Published In

Physics of Fluids

Document Type

Article

Publication Date

4-2009

Subjects

Fluid dynamics, Hydrodynamics, Fluid mechanics, Capillarity

Abstract

We analyze the effect of gravity on capillary flows in sharp corners. We consider gravity perpendicular and parallel to the channel axis. We analyze both steady and unsteady flows. In the steady analysis the main result is a closed form expression for the flow rate as a function of the two gravity components. Good agreement with steady experiments is offered as support of the model. The unsteady analysis is restricted to “small” values of the two gravity parameters and is accomplished using a similarity formulation. The similarity coefficients of the gravity corrections are fully determined by the coefficients of the gravityless problem. The main result of the unsteady analysis is the gravity corrections to the flow rate (or rate of advance) of the liquid in the channel. In addition, we obtain corrections for the liquid height as a function of position and time. We address in detail unsteady problems with select boundary conditions that are representative of typical flow types. In Appendix A we present a new exact solution to one of the gravityless similarity cases, which is analogous to a nonlinear heat conduction equation. In Appendix B we offer dimensional formulas for all the unsteady flow results, which are valuable for systems design and analysis.

Description

This is the publisher's final PDF. Copyright 2009 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

The following article appeared in Physics of Fluids, 21(4), 042106 and may be found at http://scitation.aip.org/content/aip/journal/pof2/21/4/10.1063/1.3109685

DOI

10.1063/1.3109685

Persistent Identifier

http://archives.pdx.edu/ds/psu/11345

Download

Share

COinS