Using Solid Mechanics to Evaluate the Capillary and Viscous Behavior of Noncircular Tube Shapes

Abstract

The similarity between torsion-solid mechanics and incompressible-viscous tube flow is investigated by finite element solutions of the governing partial differential equations. After the numerical solutions are validated against several well-known analytical functions for noncircular shapes, a method is presented to illustrate how hydraulic resistance factors may be computed from the polar moment of inertia. Since the results are scaleable, the macroscopic solid mechanics information can be used to predict the viscous pressure loss term for micro-machined flow features. The numerical technique is then further developed to estimate the Laplace pressure jump across the main terminal meniscus in noncircular capillaries. The solid mechanics based numerical technique is demonstrated on several special cases involving horizontal and vertical capillary flow in noncircular regimes. The numerical technique compares well to published experimental results. Then a nozzle shape figure of merit is derived, and applied to a variety of noncircular shapes. Finally, the numerical methods are merged into the LXK droplet simulation model where their effectiveness is demonstrated against lab data from a wide experimental space for thermal inkjet.