CAPILLARITY: DRAINING AND SURFACE VIBRATIONS
This thesis is comprised of two overarching pieces of work: chapters 1 and 2 analyze and simulate experimental capillary draining flight data flown aboard the International Space Station. Chapter 3 considers a spectral approach to recover the fundamental oscillatory and damping frequencies for a liquid in a rectangular channel. Each chapter formulates its own published paper; as such, each chapter comprises of an introduction and conclusion. The following introduces the general phenominon of capillary fluidics in microgravity, following by brief summaries of the two bodies of work. On earth, a hole in the bottom of a liquid-filled bucket is a convenient way to drain it. However, in the nearly weightless environment of orbiting or coast spacecraft, there is no \lq bottom' because there is effectively no gravity, and the liquid simply remains in the bucket. In fact, for many liquid handling operations aboard spacecraft, the phenomena are dominated by passive capillary forces over large length scales to which we are not accustomed. However, it is no less necessary to drain `buckets' aboard spacecraft; i.e., fuels, propellants, coolants, water. In terrestrial systems the effects of capillary forces have long been observed and exploited for sub-millimetric/micro-liter scale fluids processes where capillary forces are similarly dominant. Especially in situations where the liquid involved is precious, it is important to process it in a manner that wastes nothing; i.e., one that achieves maximum drain rates with minimum liquid hold-up as a function of initial conditions, container geometry, and fluid properties. Chapters 1 and 2: In the reduced acceleration environment aboard orbiting spacecraft, capillary forces are often exploited to access and control the location and stability of fuels, propellants, coolants, and biological liquids in containers (tanks) for life support. To access the `far reaches' of such tanks, the passive capillary pumping mechanism of interior corner networks can be employed to achieve high levels of draining. With knowledge of maximal corner drain rates, gas ingestion can be avoided and accurate drain transients predicted. In this work, we benchmark a numerical method for the symmetric draining of capillary liquids in simple interior corners. The free surface is modeled through a volume of fluid (VOF) algorithm via interFoam, a native OpenFOAM solver. The simulations are compared with rare space experiments conducted on the International Space Station. The results are also buttressed by simplified analytical predictions where practicable. The fact that the numerical model does well in all cases is encouraging for further spacecraft tank draining applications of significantly increased geometric complexity and fluid inertia. Chapter 3: A capillary surface bound by a solid rectangular channel exhibits dynamic wetting effects characterized by a constitutive law relating the dynamic contact-angle to the contact-line speed through the contact-line mobility $\Lambda$ parameter. Limiting cases correspond to the free ($\Lambda=0$) and pinned ($\Lambda=\infty$) contact-line. Viscous potential flow is used to derive the governing integrodifferential equation from a boundary integral approach. The spectrum is determined from a boundary value problem where the eigenvalue parameter appears in the boundary condition. Here we introduce a new computationally-efficient and tractable frequency scan approach to compute the spectrum, whereby we scan the complex frequency plane and compute the system response from which we identify the complex resonance frequency. Damping effects due to viscosity and Davis dissipation from finite $\Lambda$ do not attenuate signal response, but rather shift the response poles into the complex plane. Our new approach is verified against an analytical solution in the appropriate limit. We identify the critical mobility that maximizes Davis dissipation and the critical Ohnesorge number (viscosity) where the transition from underdamped to overdamped oscillations occur, as it depends upon the static contact-angle $\alpha$. Our approach is applied to a rectangular channel, but is suitable for a myriad of geometric supports.
Louge, Michel Yves; Rand, Richard Herbert
Ph. D., Aerospace Engineering
Doctor of Philosophy
dissertation or thesis