The influence of ohmic heating

In the electrochemical deposition of metals in quasi-two-dimensional geometries the electrolyte concentration changes at the electrodes. Consequently also the local fluid densities change which results in gravity driven convection rolls. However, there is another potential source of density changes: due to the small cell volume of typically less than 1 cm³, the dissipated electric energy can be the source of a significant heating. If the cell were completely thermally insulated, a solution exposed to an electrical power of 500 mW would start to boil after 500 s. While thermal conduction will confine the overall temperature increase to smaller values, considerable temperature gradients might arise and influence the density driven convection.

We studied the influence of ohmic heating by performing electrodeposition experiments in a cell with a plate separation of about 0.5 mm, the electrodes were zinc wires and the electrolyte 0.1 M ZnSO₄. The applied potential was 20 V which resulted in an average electrical power feed of 470 mW at the beginning of the experiment and 650 mW after 500 s.

Figure 1
Cell used for the infrared measurements. The bottom (white) consists of Teflon, the upper cover is a polyethylene foil stretched over an aluminium frame. The electrodes are parallel zinc wires with a distance of 4 cm. The deposit at the cathode has grown for 410 s.

In order to quantify the possible temperature gradients, a high spatial resolution of the temperature field is necessary. We measured the temperature field at both electrodes by use of the infrared camera Varioscan 302-ST from InfraTec, which contains a Stirling-cooled HgCdTe detector with 360 × 240 pixel. We achieve a spatial resolution of 140 μm and a thermal resolution ± 30 mK. Figure 2 gives an example of the thermography after 280 s, the scale at the right describes the temperature increase with respect to the beginning of the experiment.

Figure 2
Thermography taken 280 s after the start of the experiment. The size of the image is 5.0 × 3.4 cm². The white line corresponds to the position of the anodic zinc wire.

The temperature development inside the cell can be summarized as follows:

1. The temperature in the bulk increases about 7.5 K in 500 s
2. Due to the growing deposit, there is a zone of ion depletion in the vicinity of the cathode. The decreased concentration leads to higher resistivity and therefore higher dissipation and increased temperature compared to the bulk.
3. The increased Zn²⁺ ion concentration inside the convection roll at the anode results in an reduced ohmic heating. Consequently the anode remains colder than the bulk.

Figure 3
Temperature difference between the bulk of the cell and the temperature maximum in front of the growing deposit (empty circles), and the temperature at the anode (filled squares).

Figure 4 helps to estimate the influence of the temperature difference on the overall density difference driving the convection roll at the anode. After 400 s the 0.1 M solution in the bulk of the cell has reached a temperature of about 30^oC. At the anode the concentration did by that time increase to roughly 0.25 M while the temperature did only rise to 27^oC. This 3^oC temperature difference add about 4% to the overall density difference between the anode and the bulk. At the cathode the overall density difference is about 2% increased.

Figure 4
Temperature dependency of the electrolyt densities at the anode ( after 400 s the concentration is roughly 0.25 M) and in the bulk (0.1 M).

As our applied potential is above average for standard electrodeposition experiments, we conclude that ohmic heating will only be a weakly additional driving force to the density driven convection rolls.

• Phys. Rev. E 66 026307
• Phd Thesis

Francesc Sagués Universitat de Barcelona

Ingo Rehberg Universität Bayreuth

Klaus Kassner Otto-von-Guericke-Universität Magdeburg

Josep Claret Universitat de Barcelona