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The distance of closest approach of hard particles is a key parameter oftheir interaction and plays an important role in the resulting phase behavior.For non-spherical particles, the distance of closest approach depends onorientation, and its calculation is surprisingly difficult. Although overlapcriteria have been developed for use in computer simulations [1, 2], noanalytic solutions have been obtained for the distance of closest approach ofellipsoids in 3-D, or, until now, for ellipses in 2-D. We have derived ananalytic expression for the distance of closest approach of the centers of twoarbitrary hard ellipses as function of their orientation relative to the linejoining their centers. We describe our method for solving this problem,illustrate our result, and discuss its usefulness in modeling and simulatingsystems of anisometric particles such as liquid crystals.

Distance of closest approach of two arbitrary hard ellipses in 2D