The low-Reynolds-number collision and rebound of two rigid spheres moving in an ideal isothermal gas is studied in the lubrication limit. The spheres are non-Brownian in nature with radii much larger than the mean-free path of the molecules. The nature of the flow in the gap between the particles depends on the relative magnitudes of the minimum gap thickness, h ′ o , the mean-free path of the bulk gas molecules, λ o , and the gap thickness at which compressibility effects become important, h c . Both the compressible nature of the gas and the non-continuum nature of the flow in the gap are included and their effects are studied separately and in combination. The relative importance of these two effects is characterized by a dimensionless number, α o ≡ ( h c /λ o ). Incorporation of these effects in the governing equations leads to a partial differential equation for the pressure in the gap as a function of time and radial position. The dynamics of the collision depend on α o , the particle Stokes number, St o , and the initial particle separation, h ′ o . While a continuum incompressible lubrication force applied at all separations would prevent particle contact, the inclusion of either non-continuum or compressible effects allows the particles to contact. The critical Stokes number for particles to make contact, St 1 , is determined and is found to have the form St 1 = 2 [ln( h ′ o / l ) + C (α o )], where C (α o ) is an O (1) quantity and l is a characteristic length scale defined by l ≡ h c (1+α o )/ α o . The total energy dissipated during the approach and rebound of two particles when St o [Gt ] St 1 is also determined in the event of perfectly elastic or inelastic solid-body collisions.
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Gopinath et al. (1997) studied this question.