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Simulation of Random Sphere Packings Using an Evolutionary Optimization Method

Le Yan, Gordon A. & Mary Cain Department of Chemical Engineering, Louisiana State University, South Stadium Road, Baton Rouge, LA 70803 and Karsten E. Thompson, Chemical Engineering, LSU, Louisiana State University, Baton Rouge, LA 70803.

A variety of physical systems can be modeled using random sphere packings, ranging from concentrated colloids to packed beds. We develop an evolutionary optimization algorithm to simulate random sphere packings that vary in packing size, sphere-size distribution, spatial correlation, and boundary geometry. A few examples are presented here to demonstrate the efficiency and generality of this algorithm.

In the first example we show that our method is capable of generating very large packings (with over 1 million spheres) in reasonable computation times. In a second example, quantitative correlation functions are imposed as a restriction in the optimization process, which leads to sphere-packings with desired spatial structure (e.g., layering or agglomeration of like-sized particles). In a third example, we demonstrate the simulation of sphere packings inside specifc boundary geometries. These latter simulations are useful in the modeling of a number of applications in chemical engineering. For instance, packed bed reactors can be simulated by random sphere packings in a cylindrical geometry, while a packing in an aperture bounded by surfaces with irregular geometry is a good representation of hydraulically fractured oil reservoirs containing proppant particles.

The novelty of this new algorithm is that these widely varying constraints are all contained in a single objective function in the optimization procedure, which allows for a powerful and highly general algorithm. The algorithm can be extended to packings of non-spherical particles.