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IBM Journal of Research and Development  
Volume 25, Number 2/3, Page 176 (1981)
VLSI Circuit Design
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Attraction Force Characteristics Engendered by Bounded, Radially Diverging Air Flow

by J. A. Paivanas, J. K. Hassan
When axially directed air flow enters a parallel plate passage through a hole in one of the plates, the ensuing diverging radial flow is such that a depressed pressure region occurs to some extent over the inlet region of the passage. If the plate against which the inlet air stream impinges is allowed to move freely, it will, under proper flow and other conditions, assume a position of stable equilibrium reflecting a balance among plate weight, the momentum repelling force of the stream, and a net restraining attraction force due to the radial pressure distribution in the passage. This phenomenon, the "Bernoulli" or "axi-radial" effect, has long been of interest in areas such as gas film lubrication and radial diffusers, and it has been applied extensively in IBM systems for contactless transport and motion control of semiconductor wafers on an air film. A steady, laminar, incompressible flow analysis for a representative axisymmetric circular disk model is presented here. A one-dimensional approach, using the general energy equation in conjunction with a passage flow friction factor variation, is applied to obtain an approximate relationship for radial pressure distribution. The friction factor, embodying the influence of varying viscous and inertial forces, is postulated on the basis of specialized radial flow studies in the literature. By also applying the momentum balance condition, an approximate overall solution is obtained which, for arbitrary model dimensions, describes the relationship among equilibrium passage spacing, resultant reaction fluid force and free disk weight, and a flow Reynolds number. The analytical predictions are compared with results from model experiments, and generally favorable agreement is indicated.
Related Subjects: Mathematics (applied)