When and why the coffee spills

http://t.co/fBhTs48KG4 the #physics of spilling and walking with #coffee
How do we spill coffee?
(a) Either by accelerating too much for a given coffee level (fluid statics)
(b) Or, through more complicated dynamical phenomena:
  • Initial acceleration sets an initial sloshing amplitude, which is analogous to the main antisymmetric mode of sloshing.
  • This initial perturbation is amplified by the back-and-forth and pitching excitations since their frequency is close to the natural one because of the choice of normal mug dimensions.
  • Vertical motion also does not lead to resonance as it is a subharmonic excitation (Faraday phenomena).
  • Noise has higher frequency, which makes the antisymmetric mode unstable thus generating a swirl.
  • Time to spill depends on "focused"/"unfocused" regime and increases with decreasing maximum acceleration (walking speed).
How can we prevent spilling?
Lessons learned from sloshing dynamics may suggest strategies to control spilling, e.g. via using
  • a flexible container to act as a sloshing absorber in suppressing liquid oscillations.
  • a series of concentric rings (baffles) arranged around the inner wall of a container.

Text via Walking with coffee: when and why coffee spills (pdf)
More information on physics buzz blog
Paper: Mayer H.C. & Krechetnikov R. (2012). Walking with coffee: Why does it spill?, Physical Review E, 85 (4) DOI: http://dx.doi.org/10.1103/physreve.85.046117 (pdf)


  1. This explains a lot, if only I understood the math. My own observation is that the full coffee cup (or margarita glass) tends to slop more if I look at the cup. If I just walk, albeit carefully, without looking at the cup, I'm far less likely to spill any coffee. Where does this observation fit into the equations?

    1. Your observation seems correct (my father is a barman). I suppose that it could influence the walking frequency, that in some way could affect the attention you pay to the outside world during the walk.


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