Nonlinear Dynamics and Stability of Viscous Free-Surface Microcapillary Flows in V-Shaped Channels and on Curved Surfaces

Citation

White, Nicholas Conlan (2022) Nonlinear Dynamics and Stability of Viscous Free-Surface Microcapillary Flows in V-Shaped Channels and on Curved Surfaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yd3w-ck87. https://resolver.caltech.edu/CaltechTHESIS:05292022-001428228

Abstract

The last two decades have brought a revolution in miniaturization of space technology. Thanks to improved microelectronic sensors and MEMS devices, nanosatellites can perform communication and scientific studies previously limited to large satellites, significantly reducing the financial barriers to space access. But development of a reliable, long-running, small-scale propulsion system for orbital maneuvers remains a key challenge. One solution is the microfluidic electrospray propulsion (MEP) thruster under development at NASA's Jet Propulsion Laboratory (JPL).

This thesis analytically addresses aspects of the MEP system's propellant management, specifically, capillary flow in the groove network delivering fluid propellant from the reservoir to the emitters. Building upon the reduced-order model of viscous capillary flow in straight V-shaped channels ("V-grooves") of Weislogel (1996) and Romero and Yost (1996), we prove stability of steady-state and self-similar flows. Because the MEP design requires an electric field above the grooves, and further calls for grooves which curve and bend in three dimensions, we extend earlier V-groove models to include these effects, and also perform stability analyses of the new models. The results not only validate the use of V-grooves as a robust propellant delivery system, but also provide a theoretical basis for the design of future microfluidic devices with compact, three-dimensional designs and electric fields.

In order to lay the groundwork for future studies of early-time behavior of propellant on emitter tips before the Taylor cone necessary for ion emission is formed, we develop the technique of generalized linear stability analysis (Farrell and Ioannou, 1996) of capillary flow of thin viscous films coating curved surfaces (governed by the equation first developed by Roy and Schwartz, 1997). This methodology was first applied to films coating cylinders and spheres by Balestra et al. (2016, 2018); we instead apply the technique and analyze for the first time a viscous-capillary instability arising on a torus coated with a uniform thin film.

Besides the capillary fluid dynamics results, two additional pieces of work are included in the thesis. First, in an unorthodox application of Noether's Theorem to non-Lagrangian gradient flow equations, we show that each variational symmetry of the governing functional induces a constraint on the evolution of the system. Second, to support JPL's efforts to directly detect a "fifth force," we introduce and implement numerical methods for computation of the scalar Cubic Galileon Gravity (CGG) field at solar system scales.

Thesis Files