Capillary Flow Analysis and Computation of De-Wetting and Wetting Resistances in Angular Geometries

Author

Daniel Bolleddula, Portland State University

Sponsor

Portland State University. Department of Mechanical and Materials Engineering

First Advisor

Mark Weislogel

Term of Graduation

Spring 2007

Date of Publication

2007

Document Type

Thesis

Degree Name

Master of Science (M.S.) in Mechanical Engineering

Department

Mechanical and Materials Engineering

Language

English

Subjects

Capillarity, Fluid dynamics, Surface tension

Physical Description

1 online resource (2, vii, 138 pages)

Abstract

Capillary flows in containers or conduits with interior corners are commonplace in nature and industry. The majority of investigations addressing such flows solve the problem numerically in terms of a flow resistance coefficient (friction factor) for cases where spontaneous liquid spreading along the corner occurs for 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_i for partially wetting 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 narrowly banded numerical coefficient is desirable for further analysis and is achieved by careful selection of length scales x_s and y_s to nondimensionalize the problem. The optimal scaling is found to be identical to the wetting scaling, namely x_s = H and y_s = H tan a, where H is the height from the corner to the free surface and a is the corner half-angle. Employing this scaling produces a weakly varying flow resistance F_i . This result allows F_i to be treated as a constant with a maximum error of ±27% . Example solutions to steady and transient flow problems are provided that illustrate applications of this result. Capillary driven flows through gapped geometries are introduced providing the numerical and experimental foundation for analytical predictions to come. The flow resistance function is pursued in the wetting regime applied to three unique gap geometries. A local and global scaling method is employed in hopes of establishing a narrowly bounded flow resistance. Drop tower experiments are conducted in test cells of select gapped geometries. Global flow features such as tip location L ( t ), bulk meniscus location Z ( t ), and surface profile h ( z, t ) are plotted. High linearity is observed of L ( t ) and Z ( t ) with t ^{1 /2}. The numerical and experimental results accumulated in this work serve as the platform for further analytical work for the gap geometries.

Rights

Copyright 2007 Daniel Bolleddula

Recommended Citation

Bolleddula, Daniel, "Capillary Flow Analysis and Computation of De-Wetting and Wetting Resistances in Angular Geometries" (2007). Dissertations and Theses. Paper 6974.