Natural Convection in Redox Electrochemistry: Model, Simulations and Experiments
Authors: Isaac KM , Yuan Fangping 
Published: February 2020

A natural convection model has been implemented on redox species TMPD with supporting electrolyte TBAP in acetonitrile solvent. The cross section geometry used for the two-dimensional simulations is 20 mm (W) x 10 mm (H). The working electrode is a 2 mm wide strip at the center of the cell floor and the counter electrode is the entire cell ceiling. For the three-dimensional simulations, a 3mm diameter working electrode in the semi-infinite configuration was used. A uniform magnetic field was applied in the direction perpendicular the working electrode surface. The first case we have studied has an initial concentration of 10.3 mM TMPD- and no oxidized form of TMPD. The supporting electrolyte concentration was 0.5 M. The cell was operated in the potential step mode and the applied potential was high enough for operation in the diffusion-limited regime. Simulations were run for two values of the magnetic field intensity. The electrical conductivity of the bulk solution was 0.625 S/m. The density was calculated using the formulation in our natural convection model based on electroneutrality, where non-electroactive ions migrate to the diffusion layer to neutralize the charge buildup due to the redox reaction. Cases with gravity not present, and gravity applied in the +x, -x, +y and -y directions in 2D were investigated. For the 3D simulations, gravity was applied in the direction normal to the electrode, toward and away from the electrode surface. To study the effect of pure natural convection, cases were run without applying the magnetic field. For this electrochemical system, the density changes from the initial bulk density (785 kg/m3) is very small with a maximum value of 0.0231 kg/m3, which gives a difference of 0.00294% between the highest and the lowest density. Even under this small difference, the evolution of the flow field is quite remarkable. With increasing time from the start, the effect of natural convection on the flow field becomes greater. The maximum velocity increased by an order of magnitude in ~30s from the start. At larger times, the maximum velocity tends toward an asymptotic value along with the electrode current also leveling off and reaching an asymptotic value. The behavior of mixed convection characterized by competing forces of buoyancy and Lorentz force was also investigated, where two values of the magnetic field were chosen. The natural convection-only cases show that the effect is stronger when the established flow is away from the electrode than when it is toward the electrode. This can be attributed to the electrode surface acting to provide a stable flow field configuration, confirming published results. The velocity is an order of magnitude higher when the flow is away from the electrode surface. Note that the cell we used is an order of magnitude higher than a typical microfluidic cell. Work is in progress to study the effect of geometry on natural convection where buoyancy is the only body force, and mixed convection where both buoyancy and MHD are present.Experimental results have been obtained on the ferri-ferro-KCL system. Quantitative Micro-schlieren (QMS) is an instrument suitable for measuring density gradients. A lens-based design makes packaging more compact. An LED light source is used to reduce cooling requirements. All the optics are research grade, thereby improving resolution and reducing aberrations. The electrochemical cell was mounted on a three-axis stage that is mounted on the optical rail for easy alignment. This schlieren system differs from conventional schlieren systems in its compact size (~6m X 2m vs. 1.5m x 0.5m, in footprint), its use of a more uniform intensity LED light source, variable density filter, bandpass filter, lenses instead of mirrors, a digital frame camera, and modern image processing techniques to extract quantitative information from the images. While conducting the redox electrochemistry experiments, it’d be important to ensure that the data are not corrupted by natural convection induced by temperature gradients that might be introduced by sources such as LED illumination. While it is not possible to completely eliminate this source of error, it can be minimized by keeping the LED intensity as low as possible and having the LED on only when necessary. The acquired sequence of images during a time period up to ~300s from the start show a column of high density fluid that starts from the surface and grows in length with time. At larger times (>100s) the column develops a transverse instability with a wave length of ~30 mm.

Figure 1