Turbulence and Electrical Resistance in Single-Phase Electrolytes: When Flow Changes the Electrochemical Response

The so-called “electric field-line disturbance” in a bubble-free solution: current distribution, ionic gradients, convection, and the interpretation of impedance measurements.

When a liquid electrolyte is set in motion, the electrical response of an electrochemical cell may change. In some experiments, the voltage required to sustain a given current increases; in others, it decreases. Can we therefore speak of an increase in resistance associated with electrolyte motion even when the system remains entirely in the liquid phase, with no gas bubbles? The answer is yes, but it is essential to specify which resistance is being measured and by what mechanism the flow changes it.

Although the expression “electric field-line disturbance” is intuitive, it does not, by itself, identify a unique electrochemical mechanism. In a real cell, ionic current lines must be distinguished from liquid trajectories, ohmic resistance from polarization, and hydrodynamic fluctuations from persistent changes in electrolyte properties. The literature provides experimental examples and models that help separate these contributions [1–11].

Current lines do not necessarily follow the liquid

Within the bulk of an electrolyte, under ordinary electroneutrality conditions and when the diffusive contribution to current is negligible, the local relationship between current density \(\mathbf j\), conductivity \(\kappa\), and electric potential \(\phi\) can be written as:

Under quasi-steady-state conditions, charge conservation requires \(\nabla\cdot\mathbf j=0\). These two relationships give:

If conductivity is uniform, the equation reduces to \(\nabla^2\phi=0\): for a given geometry, set of electrodes, and electrical boundary conditions, the liquid velocity profile does not appear directly in this equation. A hydrodynamic vortex does not, by itself, force electrical current lines to follow its spiral path. Longer fluid trajectories do not imply longer electrical current paths.

The connection arises indirectly when flow changes concentrations near the electrodes, redistributes regions of different conductivity, changes temperature, influences interfaces, or produces electrokinetic signals. Moreover, when significant ionic gradients are present, the preceding ohmic relationship is a simplification: diffusion-driven current must also be considered.

Convection, migration, and diffusion: three distinct contributions

For an ionic species \(i\) in a sufficiently dilute, ideal solution, the molar flux can be described by the Nernst–Planck equation:

The terms represent, respectively, diffusion driven by concentration gradients, migration under the electric field, and convection due to the liquid velocity \(\mathbf u\). The ionic current density is:

In an approximately electroneutral bulk solution, \(\sum_i z_ic_i\simeq0\): the direct contribution of convective charge transport, \(F\mathbf u\sum_i z_ic_i\), vanishes under this approximation. Nevertheless, flow still changes \(c_i(\mathbf x,t)\) and, consequently, migration, diffusion, and the electrochemical response. Near charged interfaces, particularly in microchannels at low ionic strength, local electroneutrality is not a sufficient simplification to describe every electrokinetic effect [8].

For ideal dilute solutions, conductivity can be approximated by:

This expression shows why a local change in ionic concentration can become a local change in conductivity. Concentrated solutions require more accurate constitutive relationships that account for ion–ion interactions and effective transport coefficients [5].

How can resistance increase when everything remains liquid?

1. Redistribution of ionic gradients

An electrode reaction may consume species near one electrode and produce others elsewhere. Convection mixes these concentration profiles; depending on the initial composition and the reaction, it can increase or decrease conductivity in the regions carrying the most current. A direct example of flow-induced impedance increase without bubbles is the study by Ayliffe and Rabbitt (2003): in microchannels containing a saline solution, the authors observed an impedance response dependent on flow rate, including an increase in the real part of impedance under certain conditions. Their proposed model attributes the effect to convection removing a local enrichment of ions near the electrodes [1].

This is a particularly relevant finding, but it must be interpreted within its limits: it concerns microelectrodes, a confined geometry, and specific electrical conditions. It does not demonstrate that any turbulent flow increases the resistivity of a homogeneous electrolyte.

Another study, by Schalenbach and colleagues (2023), experimentally shows how concentration gradients in an aqueous copper sulfate solution are associated with an increase in cell resistance. This work helps clarify the role of local conductivity; however, it does not measure the effect of turbulence, because the model considered does not include convection [5].

2. Spatial variations in conductivity

Even without gas, an electrolyte may be nonuniform. As a simple model, consider two planar electrodes of area \(A\) separated by a distance \(L\). If conductivity varies along the direction of current:

Suppose, for illustration only, that half of the gap has conductivity \(0.8\kappa_0\) and the other half \(1.2\kappa_0\). The arithmetic mean is still \(\kappa_0\), but the two regions are electrically in series, so:

The result is an increase of approximately 4.2% relative to the uniform solution, despite the same arithmetic mean conductivity. This is not an experimental finding about turbulence: it illustrates why the spatial arrangement and electrical connection of the regions matter. In a three-dimensional cell, current can also bypass less conductive regions, making it necessary to solve the electric field coupled to species transport.

3. Changes in electrode response

Turbulence affects diffusion-layer thickness and the supply of reactants at the electrode–solution interface. However, a change in cell voltage does not necessarily correspond to a change in the electrolyte’s ohmic resistance. It may arise from concentration polarization, charge transfer, or a nonuniform distribution of reactions. Studies on flow cells and membranes show how easily physically distinct contributions can be assigned to a single “resistance” [3, 6, 7, 10].

4. Streaming potentials in confined geometries

A liquid flowing through channels with charged walls can carry ions in the electrical double layer and generate streaming currents and streaming potentials. Kostiuchenko, Cui, and Lemay (2020) studied how these effects couple with ohmic losses and Faradaic reactions in micro- and nanochannels. This is a genuine liquid-phase mechanism, especially important at low supporting-electrolyte concentrations and in miniaturized systems; it should not automatically be generalized to macroscopic cells or highly conductive solutions [8].

Turbulence can also reduce electrochemical losses

The literature cautions against a one-sided interpretation. As early as 1964, Arvia, Carrozza, and Marchiano analyzed the role of turbulent eddies in mass transfer and limiting current [2]. In a filter-press cell under turbulent flow, Pérez and colleagues (2015) distinguished primary current distribution (mainly geometry-dependent), secondary current distribution (also accounting for electrode kinetics), and limiting-current distribution (sensitive to mass transfer and hydrodynamics) [3]. Zinola (2023) analyzed velocity, concentration, and current profiles in thin-layer electrochemical cells under laminar and turbulent regimes [4].

Experiments on vanadium redox flow batteries by Ertugrul and colleagues (2020) likewise show that a higher electrolyte velocity within the electrode region can make current distribution more uniform and mitigate local depletion of reacting species. Velocity in the flow channel alone, however, is not necessarily correlated with electrode performance [10].

These studies do not contradict the findings of Ayliffe and Rabbitt. They describe different geometries, flow regimes, and physical contributions. Increasing convection may reduce a mass-transport loss in one configuration while increasing a component of measured impedance in another.

Ohmic resistance, apparent resistance, and impedance

If voltage changes with flow rate during a galvanostatic experiment, it is not correct to conclude automatically that electrolyte conductivity has changed. At a fixed current, a voltage change can schematically be attributed to several contributions:

The symbols denote changes in ohmic loss, charge-transfer overpotential, concentration overpotential, and any change in equilibrium potential. The equation is an operational decomposition, with signs to be defined according to the cell convention; it is not a universally applicable equivalent circuit.

To clarify the terminology:

Quantity	What it describes	How to interpret it
Conductivity \(\kappa\)	A local electrical property of the electrolyte	Depends on composition, temperature, and other physical factors
Ohmic resistance \(R_\Omega\)	Resistive voltage loss along ionic current paths and other ohmic elements of the cell	Must be identified with a measurement appropriate to the geometry
Apparent resistance \(V/I\)	The ratio of voltage to current under a specified condition	May include equilibrium potentials and overpotentials; it is not necessarily \(R_\Omega\)
Impedance \(Z(\omega)\)	A complex, frequency-dependent electrical response	Can help separate processes, but requires a model and sufficiently stationary conditions
Hydraulic resistance	The ratio of pressure drop to flow rate, under the appropriate definition	Is not electrical resistance and must not be confused with it

Electrochemical impedance spectroscopy (EIS) is a useful tool, provided it is applied carefully. Poujouly and colleagues (2022) experimentally verified diffusion–convection impedance at a band electrode under Poiseuille flow [6]. Długołęcki and colleagues (2010) used EIS to distinguish membrane, double-layer, and diffusion-boundary-layer contributions, demonstrating how strongly flow can influence the overall measured resistance [7]. For the principles, limitations, and interpretation of EIS spectra, the tutorial by Lazanas and Prodromidis (2023) is a useful reference [9].

A signal that fluctuates with turbulence also needs careful interpretation. Deslouis, Gil, and Tribollet (1990) studied the frequency response of electrochemical sensors to hydrodynamic fluctuations, showing that the measured signal reflects the dynamics of mass transfer and sensor response, rather than simply the resistivity of the liquid [11].

An experimental protocol for testing the mechanism in a single-phase system

To link a possible resistance increase to turbulence without introducing unproven explanations, experiments should be designed to separate the different effects.

1. Define the hydrodynamic regime. Measure flow rate, channel dimensions, viscosity, and density; estimate \(Re=\rho U D_h/\mu\) using an appropriate characteristic length. The transition threshold depends on geometry: pulsating or unsteady flow is not automatically turbulent flow.
2. Control temperature and composition. Record electrolyte conductivity and temperature at the inlet and outlet; avoid mistaking heating, dilution, or a secondary reaction for an effect of turbulence.
3. Measure liquid conductivity independently of the reaction. Use a suitably calibrated conductivity cell, preferably with four electrodes, to determine whether the liquid property actually changes as flow rate varies.
4. Separate the electrochemical contributions. Repeat measurements at controlled current and composition, using a three-electrode configuration where appropriate, EIS, and an assessment of high-frequency resistance. The location of the reference electrode is part of the electrical measurement geometry.
5. Run both increasing and decreasing flow-rate sequences. Repeat measurements after stabilization; test for hysteresis, time dependence, and fluctuations, and document the temporal averaging method.
6. Test dependence on electrical operating conditions. If the change appears only under polarization, at a particular frequency, or near limiting current, interfacial layers or species transport are more likely to be involved than a universal change in bulk conductivity.
7. Compare geometries or measurement positions. A response sensitive to electrode position or the location of the reference probe suggests a spatially nonuniform potential or current distribution.

One possible interpretation of the results is as follows: if bulk conductivity stays constant while operating voltage changes, polarization and current distribution should be examined first. If an independently identified ohmic contribution also changes, look for local changes in composition, temperature, effective geometry, or, in confined systems, electrokinetic contributions. If only the low-frequency part of the impedance changes, mass transport becomes a particularly relevant hypothesis, though it is not an automatic diagnosis.

Conclusion: a measurable effect, not a universal law

A completely liquid electrochemical system can exhibit an increase in measured resistance or impedance as flow increases. Published studies document this under specific conditions [1], while models explain how ionic concentration, potential distribution, and hydrodynamics can be coupled [3, 5–8]. Conversely, numerous experiments show that convection reduces mass-transport limitations and can make current distribution more uniform [2–4, 10].

The phrase “electric field-line disturbance” can therefore be retained as a descriptive image, but a physical explanation requires a more precise question: Has the liquid’s ohmic resistance increased, has the current distribution changed, or has electrochemical polarization changed? Only targeted measurements can distinguish these scenarios. That distinction is also essential for correctly interpreting experimental observations in a single-phase cell.

References

1. Ayliffe, H. E., & Rabbitt, R. D. (2003). An electric impedance based microelectromechanical system flow sensor for ionic solutions. Measurement Science and Technology, 14(8), 1321–1327. DOI: 10.1088/0957-0233/14/8/318.
2. Arvia, A. J., Carrozza, J. S., & Marchiano, S. L. (1964). On the mechanism of turbulent flow in mass-transfer controlled electrochemical reactions. Electrochimica Acta, 9(11), 1483–1495. DOI: 10.1016/0013-4686(64)85029-5.
3. 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. DOI: 10.1016/j.electacta.2014.11.166.
4. Zinola, C. F. (2023). Current density profiles at thin layer electrochemical cells under laminar and turbulent regimes. Electrochimica Acta, 467, 143030. DOI: 10.1016/j.electacta.2023.143030.
5. Schalenbach, M., Hecker, B., Schmid, B., Durmus, Y. E., Tempel, H., Kungl, H., & Eichel, R.-A. (2023). Ionic transport modeling for liquid electrolytes – Experimental evaluation by concentration gradients and limited currents. Electrochemical Science Advances, 3, e2100189 (published online in 2022). DOI: 10.1002/elsa.202100189.
6. Poujouly, C., Gonzalez-Losada, P., Boukraa, R., Freisa, M., Le Gall, J., Bouville, D., Deslouis, C., & Gamby, J. (2022). Diffusion–convection impedance for a micro-band electrode under microfluidic conditions. Electrochemistry Communications, 137, 107262. DOI: 10.1016/j.elecom.2022.107262.
7. Długołęcki, P., Ogonowski, P., Metz, S. J., Saakes, M., Nijmeijer, K., & Wessling, M. (2010). On the resistances of membrane, diffusion boundary layer and double layer in ion exchange membrane transport. Journal of Membrane Science, 349, 369–379. DOI: 10.1016/j.memsci.2009.11.069.
8. Kostiuchenko, Z. A., Cui, J. Z., & Lemay, S. G. (2020). Electrochemistry in Micro- and Nanochannels Controlled by Streaming Potentials. The Journal of Physical Chemistry C, 124(4), 2656–2663. DOI: 10.1021/acs.jpcc.9b08584.
9. Lazanas, A. Ch., & Prodromidis, M. I. (2023). Electrochemical Impedance Spectroscopy—A Tutorial. ACS Measurement Science Au, 3(3), 162–193. DOI: 10.1021/acsmeasuresciau.2c00070.
10. Ertugrul, T. Y., Daugherty, M. C., Houser, J. R., Aaron, D. S., & Mench, M. M. (2020). Computational and Experimental Study of Convection in a Vanadium Redox Flow Battery Strip Cell Architecture. Energies, 13(18), 4767. DOI: 10.3390/en13184767.
11. Deslouis, C., Gil, O., & Tribollet, B. (1990). Frequency response of electrochemical sensors to hydrodynamic fluctuations. Journal of Fluid Mechanics, 215, 85–100. DOI: 10.1017/S0022112090002567.