The 'Cheerios Effect'
Entry by Andrew Capulli, AP225 Fall 2011
Vella, D; Mahadevan, L. "The Cheerios Effect", American Journal of Physics, 73, 817-825. 2005.
As the physics and engineering sciences (all sciences really) have gone increasingly 'nano' in the hopes of addressing fundamental questions in the respective fields, there has been debate over what phenomena are most important (ie what should should we be looking into as scientists?) In this paper "The Cheerios Effect," which appears friendly enough with such a title, the authors address some fundamental questions concerning capillarity and buoyancy using some simple experiments to demonstrate their claims. Why do cheerios or bubbles seem to 'attract' and further, are they really 'attracted' to the side of the bowl or glass? Vella and Mahadevan put the science behind these (and more) phenomena demonstrating the importance of buoyancy of small particles in contrast to the traditional mindset of capillarity dominance.
Capillarity vs Buoyancy: Attraction and Repulsion
The authors begin with a discussion of buoyancy and capillarity as it pertains to bubbles and, living up to the title, cheerios. To generalize my discussion I'll just refer to the bubbles and cheerios as particles. The authors argue that the typical mentality of purely analyzing particle behavior at the liquid-particle-gas interface in terms of capillarity does not suffice (this is simply too 1 dimensional, it neglects the the up/down forces due to buoyancy). So what effects does buoyancy have and how can this explain the 'attraction' of floating particles to each other and to the side of the container? Particles light enough (small and less dense than the liquid they displace) have a positive buoyancy. This positive buoyancy 'wants' to push the particle up and out of the liquid but the particle is kept at the interface by surface tension and capillarity which come to a 'compromise' with the particle somewhat submerged and somewhat protruding from the liquid. This is a very boiled down summary of what is happening to the particle; Vella and Mahadevan more eloquently establish this argument in the first few pages of the article and demonstrate their point via the description of simple-cereal-experiments. Below I've attempted to draw these points out to help with my description. So how does buoyancy explain particle aggregation and 'attraction' to container walls? The positive buoyancy seen in the drawing [A] results in, as previously described, an upward net force on the particle out of the liquid. However, since the particle cannot simply float away into the air (because of the capillarity and surface tension of the liquid) it does, as the authors describe, "the next best thing." the "next best thing" is to rise up the meniscus of the liquid on the container wall [C] or the meniscus (contact angle) on another particle [B] (see my power point sketches below).