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A method is presented for the numerical solution of the transient, low Reynolds number flow of incompressible fluids with free surfaces. The usual numerical stability restrictions related to the viscous diffusion coefficient are avoided by an implicit differencing scheme. The properties of the method are illustrated by several calculational examples.

The problem of diffusion-controlled growth or collapse of a bubble or droplet that is moving relative to a surrounding fluid is solved by means of a similarity transformation previously proposed by Ruckenstein. The cases of low Reynolds number flow ( Re Re

A technique is suggested by which the effects of permeable materials on the low Reynolds number flow of viscous liquids may be evaluated. In particular, we show that Darcy's law and the asymptotic equations (Re O) of Stokes may be used to formulate boundary value problems generating solutions valid for both porous and non-porous regions and matched at common boundaries. The coupled problem of the streaming of a viscous liquid past a permeable sphere is considered and closed solutions which depend simply on the permeability on the sphere are derived. The drag on a permeable sphere is shown to be the same as the drag on an impermeable sphere of reduced radius. Es wird ein Verfahren vorgeschlagen, mit dem der Einflus von durchlassigem Material auf eine mit niedriger Reynoldszahl stromende viskose Flussigkeit berechnet werden kann. Speziell wird gezeigt, das man das Gesetz von Darcy und die asymptotischen Gleichungen (Re 0) von Stokes benutzen kann, um Randwertprobleme zu formulieren, die Losungen liefern, die fur porose und nichtporose Gebiete gelten. Es wird das Problem der Stromung einer viskosen Flussigkeit hinter einer durchlassigen Kugel betrachtet. Dafur werden geschlossene Losungen abgeleitet, die in einfacher Weise von der Durchlassigkeit der Kugel abhangen. Es wird gezeigt, das der Widerstand einer durchlassigen Kugel derselbe ist wie der einer undurchlassigen mit kleinerem Radius.

Low Reynolds number flow past a circular porous cylinder is studied in this paper. The problem is formulated using the full Navier-Stokes equations and Darcy Law; the solution is, then, derived by a singular perturbation method involving three simultaneous expansions. A systematic matching process between these expansions is established, and the solution, including higher-order terms, is derived. In addition, the formula for the drag is evaluated to higher order. By comparing the present results with those of Kaplun and Proudman and Pearson for the corresponding nonporous case, the effect of the permeability on the drag of a circular porous cylinder is shown to be equivalent to a reduction of the radius by a factor of exp (k′/a2), where k′ is the permeability and a is the radius of the cylinder. The senior author wishes to thank Dr. T. E. Stelson, Alcoa Professor, and Dr. McCabe, Vice President, Carnegie Institute of Technology, for their kind encouragement

The low Reynolds number flow of a gas past an infinite heated circular cylinder is studied for the case of variable property flow when the temperature difference between the cylinder and free stream is small. The perturbation to the corresponding incompressible velocity field is calculated by the method of matched asymptotic expansions developed by Kaplun, and Proudman and Pearson. When the temperature difference between the cylinder and free stream is appreciable, a solution for the velocity field is found on the assumption that the viscosity and thermal conductivity of the gas are invariant. This solution possesses the interesting property that the zero‐order solution for the velocity field near the cylinder is a uniformly valid solution of the problem.

The Stokes region (where diffusion dominates) is shown to contain two subregions of distinct character—an inner region near the cylinder where the variable transport properties of the gas are of secondary importance and an intermediate region (remainder of Stokes region) where they are of primary importance.