Friday, June 25, 2010

Pushing a model too far

As scientists and engineers, we all work with models and theories. All of these have their limitations where their predictions break down and become useless. At that point, two options are available A) try tweaking the model with various extensions [1] or B) throw it away and start from scratch [2].

Consider fluid mechanics. One of the primary assumptions is that the fluid is a continuum - it is the same at all size scales – and that at small size scales, molecules and atoms and the granularity that they provide do not exist. This is a good assumption for the macroscopic world that we encounter on a regular basis.

So now you can see my confusion about a new report describing work on viscosity inside of cells, a scale that is small enough that the continuum assumption should break down. At this scale, we can observed localized attractiveness between molecules, largely dispersion forces, but also from dipole-dipole interactions. At the macroscopic scale, these interactions are averaged out to become “viscosity”. This means that at a molecular scale, viscosity doesn’t exist, not unless we want to take the concept to that level and somehow force it in there.

These researchers nonetheless try to do so:

“At a snail's pace - this is how proteins should move inside living cells where viscosity of environment exceeds the viscosity of water even by million times. However, proteins move not much slower than in water!”

This is a great example of overapplying a model. Don’t keep hacking away at it with an old concept like viscosity – develop something new. Look at the specific interactions at that scale and work with that, not some macroscopic average. Bohr didn’t try and figure out how to extend EM laws to electron spinning around the nucleus, he quantized the energy levels and look at the magic that fell out.

You could appropriate that old adage about there are “two kinds of people in the world…” As you can infer, I prefer new models in new situations, others clearly don’t. I just never saw the value of worrying about the 3rd virial coefficient.

[1] An example is the ideal gas law, which breaks down at high pressures and/or low temperatures. Many extensions have been proposed and are used such as the van der Waals equation, the virial equation, the Redlich-Kwong equation…

[2] An example is Newtonian mechanics. Einstein threw it out and devised relativity when Newtonian mechanics couldn’t explain what was being observed by astronomers, and Bohr started quantum mechanics because Newtonian mechanics couldn’t explain what we being observed at atomic and subatomic scales.


Materialist said...

Well, it is part of the great viscosity-friction-dissipation cycle. Any definition of one tends to include a hand-waving variable given one of the other two names.

孙尉翔 said...

This is not a cycle. Friction does not need the concept of viscosity to be defined. Dissipation does not need the concepts of friction or viscosity to be defined, either, although dissipation may happen in friction.

Viscosity, in contrast, need the concept of friction to be "defined", although it can "calculated" by dividing stress with strain rate.

John said...

"Viscosity, in contrast, need the concept of friction to be "defined", although it can "calculated" by dividing stress with strain rate."

I'd take the rheological viewpoint that the storage and loss moduli are more fundamental properties. From these quantities, you can get the viscosity. You cannot run that calculation in reverse.