Diffusion and Cyclic Voltammetry in Microfluidic Channels

Key Concepts

• Electrode Geometry: The size and shape of the electrode influence mass transport and the resulting cyclic voltammogram.
• Radial Diffusion: At small electrodes, diffusion from the edges becomes important, favouring a steady-state voltammetric response.
• Thin-Layer Behaviour: When the channel height is small compared with the diffusion-layer thickness, the electroactive species can be completely depleted within the microfluidic channel.
• Scan Rate: Controls the experimental timescale and it influences the transition between steady-state, transient and thin-layer voltammetric behaviour.

Introduction

Mass transport is a phenomenon that is present in all electrochemical experiments. It simply occurs when the concentration of the electroactive species starts to decrease at the electrode-electrolyte interface, which generates a diffusion gradient, causing the movement of the species from the bulk towards the electrode-electrolyte interface.

The difficulty is that mass transport does not depend exclusively on the diffusion coefficient, but mainly on the geometry of the gradient. This geometry depends on the shape and size of the electrode, and the dimension of the electrochemical cell. In more complex systems, such as porous electrodes, the situation becomes even more complicated because species do not move through a straight path, but through a network of pores and channels.

For large electrodes, usually in the macroelectrode range (Diameter>500 µm), diffusion is often treated as planar. This means that species mainly move in one direction, perpendicular to the electrode surface. This case is easier to describe, and many classical electrochemical models are based on this idea.

However, many modern electrochemical systems are much smaller, such as biosensors, microfluidic devices, thin-layer cells, in vivo sensors, and microelectrodes. These electrodes often have dimensions smaller than 500 µm. In these cases, diffusion is not only planar, but the electrode edges become more relevant, and radial diffusion starts to contribute to the electrochemical response. See figure below.

Figure 1. Schematic comparison between planar diffusion at larger electrodes and radial diffusion at microelectrodes.

The aim of this blog post is to show how the diffusion profile changes with electrode geometry and how these changes affect the cyclic voltametric response. It will focus on the transition from planar diffusion at larger electrodes, to mixed planar–radial diffusion at smaller electrodes, and finally to predominantly radial diffusion at ultramicroelectrodes.

Case Study

To illustrate how the geometry of the electrochemical cell affects mass transport, the system shown in Figure 2 will be studied. The system consists of a disk electrode with diameter \(d\) µm, confined inside a microchannel with height \(y\) µm and width \(x\) µm.

The electrode and channel dimensions will vary. For instance, the electrode diameter \(d\) will be changed from 10 to 100 µm, while the channel height \(y\) will be varied from 40 to 200 µm. The width of the electrochemical chamber, \(x\), will be kept constant at 300 µm.

For simplicity, a reversible one-electron redox reaction will be considered

\[ \text{Red}\rightleftharpoons\text{Ox} + e^- \]

No additional phenomena, such as adsorption, coupled chemical reactions, electrode defects or porous electrode effects, will be included. The electrode surface will be treated as smooth, flat and non-porous.

Figure 2. Schematic representation of the electrochemical cell geometry. The disk electrode has diameter \(d\), while the microchannel is defined by its height \(y\) and width \(x\).

Effect of Electrode Diameter

Electrode size strongly influences the diffusion. At relatively large electrodes (above 500 µm), diffusion is often predominantly planar, species moving mainly perpendicular to the electrode surface. However, as the electrode becomes smaller, diffusion from the electrode edges becomes important, resulting in a combination of planar and radial diffusion. Finally, at ultramicroelectrodes, radial diffusion dominates the mass transport mechanism, as illustrated in Figure 1.

This change in diffusion behaviour has a significant effect on the shape of the cyclic voltammogram. At ultramicroelectrodes, mass transport is enhanced because electroactive species can diffuse towards the electrode from multiple directions. This allows a steady state to be established between the rate at which the electroactive species are consumed at the electrode surface and the rate at which they are replenished by diffusion during the anodic or cathodic sweep. Consequently, the current approaches a steady-state value, producing a sigmoidal voltammogram.

As the electrode diameter increases, the contribution of radial diffusion becomes less important, and the limitations associated with planar diffusion become more noticeable. Consequently, after reaching a maximum, the current starts to diminish because the electroactive species near the electrode surface are depleted faster than the diffusion from the bulk. At sufficiently large electrodes, this behaviour produces the classical peak-shaped voltammogram, the classical duck shape.

The following animation shows how the cyclic voltammetric response changes with electrode diameter, from the sigmoidal shape of ultramicroelectrodes to the classical duck-shaped at larger electrodes. It also shows the concentration profile of the reduced species (Red) when oxidation depletes near the electrode surface. Notice how the diffusion layer becomes increasingly curved around smaller electrodes (radial diffusion contribution).

Animation 1. Effect of electrode diameter, \(d\), on the cyclic voltammetric response and the concentration profile of the reduced species (Red), showing the transition from predominantly radial to planar diffusion.

Effect of Channel Height

Under many experimental conditions, the diffusion layer has a characteristic thickness of less than 150 µm, although this depends on the diffusion coefficient of the electroactive species, the experimental timescale and the electrode geometry. Many microfluidic devices operate under thin-layer conditions, where the channel height is comparable to or smaller than the diffusion-layer thickness. In such confined geometries, the small volume of solution limits the amount of electroactive species available near the electrode. Consequently, the analyte can be depleted more rapidly which changes electrochemical response.

The following animation shows how the cyclic voltammogram of a 100 µm diameter electrode changes with channel height at a scan rate of 100 mV/s. When the channel height becomes comparable to or smaller than the diffusion-layer thickness, the peak current decreases, and the current approaches zero after the redox peak due to the depletion of electroactive species within the microfluidic channel.

Animation 2. Effect of channel height on the cyclic voltammogram of a 100 µm diameter electrode at a scan rate of 100 mV/s.

When the electrode diameter is reduced to 10 µm while maintaining the same scan rate (100 mV/s), the cyclic voltammogram changes from a sigmoidal shape to a peak-shaped response, as shown in the following animation. Due to the small electrode size, the electroactive species are not completely depleted within the microfluidic channel.

Animation 3. Effect of channel height on the cyclic voltammogram of a 10 µm diameter electrode at a scan rate of 100 mV/s.

Effect of Scan Rate

As shown above, the depletion of electroactive species within the microfluidic channel is the main factor responsible for the changes observed in the cyclic voltammogram. At lower scan rates, the longer experimental timescale allows more extensive depletion of the analyte, leading to thin-layer behaviour. Under these conditions, the integrated charge of the voltammetric peak is proportional to the concentration of the electroactive species within the microfluidic channel.

The following animation shows that, at scan rates below 20 mV/s, the cyclic voltammogram exhibits thin-layer behaviour, as the electroactive species are completely depleted within the microfluidic channel.

Animation 4. Effect of scan rate on the cyclic voltammogram of a 100 µm diameter electrode.

Similar behaviour is observed at ultramicroelectrodes. At scan rates below 10 mV/s, the voltammogram exhibits thin-layer behaviour.

Animation 5. Effect of scan rate on the cyclic voltammogram of a 10 µm diameter electrode.

Voltammogram Simulator

This interactive application simulates a cyclic voltammogram using a 2D diffusion model for a microelectrode confined within a microfluidic channel (Figure 2). The application displays the cyclic voltammogram and the corresponding 2D concentration profile of the reduced species (Red). You can explore how the following parameters influence the voltammetric response:

1. Electrode width (µm): Smaller electrodes favour radial diffusion, while larger electrodes exhibit a greater contribution from planar diffusion.
2. Channel height (x domain, µm): Smaller channel heights favour thin-layer behaviour.
3. Channel width (y domain, µm): Defines the lateral dimension of the simulated microfluidic channel.
4. Scan rate (V/s): Controls the experimental timescale.
5. Initial concentration ([Red]₀, mM): Determines the amount of electroactive species initially present in the microfluidic channel
6. Standard electron-transfer rate constant (k₀): Controls the electron-transfer kinetics and the reversibility of the voltammetric response. This parameter is adjusted on a logarithmic scale.
7. Charge-transfer coefficient (α): Influences the electron-transfer kinetics, particularly when the electron-transfer rate is relatively slow.
8. Number of transferred electrons (nₑ): Defines the number of electrons involved in the electrochemical reaction.
9. Potential window (Ei and Ef): Defines the initial and switching potentials of the cyclic voltammetric scan.

The concentration profile can be examined at different times to visualise the development of the diffusion layer and the depletion of Red near the electrode.

By adjusting these parameters, you can explore the transition between planar and radial diffusion, as well as the development of thin-layer behaviour in confined microfluidic channels. The voltammogram, concentration profile and simulation grid can also be exported as CSV files for further analysis.

If you want to cite this blog post, use:
Robayo, I. (2026). Diffusion and Cyclic Voltammetry in Microfluidic Channels. Available at: https://electrochemeisbasics.blogspot.com/2026/10/radial-diffusion.html [Accessed Date Accessed].