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Gravity driven convection rolls
Motivation
Electrodeposition is often accompanied by buoyancy-driven convection rolls. The driving force for the convection are the concentration changes at the electrodes as shown in the side view of an electrodeposition cell:
|
At the anode |
At the cathode |
- ions go into solution
- density of the electrolyte increases
- heavier electrolyte descends and spreads at the bottom plate
- lighter bulk solution flows in along the top plate
- -> convection roll
|
- ions get deposited
- density of the electrolyte decreases
- lighter electrolyte ascends and spreads at the top plate
- heavier bulk solution flows in along the bottom plate
- -> convection roll
|
In cells with a plate separation bigger than 100 μm these gravity driven convection rolls are the main ion transport mechanism. As they strongly influence the growing morphology, a quantitative understanding is desirable. Aim of this work is a) to test the theory of Chazalviel et al (1996) for the anodic convection roll, and b) a quantitative comparison of the convection roll at the two electrodes.
Experimental Setup
Figure 2
Side view of the dark field microscopy used for the PIV. The direct light misses the lens, only scattered light is visible.
To measure the velocity field inside the cell, we used Particle Image Velocimetry (PIV). Because of the changing electrolyte density, we had to use tracer particles with 0.3 μm diameter, which stay suspended due to Brownian motion. As these particles cannot be resolved with our optical system, we used dark-field microscopy: as shown in figure 2, only light scattered from objects inside the cell falls into the lens. The movie on the left side of Figure 3 gives an example, the small, white points correspond to tracer particles.
Due to the small plate separation the images don't allow to distinguish between tracers moving in different heights. Consequently PIV methods based on the cross correlation of image segments don't work and we had to develop an algorithm tracking individual particles. The name of this software package is Artemis, it is published under the Gnu Public License and can be downloaded here. Figure 3b shows Artemis at work. The white pixels correspond to the particles in the left movie, which move faster then 5 μm/s.
Figure 3a
Dark field images of the convection roll in front of the anode (white area at the bottom). The tracer particles move either towards or away from the anode, depending on their height in the cell. Nonmoving particles have already sedimented to the bottom plate.
Figure 3b
Result of the particle tracking using Artemis. All particles moving faster than 5 μm/s are indicated as white pixels. The blue area corresponds to the anode.
Results
Figure 4
Velocities of the tracer particles in front of the anode. Particles with a positive velocity are moving away from the anode, with a negative velocity towards the anode.
Figure 4 shows the velocities of the tracer particles in a fully developed convection roll like in Figure 3. All particles move either away from or towards the anode. We can't distinguish between particles at different heights relativ to the plates. Therefore we observe for a given distance to the anode all velocities in the range between plus and minus a maximum velocity vmax. This maximum velocity decreases to zero in a certain distance to the anode (in Figure 4 roughly 5.8 mm) which marks the length L of the convection roll. We find that the dependency of vmax on the distance to the anode as well as the development of L with time are well described by the analytical theory of Chazalviel et al.
Figure 5
Comparison of the flow behavior at the two electrodes under identical experimental conditions. Part (a) shows the temporal evolution of the overall length of the convection roll. Part (b) gives the temporal evolution of the maximal velocity inside the rolls.
Figure 5 is devoted to a comparison between the flow behavior at the two electrodes. The developments of L displayed in Figure 5(a) differ significantly from each other. While the anodic convection roll grows with t0.5, the cathodic convection roll is pushed by the constantly advancing deposit, so that L becomes roughly constant. However the comparison of the maximal fluid velocities (measured immediately in front of the anode resp. growing deposit) in Figure 5(b) show similarities with respect to the absolute value and the approximate temporal constance.
Conclusion
The length of the andic convection roll grows with t0.5, its flow field is well described by the analytical model of Chazalviel et al. At the cathode the maximal fluid velocity inside the convection roll is of the same order as at the anode, but being pushed by the growing deposit the length of the convection roll becomes constant.
Publications
Further results including the relation between the flow field and the growth of the finger morphology can be found in the following publications:
In collaboration with
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Last modified: Tue Aug 16 21:52:18 CDT 2005
