Many researches are conducted on the effect of particles on lubricated friction and wear of contact surfaces, which shows that particles between two contact surfaces increase lubricated friction and do a great effect to the wear of two sliding surfaces. Similar phenomena also occur when a hard containment particle is being entrained into the lubricated contact. This paper presents a simple two dimensional model which describes the entrainment of particles in a gap. Considering elasticity of the sliding surfaces, the model treats conditions under which a spherical particle of size d can be entrained into a gap between a sliding surface and a fixed plane surface. These conditions are determined by size of the particles, d, and friction coefficients between the particle and the sliding surface, and the particle and the plane, denoted by μs and μp respectively. For the particles to be entrained into the contact, this model predicts the maximum of particles size and the relationship of μs and μp.

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