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Title: Spinning rough disc moving in a rarefied medium
Author: Plakhov, A.
Tchemisova, T.
Gouveia, P.
Keywords: Billiards
Free molecular flow
Inverse Magnus effect
Optimal mass transport
Rough surface
Body surface
Dense gas
Free molecular flow
Gas particles
Magnus effect
Multiple collisions
Mutual interaction
Rarefied gas
Rough surfaces
Spinning bodies
Transversal force
Zero temperatures
Mass transfer
Numerical methods
Surface measurement
Two dimensional
Issue Date: 2010
Abstract: We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from nonelastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on 'shape of the roughness;, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge-Kantorovich optimal mass transport and by numerical methods. This journal is © 2010 The Royal Society.
Peer review: yes
DOI: 10.1098/rspa.2009.0518
ISSN: 1364-5021
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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