Capillary Corner Flows With Partial and Nonwetting Fluids

Capillary flow in containers or conduits with interior corners are common place in nature and industry. The majority of investigations addressing such flows solve the problem numerically in terms of a friction factor for flows along corners with contact angles below the Concus-Finn critical wetting condition for the particular conduit geometry of interest. This research effort provides missing numerical data for the flow resistance function F(sub i) for partially and nonwetting systems above the Concus-Finn condition. In such cases the fluid spontaneously de-wets the interior corner and often retracts into corner-bound drops. A banded numerical coefficient is desirable for further analysis and is achieved by careful selection of length scales x(sub s) and y(sub s) to nondimensionalize the problem. The optimal scaling is found to be identical to the wetting scaling, namely x(sub s) = H and y(sub s) = Htan (alpha), where H is the height from the corner to the free surface and a is the corner half-angle. Employing this scaling produces a relatively weakly varying flow resistance F(sub i) and for subsequent analyses is treated as a constant. Example solutions to steady and transient flow problems are provided that illustrate applications of this result.