The Positional and Angular Distribution of Molecules Flowing through Cylindrical Tube in Free Molecular Flow

To investigate the distribution of gas molecules passing through cylindrical tube in free molecular flow, the molecules are divided into “directly passing” ones which pass through from inlet to outlet directly and “reflective” ones which are reflected from inner wall to outlet and inlet, and mathematical models for the two kinds are established. The relative molecular incident rates (equal to the reflectivity) along tube wall are obtained by means of discretization and series accumulation, and they are illustrated as a series of straight lines. The molecular positional distribution is described by the local relative molecular areal density at different position of orifices and is researched in detail with analytical derivation, numerical integration and graphics. The “positional beaming effect” at outlet is demonstrated. The molecular directional distribution graphs at different positions are drawn as the curved surfaces within a unit sphere which corresponds to the cosine distribution style. The graphs at each point show the characteristics of sub-zone, discontinuation and axis asymmetry. It is also proved that the distributions at every point of outlet and inlet are complementary with each other both positionally and angularly.