# Are coffee's properties different enough from water's to cause increased spillage while walking?

I recently found this article, which describes how...

It just so happens that the human stride has almost exactly the right frequency to drive the natural oscillations of coffee, when the fluid is in a typically sized coffee mug.

Judging by appearance, coffee and water's fluid dynamics seem rather similar. Unfortunately,they do not site a source, but they mention that the study was done by "a pair of fluid physicists at the University of California at Santa Barbara (UCSB)".

My question is how different are the properties of water and coffee? Is this difference significant enough to cause a dramatic change in how either fluid behaves in a mug (while walking)?

EDIT: Here is the actual published article.

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Without a whit of evidence I would suspect surface tension or viscosity before density. // and "Go, Gauchos! //// spent a little time at U Can Study Buzzed –  dmckee Aug 15 '12 at 15:00
Your quote isn't really about coffee in particular - water (or orange juice, or tea...) in a coffee mug would slosh in just the same way as coffee does. –  Benjamin Hodgson Aug 15 '12 at 15:00
@LanceLafontaine Not necessarily. That has the smell of a "fun" paper, and coffee may have been used because it let them write an amusing story for publication in a serious venue. That kind of things gets people's attention. Think Alpher, Bethe, Gamow. –  dmckee Aug 15 '12 at 15:28
Here's a link to a link to the the paper: physics.aps.org/synopsis-for/10.1103/PhysRevE.85.046117 Behind a paywall I'm afraid. ::sets browser to proxy through the local university, reloads, downloads, unsets proxy:: –  dmckee Aug 15 '12 at 15:31
the proper link is engineering.ucsb.edu/~rkrechet-lab/files/publications/… –  Yrogirg Aug 15 '12 at 16:59
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## 1 Answer

The article's preprint

Mayer H. C., Krechetnikov R. "Walking with coffee: why does it spill?," Phys. Rev. E 85, 046117 (2012).

is available from the UCSB site.

From a glance of the article the phenomenon is not specific only to coffee. The authors make use of the next formula:

The natural frequencies of oscillations of a frictionless, vorticity-free, and incompressible liquid in an upright cylindrical container (cup) with a free liquid surface are well known from liquid sloshing engineering:

$$\omega_{mn}^2 = \frac{g \epsilon_{mn}}{R} \tanh\left(\epsilon_{mn} \frac{H}{R} \right) \left[1 +\frac{\sigma}{\rho g} \left( \frac{\epsilon_{mn}}{R} \right)^2 \right]$$

$H$ is the liquid height, $R$ is the cup radius, $\rho$ is the liquid density, $\sigma$ is its surface tension, $g$ is thethe gravity acceleration. $\epsilon_{mn}$ are coefficients connected to Bessel functions.

The only parameter that can be significantly different between water and coffee is surface tension $\sigma$, but then the authors rule it out:

For a typical common size of a coffee cup, $R$ $3.5$ cm and $H$ $10$ cm, which is studied here, the surface tension $\sigma$ effect is negligible.

That is their calculations are applicable both to water and coffee. Their work seems to be all about biomechanics, the way human moves with unwanted frequencies.

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Exactly the type of answer I was looking for. Thanks, _1. –  LanceLafontaine Aug 15 '12 at 17:52
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