic overpotential by obstructing ionic pathways. For this reason, the total cell voltage alone cannot identify the origin of energy losses. [8]

From experimental observations to practical implications

The effect has also been observed in configurations resembling practical electrolyzers. Studying a narrow-gap cell with a separator, Qiu and colleagues associated an increase in high-frequency resistance with bubble accumulation at the electrode–separator interface. In situ visualization made it possible to link a physical obstruction to an additional ohmic contribution. [9]

In a 2025 study, Logar and colleagues investigated bubble effects in rotating disk electrode measurements, combining experiments and modeling. In the system studied, the bubble-induced increase in uncompensated resistance proved to be a major contributor to the apparent loss of electrocatalytic activity. The authors also showed that inadequate correction for this contribution can introduce substantial errors into estimates of activity and Tafel slopes. [10]

In other words, a change in electrical performance does not necessarily mean that the electrode material has become less active: part of the change may arise from the medium through which the current passes.

How to distinguish the different contributions experimentally

A convincing investigation should separate the effects of fluid motion, gas presence, and reaction kinetics. In practice, it is useful to:

1. Establish a reference condition by measuring temperature, composition, electrolyte conductivity, and cell geometry.
2. Vary the flow rate while keeping other conditions unchanged, distinguishing single-phase and two-phase tests whenever possible. Flow rate alone does not necessarily establish whether the flow is turbulent.
3. Measure the ohmic contribution, for example through electrochemical impedance spectroscopy (EIS) and high-frequency resistance (HFR) analysis, or with suitable transient methods. The reference electrode position and possible nonstationarity of the system must be considered.
4. Observe the bubbles, documenting their surface coverage, size, distribution, and detachment, ideally at the same time as the electrical measurements.
5. Compare RΩ, overpotentials, and current behavior, rather than interpreting a change in cell voltage alone as proof of increased electrolyte resistivity.

One particularly informative check is to determine whether resistance rises as gas accumulates and falls when bubbles are removed. Temporal correlation, together with measurements that isolate the electrical contributions, strengthens the physical interpretation of the phenomenon. [3, 8–10]

Conclusion

The expression “disturbance of electric field lines” can help visualize what happens when ionic current must flow around regions of low conductivity. The phenomenon is supported by substantial experimental and theoretical evidence, but attributing it to turbulence alone would be misleading.

The central issue is the coupling between hydrodynamics, conductivity distribution, and electrochemical processes. Bubbles can increase ohmic resistance and perturb current lines; at the same time, convection can alleviate concentration polarization. Determining which contribution dominates requires separating the components of the cell voltage and measuring the system’s properties under its actual operating conditions.

References

1. Bongenaar-Schlenter, B. E., Janssen, L. J. J., van Stralen, S. J. D., & Barendrecht, E. (1985). The effect of the gas void distribution on the ohmic resistance during water electrolysis. Journal of Applied Electrochemistry, 15(4), 537–548. https://doi.org/10.1007/BF01059295
2. Mandin, P., Hamburger, J., Bessou, S., & Picard, G. (2005). Modelling and calculation of the current density distribution evolution at vertical gas-evolving electrodes. Electrochimica Acta, 51(6), 1140–1156. https://doi.org/10.1016/j.electacta.2005.06.007
3. Gabrielli, C., Huet, F., & Nogueira, R. P. (2005). Fluctuations of concentration overpotential generated at gas-evolving electrodes. Electrochimica Acta, 50(18), 3726–3736. https://doi.org/10.1016/j.electacta.2005.01.019
4. Pérez, T., Ponce de León, C., Walsh, F. C., & Nava, J. L. (2015). Simulation of current distribution along a planar electrode under turbulent flow conditions in a laboratory filter-press flow cell. Electrochimica Acta, 154, 352–360. https://doi.org/10.1016/j.electacta.2014.11.166
5. Taqieddin, A., Allshouse, M. R., & Alshawabkeh, A. N. (2018). Review—Mathematical Formulations of Electrochemically Gas-Evolving Systems. Journal of The Electrochemical Society, 165(13), E694–E711. https://doi.org/10.1149/2.0791813jes
6. Angulo, A., van der Linde, P., Gardeniers, H., Modestino, M., & Fernández Rivas, D. (2020). Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors. Joule, 4(3), 555–579. https://doi.org/10.1016/j.joule.2020.01.005
7. Cao, Y., Soares, C., Padoin, N., & Noël, T. (2021). Gas bubbles have controversial effects on Taylor flow electrochemistry. Chemical Engineering Journal, 406, 126811. https://doi.org/10.1016/j.cej.2020.126811
8. Raman, A., Peñas, P., van der Meer, D., Lohse, D., Gardeniers, H., & Fernández Rivas, D. (2022). Potential response of single successive constant-current-driven electrolytic hydrogen bubbles spatially separated from the electrode. Electrochimica Acta, 425, 140691. https://doi.org/10.1016/j.electacta.2022.140691
9. Qiu, H., Obata, K., Tsuburaya, K., Nishimoto, T., Nagato, K., & Takanabe, K. (2024). Impact of gas bubble slug on high-frequency resistance and cell voltage in water electrolysis device. Journal of Power Sources, 611, 234765. https://doi.org/10.1016/j.jpowsour.2024.234765
10. Logar, A., Kozlica, D. K., Vodeb, O., Gaberšček, M., Hodnik, N., & Strmčnik, D. (2025). Bubble Trouble: Quantifying the Effects of Bubbles on the Electrochemical Interface. ACS Catalysis, 15(8), 6380–6385. https://doi.org/10.1021/acscatal.5c00144