Tag Archives: diffusion

Molecular diffusion at different temperatures (involving tea bags and some convection)

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I thought I had posted the picture below some time in winter already, but when I recently searched for it, I couldn’t find it. So either I didn’t post it, or I didn’t post any sensible search terms with it, in any case: It’s useless. So here we go again.

Below you see two tea bags that were placed into cold (left) and hot (right) water at the same time. On the left, the tea is sinking down in streaks, while at the same time on the right everything  is completely mixed through and through, showing how molecular diffusion depends on the temperature. Which is why we usually make hot tea.

Funnily enough, as I was about to write this blog post and had the picture already open on my laptop, I felt thirsty and decided to prepare a cold brew tea, which you see in the picture below. Here again you see the tea spreading from the tea bag, but it comes out in those plumes and only slowly diffuses throughout the whole carafe.

This would of course be easier to see had I chosen a white background, but since I am still so touched that my friends showed up at the train station with a flower and a flag on Friday, and also since this is literally the spot I put the tea down after I had prepared it, you get to enjoy a view of my flower and flag!

Also that fake flower on the left makes for really interesting reflections on the carafe. Especially the top two that are joint in the middle!

Layered latte: A great real-life example of double-diffusive mixing!

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Sometimes sitting in a café for a work meeting with #lieblingskollegin Julia can lead to unexpected discoveries of oceanographic processes — in my latte! It’s those little things that inspire blog posts…

“Kitchen oceanography” brings the ocean to your house or class room!

Oceanography is often taught in a highly theoretical way without much reference to students’ real life experience. Of course a sound theoretical basis is needed to understand the complexity of the climate system, but sometimes a little “kitchen oceanography” — doing experiments on oceanographic topics with household items — goes a long way to raise interest in the kind of processes that are not easily observed in the real world. I’ve previously written a lot about simple experiments you can perform just using plastic cups, water, ice cubes, and a little salt. But sometimes it’s even easier: Sometimes your oceanography is being served to you in a cafe!

Oceanic processes can be observed in your coffee!

Have you ever looked at your latte and been fascinated by what is going on in there? Many times you don’t just see a homogenous color, but sometimes you see convection cells and sometimes even layers, like in the picture below.

Layers in a latte.

Layers in a latte.

But do you have any ideas why sometimes your latte looks like this and other times it doesn’t?

When you prepare latte in the right way, many layers form

Layers forming in latte (and in the ocean or in engineering applications) are an active research field! In the article “laboratory layered latte” by Xue et al. (2017), the authors describe that the “injection velocity” of espresso into the warm milk has to be above a critical value in order for these pretty structures to form in a latte. They even provide a movie where you can watch the layers develop over a period of several minutes.

The homogeneous layers with sharp boundaries are caused by double-diffusive mixing

Double-diffusive mixing, which is causing the formation of these layers, is the coolest process in oceanography. In a nutshell, double diffusive mixing is caused by two properties influencing density having different rates of molecular diffusion. These different rates can change density in unexpected ways and an initially stable stratification (high density at the bottom, low density on top) can, over time, become statically unstable. And static instability leads to adjustment processes, where water parcels move in order to reach the position in the fluid where they are statically stable — the fluid mixes.

Layers in half a glass of latte.

Layers in half a glass of latte.

But there are more fascinating things going on with the latte. Would you expect this stratification to remain as clearly visible as it is in the picture above even though the glass is now half empty? I did not! And then check out what happens when you move the glass: Internal waves can travel on the boundaries between layers!

You can use this in class to teach about mixing!

Mixing in the ocean is mostly observed by properties changing over time or in space, and even though (dye) tracer release experiments exist, they are typically happening on scales that provide information on the large-scale effects of mixing and not so much on the mixing itself. And they are difficult to bring inside the classroom! But this is where kitchen oceanography and experiments on double-diffusive mixing come in. If you need inspiration on how to do that, I’ve recently published an article on this (unfortunately only in German), but there are plenty of resources on this blog, too. Or shoot me an email and we’ll talk!

P.S.: Even though the coffee company is displayed prominently in the pictures above, they did not pay for my coffee (or anything else). But if they’d be interested and make me a good offer, I’d definitely write up some fun stuff on learning oceanography with coffee for them ;-)

“Laboratory layered latte” – combining latte and double diffusion. Easily my favourite paper ever!

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My friends know me well. Especially A&I, which was proven again when they sent me the link to an article about two things that I am mildly obsessed with: Latte and double-diffusive mixing.

My obsession with latte is a fairly recent thing, but I have been known to blog about interesting convection pattern in it (for example here). The obsession with double-diffusive mixing, however, is well documented for more than the last 12 years (for example when I am writing experimental instructions, poems or scientific articles about it).

The double-diffusive process that I have been most concerned with is salt fingering, because it is oh-so-pretty, and also fool-proof to create for teaching purposes (when you know how to do it).

Diffusive layering I seem have to be a little frustrated with, at least in teaching (but reading back this post now, it turns out that that was entirely my own fault and not my students’. Oh well, you live and learn! Isn’t this exactly the kind of stuff that makes for great teaching portfolios? ;-)).

And it also turns out that I did the experiments themselves all wrong. According to the article “laboratory layered latte” by Xue et al. (2017). I should not have been trying to carefully stratify a tank in order to see diffusive layering. Instead, I should just have quickly poured the lower density fluid into the higher density one, and layers would have formed by themselves!

So there is one thing that you won’t see any time soon:

Yep. Me drinking latte from any kind of vessel that doesn’t let me look at the stratification! I don’t know how I could ever have fallen into the trap of missing out on observing fluid dynamics while having my early morning coffee in the office. Now I urgently need a nice glass mug!

And you should go check out the article, it’s a really nice read. My new ambition in life: Write a fluid dynamics research article that applies the FD to some really cool, yet mundane, every day thing. Are you in, Elin? :-)

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Xue, Nan and Khodaparast, Sepideh and Zhu, Lailai and Nunes, Janine K. and Kim, Hyoungsoo and Stone, Howard A., Laboratory layered latte. Nature Communications 8(1), 2017

Salt fingering

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My absolute favorite experiment ever: salt fingering.

I know I’ve said it before about another experiment, even today, but this is my absolute favorite experiment and I still get endlessly fascinated. I’ve written about salt fingering before, and given tips on run the experiment, but today we tried a different setup.

We used the same tank as in the “influence of salinity and temperature on density“, put warm, dyed water on the one side of the dam and cold fresh water on the other side.

Contrary to Rolf’s advice, we didn’t aim for specific temperatures and salinities to hit the density ratio in a specific way, but just went for really hot and really cold.

We pulled the parting out, and after a couple of minutes, salt fingers started to develop.

Unfortunately, they are really difficult to take pictures of.

But a lot of students watched and will hopefully remember what they saw.

And even if not – I thought it was awesome and Rolf said they were the best salt fingers he had seen yet – even though we just winged it ;-)

Molecular diffusion of heat and salt

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Why heat and salt diffuse at different rates.

Why do heat and salt diffuse at different rates? This seems to always be puzzling students when talking about double diffusion.

Well, why should they diffuse at the same rate? The processes of molecular diffusion of heat and salt are very different.

In the case of heat, a transfer of heat only means that particles hit and transfer energy. The warmer the substance, the faster the particles’ movements. So faster particles hitting slower particles will transfer momentum, and by slowing down one of the particles and speeding up the other one, this is de facto a heat exchange.

A transfer of salt on the other hand means that ions have to be transported from a region of higher concentration to a region of lower concentration. In order for this to happen, they have to travel over physical distances larger than just the wiggling connected to molecular movement, and they have to exchange place with water molecules and clusters.

Clearly, this second process is a lot more time-consuming than the first one?

Salt fingering – DIY

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How to easily set up the stratification for the salt fingering process.

Setting up stratifications in tanks is a pain. Of course there are sophisticated methods, but when you want to just quickly set something up in class (or in your own kitchen) you don’t necessarily want to go through the whole hassle of a proper lab setup.

For double diffusive mixing, there are several methods out there that people routinely use.

For example the hose-and-funnel technique, where the less dense fluid is filled in the tank first and then the denser fluid is slid underneath with the help of a hose and a funnel. And a diffuser at the end of the hose. And careful pouring. And usually a lot more mixing than desired.

Or the plastic-wrap-to-prevent-mixing technique, where the dense fluid is put into the tank, covered by plastic wrap, and then the lighter fluid is poured on top. Then the plastic wrap is removed and by doing so the stratification is being destroyed. (No video because I was frustrated and deleted it right away)

Or some other techniques that I tried and didn’t find too impressive. (No videos either for the same reason as above)

But then accidentally I came across this one:

Granted, this is not a realistic model of an oceanic stratification. But as you can see towards the end of that movie, that turns out to be a blessing in disguise if you want to talk about the process in detail. As you see in the movie, the salt fingers inside the bottle are much smaller than the salt fingers outside the bottle. Because, clearly, inside the bottle the warm water is cooled both at the interface with the cold water inside the bottle, and by heat conduction through the walls of the bottle, since the water is surrounded by cold water. The warm water that flowed out of the bottle and up towards the water’s surface is only cooled at the interface with the water below (the air above is warmer than the cold water). So this gives you the perfect opportunity to discuss the scaling of salt fingers depending on the stratification without having to go through the pains of actually preparing stratifications with different gradients in temperature or salinity.

Diffusive layering. Or: This is not a trick question!

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The “other” double-diffusive mixing process.

After having talked extensively about double diffusive mixing in my courses, I tend to assume that students not only remember that there is such thing as double-diffusive mixing, but that they also remember our discussions on how the process works, and that they would be able to transfer this to processes other than salt fingering.

So in two courses (at different universities) I asked students in the exam to describe what would happen in a stably stratified body of water, where cold and fresh water overlies warm and salty water. And in both courses I have been surprised (read: shocked) by the responses I got.

The by far most common response goes along these lines: “Cold water is denser than warm water, so it will sink to the bottom and the warm water will rise”.

What I find frustrating about this (besides the fact that they didn’t notice that I clearly stated in the question that the stratification was stably stratified) is that whenever I talked about density, I mention how density depends on both temperature and salinity.

The next most common response is then this: “Heat diffuses a factor 100 faster than salt. Hence, salt fingers will form at the interface”. This answer then continues on describing salt fingering and never even mentions that the stratification I described in the question was actually the opposite one to the one they are assuming. So here, students clearly jumped to the conclusion that if I bothered describing a stratification, it clearly had to be the one for my favorite process (even though during those discussions I made sure to mention diffusive layering, too, but without talking it through in as much detail as salt fingering).

But then there are always students (usually the ones who don’t have a lot of confidence in their oceanography skills) who take the questions I ask at face value. Those are the students who go on to write something like this (numbering referring to the sketch below):

1) The initial stratification is stable in density, with cold and fresh water over warm and salty water. This means that the salinity stratification outweighs the temperature stratification in terms of density.

2) Since temperature diffuses a factor 100 faster than salinity, a thin layer with an intermediate temperature will form around the interface in salinity, that will persist for a while.

3) Focussing above the interface now, we have a stratification where cold and fresh water overlies lukewarm and fresh water. This stratification is hence unstable in temperature and convective overturning will occur. Below the interface, a similarly unstable layer has formed: lukewarm and salty water over warm and salty water. Again, convective overturning will occur.

The thickness of those layers depends on the initial temperature stratification and on how quickly temperature exchange happens during the overturning. In the end, two new temperature interfaces will have formed.

IMG_5958_DL

Sketch of the diffusive layering process. The red shading indicates warmer temperatures, the black dots indicate higher salinities.

And yes – that is exactly the response I wanted to hear!

So why do only so few students answer this question correctly? Don’t they understand that when I talk about salt fingering it is only an example of a double-diffusive process and not the only double-diffusive process there is? That was my initial thought after I saw the exams in the first class. So for the second class, I made sure to mention diffusive layering even more, and to explicitly say that I was talking through only one of the processes and that it might be helpful if they went through the other one on their own. Yet in the exams, the results did not change. And I have no idea. Do you? Then please let me know!

Salt fingering

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How to show my favorite oceanographic process in class, and why.

As I mentioned in this post, I have used double-diffusive mixing extensively in my teaching. For several reasons: Firstly, I think that the process is just really cool (watch the movie in this post and tell me that it isn’t!!!) and that the experiments are neat and that everybody will surely be as excited about them as I am. Secondly, because it shows that understanding of small processes can be really important in order to understand the whole eco- and even climate system. And thirdly, because it helps to demonstrate a way of thinking about oceanography.

When I introduce salt fingering, I talk students through the process in very small steps. It goes something like this (Numbering is referring to the sketch below):

1) Initially, you have a stratification where warm and salty overlies cold and fresh water. This stratification is stable in density (meaning the influence of the temperature stratification on density outweighs that of the salinity stratification).

2) Since molecular diffusion of temperature is about a factor 100 faster than that of salinity (we will talk about why that is in a later blog post), the interface in salinity is initially basically unchanged, whereas a temperature exchange is happening across that interface, and a layer of medium temperature is forming.

3) At the salinity interface, we now have a stratification that is no longer stable in density: while the water now has the same temperature in a thin layer above and below the interface, it is still more salty on top and less salty below the interface. This means that the saltier water in this thin layer is denser than the less salty water below. This leads to finger-shaped instabilities at the interface: The salty water will sink and the fresh water will rise.

The individual salt fingers now have a much larger surface than the original interface, hence molecular diffusion of salt will happen much more efficiently and eventually the salinity inside and outside of the salt fingers will be the same, hence the growth of the fingers will stop.

At the depth where the salt fingers stopped, a new interface has formed. This new interface can also develop salt fingering, leading to a staircase-like structure in temperature and salinity.

After salt fingering has been introduced, there are usually several other occasions where it, or its effects, can be pointed out, like for example when showing this experiment (see picture below), when talking about the hydrographic properties in the area of the Mediterranean outflow or the Arctic, or when talking about nutrients in subtropical gyres.

IMG_4233_sehr_klein

This is a zoom in on one of the bottles shown in this experiment: In the warm bottle, the red food dye acts as salt to form salt fingers!

While talking about salt fingering, since I focus so much on the process, I have always been under the illusion that students actually understand the reasoning behind it and that they can reproduce and transfer it. Reproduce they can – transfer not so much. Stay tuned for the next post discussing reasons and possible ways around it.

Double-diffusive mixing

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On the coolest process in oceanography.

My favorite oceanographic process, as all of my students and many of my acquaintances know, is double-diffusive mixing. Look at how awesome it is:

Double-diffusive mixing happens because heat and salt’s molecular diffusion are very different: Heat diffuses about a factor 100 faster than salt. This can lead to curious phenomena: Bodies of water with a stable stratification in density will start to mix much more efficiently than one would have thought.

In the specific case of a stable density stratification with warm, salty water over cold, fresh water, finger-like structures form. Those structures are called “salt fingers”, the process is “salt fingering”.

IMG_4233_sehr_klein

Salt fingering happening with the red food dye acting as “salt”.

Even though salt fingers are tiny compared to the dimensions of the ocean, they still have a measurable effect on the oceanic stratification in the form of large-scale layers and stair cases, and not only the stratification in temperature and salinity, but also on nutrient availability in the subtropical gyres, for example, or on CO2 drawdown.

Over the next couple of posts, I will focus on double diffusive mixing, but less on the science and more on how it can be used in teaching. (If you want to know more about the science, there are tons of interesting papers around, for example my very first paper)