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What is the shape
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What is the shape of a falling Raindrop?
arron wrote: > What is the shape of a falling Raindrop? Arron, The quick answer is 'roughly spherical'. Here is a long, drawn-out answer. The static shape of a fluid drop, jet, bridge, or film is determined by a dimensionless number called the Bond number. (Note the contact angle is important, too) The Bond number is the ratio of gravitational force to surface tension force. Thus, a large drop, jet, or bridge will look the same as a small one provided the Bond numbers for the two are the same. Two possible static drop configurations are the 'pendant' and 'sessile' drop shapes (consider a drop in zero-gravity a limit of a pendant drop as either the radius of the drop goes to infinity or the radius of the support goes to zero), and these are easily observed: raindrops on a freshly-waxed car is a typical sessile drop shape. Now for dynamics: the basic problem is that the raindrop has a free surface. That is, the boundary condition for the flowfield within the drop depends on the drop shape, but the drop shape is not a given. In dynamic situations, the important quantity (in addition to the Bond number) is the relative viscosities of the two fluids. Usually, it is assumed that the drop/bridge/jet is axisymmetric, unless there is a good reason to do otherwise. The thing the remember is that large drops and small drops look the same, given identical Bond numbers and relative viscosities. It is very difficult to model the process of a drop pinching off from a jet because the topological qualities of the flow change: we start with one continuous fluid body, and then undergo a non-reversable transformation to two disconnected fluid bodies, picking up a singularity or two along the way. However, we can do a few things by considering the drop to have a static shape, and then subject it to a uniform axially-directed flow. Then we have an iterated process: calculate the induced surface flow -> calculate the bulk flow -> calculate the shape change -> calculate the surface flow -> etc... It's done by balancing forces, basic Newtonian physics, but it's rather tedious. I know of one calculation done for the purposes of modeling ink-jet printers: Fromm, J. E. (1984), Numerical calculation of the fluid dynamics of drop-on demand jets, IBM Journal Research Dev. vol 28, p 322. And a paper about two drops interacting in a dispersion, either side-by-side or motion in a row: Lanbein, D., (1993), Theoretical Aspects of Particle Interactions in Dispersions, Advances in Colloid and Interface Science, vol 46, p 91. Like I first said, the drop shape is roughly spherical. It is not like most artist renderings of some sort of exaggerated pendant shape. Andy Resnick