A Study on the Coffee Spilling Phenomena in the Low Impulse Regime

When a half-full Bordeaux glass is oscillated sideways at 4 Hz, calm waves of wine gently ripple upon the surface. However, when a cylindrical mug is subject to the same motion, it does not take long for the liquid to splash aggressively against the cup and ultimately spill. This is a manifestation of the same principles that also make us spill coffee when we walk. In this study, we first investigate the physical properties of the fluid-structure interaction of the coffee cup; in particular, the frequency spectrum of each oscillating component is examined methodically. It is revealed that the cup's oscillation is not monochromatic: harmonic modes exist, and their proportions are significant. As a result, although the base frequency of the cup is considerably displaced from the resonance region, maximum spillage is initiated by the second harmonic mode of driving force that the cup exerts on its contents. Thus, we spill coffee. As an application of these experimental findings, a number of methods to reduce liquid spillage are investigated. Most notably, an alternative method to hold the cup is suggested; in essence, by altering the mechanical structure of the cup-holding posture, we can effectively suppress the higher frequency components of the driving force and thus stabilize the liquid oscillation. In an attempt to rationalize all we have investigated above, a mechanical model is proposed. Due to practicalities, rather than to construct a dynamical system using Newton's equation of motion, we choose to utilize the Euler-Lagrangian equations. Extensive simulation studies reveal that our model, crude in its form, successfully embodies the essential facets of reality. This liberates us to make two predictions that were beyond our experimental limits: the change in magnitude of the driving force and the temporal stabilization process.