Vortex stretching, turbulent film layers, and mass transfer

Sometimes in science, a previous observation that seemed insignificant at the time is later found to corroborate a novel idea. In our previous blog post we discussed the formation of bubbles in a rotor-stator spinning disc reactor. For the data analysis of the underlying model I had to endure many many hours of repetitious and hard labour looking at and inspecting literally hundreds of thousands of pictures of bubbles. Oh… the things we do for science, if only she would love us back! A few typical example of such bubbles can be seen on the right. Now, let us continue onwards from this seemingly silly introduction and delve into the topic of the next post; turbulence and gas-liquid mass transfer in a rotor-stator spinning disc reactor. However, keep in mind this image and the Herculean task it represented for yours truly when processing these images.

It is an empirically well established feature of the rotor-stator spinning disc reactor that it greatly increases mass transfer rates in comparison to conventional reactor technologies. In fact, research by Meeuwse et al. (2010) have shown that the overall gas-liquid mass transfer coefficient per volume of gas can be as high as kGLaGL = 20.5 m3L m–3G s–1, which is around 40 times higher than typical values in bubble columns! One could consider this all to be very splendid and immediately start reaping the fruits of this discovery in chemical industry. Don’t get me wrong, it is very grand indeed, and we should certainly start introducing spinning disc tech in industry, but as a scientist, we unknowingly broke reactor engineering…

There is no theory or engineering model in the field of chemical reactor engineering that can explain this huge increase in mass transfer rates!

Common engineering models to describe mass transfer were all developed in an era where chemical reactors could not efficiently harness the power of torsion, turbulence, and gravity as we can today. Unsurprisingly, these predictions thus fail to describe gas-liquid mass transfer coefficients in a modern spinning disc reactor by several orders of magnitude. Only by Direct Numerical Simulation (DNS) of the turbulent flow field around a bubble in a rotor-stator flow were we able to get information on the mechanism behind this large increase in mass transfer.

A typical example of such a simulation is given below and a high quality video can be found here. In this simulation, our point of reference is fixed to the bubble so we find a moving wall at the bottom of the simulation moving with half the disc speed in one direction, while at the top, the wall is moving with half the velocity in the other direction. The colour-coding corresponds to the component of velocity of the fluid parallel to the motion of the disc.

Closer inspection of this turbulent flow field revealed that the liquid approaching the bubble, close to the upper and lower bounding walls is squeezed into the narrow film layer between the bubble and the walls. As this liquid is squeezed inside this film, the component of vorticity perpendicular to this direction is increased due to vortex stretching. This increases the turbulence intensity in the thin liquid film, which subsequently increases the turbulent dispersion rate of chemical species diffusing from the gas into the liquid. In fact, with the so obtained turbulence dispersion coefficients, we were finally able to explain values for kGLaGL of the correct order of magnitude as experimentally observed.

Now, to justify the seemingly silly introduction of the beginning of this post… When we carefully look at the waves that are visible on the bubble surface next to this film layer, we see that the nodal lines of maxima and minima of this wavy motion are all directed perpendicular to the rotational direction of the disc. This feature is directly explained by the vortex stretching mechanism that is behind the increase in gas-liquid mass transfer as described above. Not only did we explain the physical mechanism behind the increased gas-liquid mass transfer in a rotor-stator spinning disc reactor, we also learned a valuable lesson… the seeds for discovering a new physical mechanism are often staring us right in the face already, all we need to do is recognise them.

 

 

The contents of this blog are based on the following publication, which I co-wrote in an external collaboration with prof. Roberto Verzicco at the University of Rome “Tor Vergata”:
http://www.sciencedirect.com/science/article/pii/S0009250915001268

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