This ground-breaking work pointed out that "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."
After some empirical observation, the following conclusions were made:
"We spill coffee either by accelerating too much for a given coffee level (fluid statics) or through more complicated dynamical phenomena due to the particular range of sizes of common coffee cups, which is dictated by the convenience of carrying them and the normal consumption of coffee by humans. Namely, first the maximum acceleration occurring early on in the walking sets an initial sloshing amplitude. This interface deflection is then amplified by the back-and-forth and pitching excitations. Vertical excitation does not lead to resonance as it is a subharmonic excitation (Faraday phenomenon). The noise component of motion contains higher-frequency harmonics, which make the antisymmetric mode unstable, thus generating a swirl [although the swirl does not contribute much to coffee spillage]. Time to spill generally depends on whether walking is in a focused [i.e., trying not to spill] or unfocused regime and increases with decreasing maximum acceleration (walking speed)."
Sadly, the discovery of the Higgs boson may prevent this work from getting the attention it deserves.
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