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Reverse Diffusion Demonstration

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S_Ch_S:
Can anyone recommend how to show an inverse diffusion process? Is it possible? Any hint or link much appreciated. Thank you.

Corribus:
What do you mean by reverse diffusion? Diffusion is process in which species tend to move along a concentration gradient from high concentration to low concentration. It is driven primarily by entropy. You cannot "reverse" this process short of reversing the second law of thermodynamics. That would be a neat trick.

But, there are examples in which molecules do not diffuse because entropy is not the only consideration at play - there is also enthalpy. When the energy cost of molecules moving to a new location exceeds the entropy gain, molecules will not diffuse to areas of lower concentration. Indeed, if you start in a mixed state, they will appear to separate, which may look like "reverse" diffusion.

Take oil and vinegar. The water will not diffuse into the vinegar. In fact, if you shake the mixture up, it will, over time, spontaneously separate. Water will go from a state of low concentration to locally high concentration. This I guess might be taken as "reverse diffusion", although I don't know that I've ever heard it called that. The reason the mixture separates is because there's an energy cost to water mixing with fat. In this case, the energy cost of having fat molecules next to water molecules exceeds the entropy gain of having water molecules (and fat molecules) spread out. As you might surmise, you can change the energy balance equation by adding a small amount of new molecules that reduce the energy cost of mixing. Add a little egg yolk that contains lecithin to your oil and vinegar mixture, and the energy cost goes down considerably because the lecithin molecules make it more energetically favorable for fat molecules to be near water molecules, and now the entropy factor becomes more competitive. The mixture will persist for much longer. This is the magic of a surfactant.

So, you want an example of "reverse diffusion"? Make a vinaigrette!

S_Ch_S:
Hi! Many thanks for the great explanation and the entertaining response:) Would it be possible to create a model of "reverse diffusion" by applying current? For example to pull one liquid/element apart from another by applying current as in electrolysis and when releasing going back to a diffusion state? Would something like this be possible (and visible)? Any hint, link, suggestion highly appreciated. Many thanks.

Corribus:
Sure, in principle. Suppose the following thought experiment: you take a sodium chloride solution and sandwich it between two metal plates connected by a wire. Apply a voltage across the wire using a battery or something. You basically now have a capacitor. On one plate you build up a negative charge and on the other you build up a positive charge, creating an electrical field across the solution. Without the electrical bias, the charge distribution in the solution is uniform. With the electrical bias, the positively charged sodium atoms should move toward the negatively charged plate and the negatively charged chloride atoms should move toward the positively charged plate. So you've basically increased the concentration gradient for both sodium and chloride ions - sort of "reverse diffusion" if you want to call it that. This was enabled by the fact that you've applied energy to the system, when compensates for the decrease in entropy that accompanies the creation of a concentration gradient. Remove the electrical bias, and the electric field disappears, and the ions will diffuse back to the normal equilibrium position (zero concentration gradient). This is both because of the tendency to maximize the system's entropy but also to minimize charge interaction energies. (So, even in this direction it's not a pure Fickian diffusion.)

There are some practical reasons this experiment wouldn't work that well due to the nature of capacitors, but hopefully you get the principle I am trying to illustrate - to "reverse" diffusion you need to apply energy to the system.

Incidentally, biology figured this out a long time ago. Every cell in your body uses chemical energy from cellular respiration to propel ions across a membrane against a concentration gradient. These ions then flow back across the membrane through ion channels to create ATP, which can then be used to drive reactions elsewhere in the cell. Signal transduction in neurons is also facilitated by the creation of ion gradients across cell membranes using similar "reverse diffusion" processes driven by the consumption of cellular energy provided by ATP.

S_Ch_S:
Hi! Thanks for another amazing answer! I tried out the setup that you described: water, sodium chloride, 12V. See Attachment. So when I apply voltage I have a visible movement of particles. But phenomenologically speaking, there is a paradox here if I am not wrong: When I apply the voltage the water gets diffused because of the particle movement (but this is the moment when I have the "inverse diffusion", right?). When I turn the voltage off, the heavier sodium chloride resides at the bottom of my water tank so my water (tank) gets clear and does not look diffused anymore. It seems turning on and off the voltage will make the effect more intense and visible. Would applying more voltage (from 12V to 24V) create a more intense effect? And could theoretically speaking this system run "perpetually"? Thank you for your amazing explanations.

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