Abrasion of flat rotating shapes

Details Abrasion of flat rotating shapes Abrasion of flat rotating shapes

2010-09-17

arxiv.org/abs/1009.3492v2

Phys. Rev. E 83, 031303 (2011)

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1103/PhysRevE.83.031303

We report on the erosion of flat linoleum "pebbles" under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels in a digital camera. This reduces digitization noise, and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle.

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