Work I’ve recently done with my colleagues has just been published in the journal Physical Review Fluids. The paper, Continuity waves in resolved-particle simulations of fluidized beds, analyzes a series of computational simulations performed by software I developed that look a lot like this, only with more particles:
Though not at all obvious from this video, these particles are actually bumping into each other and sending waves of high particle density up the column even though the mean particle velocity is zero. This behavior had not previously been investigated in three-dimensional columns of fluid. We found many interesting details about the way these particles move around, including that a theory developed for one-dimensional motion still does a good job of predicting the speed of the high density waves in a three-dimensional setting.
The results of a fully resolved simulation of up to 2000 spheres suspended in a vertical liquid stream are analyzed by a method based on a truncated Fourier series expansion. It is shown that, in this way, it is possible to identify continuity (or kinematic) waves and to determine their velocity, which is found to closely agree with the theory of one-dimensional continuity waves based on the Richardson-Zaki drag correlation.