Can you heat up your coffee by stirring?

A fun question asked by a student in my class:  To what extent do you heat up your coffee by stirring it? 

It was a huge conceptual advance when James Prescott Joule demonstrated that "heat", as inferred by the increase in the temperature of some system, is a form of energy.  In 1876, Joule set up an experiment described here, where a known mass falling a known distance turns a paddle-wheel within a volume of liquid in an insulated container.  The paddle-wheel stirs the liquid, and eventually the liquid's viscosity, the frictional transfer of momentum between adjacent layers of fluid moving at slightly different velocities, damps out the paddle-wheel's rotation and, if you wait long enough, the fluid's motion.  Joule found that this was accompanied by an increase in the fluid's temperature, an increase directly proportional to the distance fallen by the mass.  The viscosity is the means by which the energy of the organized motion of the swirling fluid is transferred to the kinetic energy of the disorganized motion of individual fluid molecules.

Suppose you stir your coffee at a roughly constant stirring speed.  This is adding at a steady rate to the (disorganized) energy content of the coffee.  If we are content with rough estimates, we can get a sense of the power you are dumping into the coffee by an approach close to dimensional analysis.

The way viscosity \(\mu\) is defined, the frictional shear force per unit area is given by the viscosity times the velocity gradient - that is, the frictional force per area in the \(x\)-direction at some piece of the \(x-y\) plane for fluid flowing in the x direction is going to be given by \(\mu (\partial u/\partial z) \), where \(z\) is the normal direction and \(u\) is the \(x\)-component of the fluid velocity).

Very very roughly (because the actual fluid flow geometry and velocity field are messy and complicated), the power dumped in by stirring is going to be something like (volume of cup)*(viscosity)*(typical velocity gradient)^2.  A mug holds about 0.35L = 3.5e-4 m^3 of coffee.  The viscosity of coffee is going to be something like that of warm water.  Looking that up here, the viscosity is going to be something like 3.54e-4 Pa-s.  A really rough velocity gradient is something like the steady maximum stirring velocity (say 20 cm/s) divided by the radius of the mug (say 3 cm).  If you put all that together, you get that the effective input power to your coffee from stirring is at the level of a few microwatts.  Pretty meager, and unlikely to balance the rate at which energy leaves by thermal conduction through the mug walls and evaporation of the hottest water molecules.

Still, when you stir your coffee, you are veeeerrry slightly heating it!  update:  As the comments point out, and as I tried to imply above, you are unlikely to produce a net increase in temperature through stirring.  When you stir you improve the heat transfer between the coffee and the mug walls (basically short-circuiting the convective processes that would tend to circulate the coffee around if you left the coffee alone). 

Annual Nobel speculation thread

As my friend DanM pointed out in the comments of a previous post, it's Nobel season again, next Tuesday for physics.  Dan puts forward his prediction of Pendry and Smith for metamaterials/negative index of refraction.  (You could throw in Yablonovitch for metamaterials.)  I will, once again, make my annual (almost certainly wrong) prediction of Aharonov and Berry for geometric phases.   Another possibility in this dawning age of quantum information is Aspect, Zeilinger, and Clauser for Bell's inequality tests.   Probably not an astrophysics one, since gravitational radiation was the winner last year.

What’s in a name? CMP

At a recent DCMP meeting, my colleague Erica Carlson raised an important point:  Condensed matter physics as a discipline is almost certainly hurt relative to other areas, and in the eye of the public, by having the least interesting, most obscure descriptive name.  Seemingly every other branch of physics has a name that either sounds cool, describes the discipline at a level immediately appreciated by the general public, or both.  Astrophysics is astro-physics, and just sounds badass.  Plasma physics is exciting because, come on, plasma.  Biophysics is clearly the physics relevant to biology.  High energy or particle physics are descriptive and have no shortage of public promotion.  Atomic physics has a certain retro-future vibe.

In contrast, condensed matter, while accurate, really does not conjure any imagery at all for the general public, or sound very interesting.  If the first thing you have to do after saying “condensed matter” is use two or three sentences to explain what that means, then the name has failed in one of its essential missions.

So, what would be better alternatives?  “Quantum matter” sounds cool, but doesn’t really explain much, and leaves out soft CM.  The physics of everything you can touch is interesting, but prosaic.  Suggestions in the comments, please!

Recently on the arxiv

While it's been a busy time, a couple of interesting papers caught my eye:

arxiv:1808.07865 - Yankowitz et al., Tuning superconductivity in twisted bilayer graphene
This lengthy paper, a collaboration between the groups of Andrea Young at UCSB and Cory Dean at Columbia, is (as far as I know) the first independent confirmation of the result from Pablo Jarillo-Herrero's group at MIT about superconductivity in twisted bilayer graphene.  The new paper also shows how tuning the interlayer coupling via in situ pressure (a capability of the Dean lab) affects the phase diagram.  Cool stuff.

arXiv:1809.04637 - Fatemi et al., Electrically Tunable Low Density Superconductivity in a Monolayer Topological Insulator
arxiv:1809.04691 - Sajadi et al., Gate-induced superconductivity in a monolayer topological insulator
While I haven't had a chance to read them in any depth, these two papers report superconductivity in gated monolayer WTe2, a remarkable material already shown to act as a 2D topological insulator (quantum spin Hall insulator). 

Seems like there is plenty of interesting physics that is going to keep turning up in these layered systems as material quality and device fabrication processes continue to improve.

Looking back at the Schön scandal

As I mentioned previously, I've realized in recent weeks that many current students out there may never have heard of Jan Hendrik Schön, and that seems wrong, a missed opportunity for a cautionary tale about responsible conduct of research.  It's also a story that gives a flavor of the time and touches on other issues still current today - faddishness and competitiveness in top-level science, the allure of glossy publications, etc.  It ended up being too long for a blog post, and it seemed inappropriate to drag out over many posts, so here is a link to a pdf.  Any errors are mine and are probably the result of middle-aged memory.  After all, this story did start twenty years ago.  I'm happy to make corrections if appropriate.  update 9/9/18 - corrected typos and added a couple of sentences to clarify things. update, 2020:  This write-up is now deposited at Rice's scholarship and has a doi:  https://doi.org/10.25611/8P39-3K49 .