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Dynamics and Design of Open, Self-Regulating, Capillary Flow Networks for Space Micropropulsion Applications

Nicholas White
California Institute of Technology

Our program is designed to explore an unconventional analogy between electrical networks and capillary flow networks. The goal is to develop a toolkit of components for regulating thin film flow, much like components can be assembled into an electrical circuit for regulating electrical current. This toolkit will consist of individual elements based on free surface flow along complex-shaped substrates, intended to mimic the behavior electrical resistors, capacitors, diodes, switches, transistors, integrators and the like. These primary elements will be strung together to form self-regulating capillary networks optimized to transport thin propellant liquid films for a novel class of miniature space propulsion systems. These networks will not only facilitate fluid storage and handling within the propellant management system but also supply propellant to remote regions of the device where other mechanisms can be enforced to induce propulsion capability, such as droplet emission. Surface tension plays a dominant role in the flow of thin liquid films given the large surface to volume ratios involved. The governing equations of motions for the moving boundary representing the vacuum/liquid interface range from highly nonlinear, second order to fourth order, depending on whether the topography of the supporting substrate is relatively flat and uniform or patterned by topographical features such as protrusions or indentations. Typically, the spatiotemporal variations in the curvature of the liquid interface lead to variations in the capillary pressure which operate as a self-regulating pump. Our goal is to extend this analysis to include spatially non-uniform topographies and to develop the appropriate equations of motion for configurations which mimic the functions of basic electrical components. This program will involve identification of the base flow states and the stability characteristics of various classes of solutions, both time dependent and independent. We intend to use theoretical analysis, coupled closely with numerical simulations, to examine the dynamics and stability of such open, capillary flow networks. The analysis will be extended to include stochasticity as well, to account for surface roughness since the processing and fabrication of the underlying substrates typically generate significant surface roughness, whose mean value is often of the order of the thickness of the spreading liquid film. This can be accomplished by a stochastic mapping whereby the original deterministic problem subject to a random domain is mapped into a stochastic problem in a deterministic domain. It is anticipated that proper sequences of individual flow components can be assembled to form super-stable networks capable of highly robust, flow self-regulation, ideally suited to space micropropulsion applications. The design and development of such flow networks will benefit many different NASA microfluidic based technologies, including lab-on-a-chip systems for analyzing Martian samples, to analysis of bodily fluids of space astronauts for health monitoring. For our purposes, the ultimate goal is to design a highly integrated and compact propellant system consisting of interconnected, self-regulating flow conduits, whereby propellant is distributed from the reservoir region to the propulsion head without the use of any valves, pressurized reservoirs or moving parts. We anticipate that optimized design of such highly distributable propulsion architectures will introduce new paradigms for small spacecraft control including propulsion and attitude control for small planetary spacecraft, precision pointing for exoplanet observation, and primary propulsion and attitude control for CubeSats. Such designs will also benefit NASA’s stated goal of developing next generation, low-cost, small scale spacecraft technologies to enable multipoint observation for advancing geospace and atmospheric research.

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