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Dissertation/Thesis Abstract

Emergent Flows, Irreversibility and Unsteady Effects in Asymmetric and Looped Geometries
by Nguyen, Quynh Minh, Ph.D., New York University, 2021, 133; 28095508
Abstract (Summary)

Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plant. Understanding how network topology, connectivity, internal boundaries and other geometrical aspects aspect the global flow state is a challenging problem that depends on complex fluid properties characterized by different length and time scales. The study of flow in micro-scale networks including microvascular network of small animals, plant vasculature and artificial microfluidics focuses on low Reynolds numbers where small volumes of fluids move at slow speeds. The flow physics at these scales is dominated by pressures overcoming viscous impedance, and the governing Stokes equation is linear. This linearity property allows for relatively simple theoretical and computational solutions that greatly aid in the understanding, modeling and designing of micro-scale networks.

At larger scales and faster flow rates, macrofluidic networks such as in the cardiovascular and respiratory systems of larger animals and numerous engineering applications are also important but the flow physics quite different. The underlying Navier-Stokes equation is nonlinear, theoretical results are few, simulations are challenging, and the mapping between geometry and desired flow objectives all much more complex. The phenomenology for such high-Reynolds-number or inertially-dominated flows is well documented and well-studied: Flows are retarded in thin boundary layers near solid surfaces; such flows are sensitive to geometry and tend to separate from surfaces; and vortices, wakes, jets and unsteadiness abound. The counter-intuitive nature of inertial flows is exemplified by the breakdown of reversibility: Running a given system in reverse, say by inverting pressures, does not necessarily cause the fluid to move in reverse but can instead trigger altogether different flow patterns. This dissertation explores two general ways of how rectified flows emerge in macrofluidic networks because of irreversibility and unsteady effects: When branches or channel of network have asymmetric internal geometry and the second when a network contains loops. For the former, we focus on Tesla’s valvular conduit or Tesla valve and for the later, the bird respiratory system. Emergent circulation allows forvalveless pumping that are of interesting in both engineering and biological contexts.

More than 100 years ago, the famous inventor Nikola Tesla was doing experiments in lower Manhattan, not far from the Applied Math Lab. Tesla was better known as an “electric wizard” of the time, but he dabbled in fluid mechanics as well. In 1920, he patented the earliest fluidic device, the Tesla valve which is an asymmetric channel that intended to have strong asymmetric resistance. Since its invention, the device has spurred a lot of studies on its usage as a microfluidic devices. However, fluid mechanical characterization of the device and related physics have been overlooked, especially at higher Reynolds number. We faithfully reproduce the device, and design an experimental system that can apply and control steady pressures on the device while measuring the resulted flow rate. This allow measuring resistances under steady condition extensively over a wide range of Reynolds number. We discover that Tesla valve works by inducing early turbulence. Flows in Tesla valve transition to turbulence at an expected low Reynolds number of 200. Our flow visualization at this transitional Reynolds number reveals the destabilization mechanism in the reverse direction that is a hallmark of turbulence.

Another area that is also overlooked by existing literature is the behavior of the device under unsteady conditions. Nikola Tesla himself conjectured that the diodic behavior is significantly improved with pulsatile flows. To address that, we designed a fluidic circuit that acts as an AC-to-DC converter - converting oscillatory flows to directed flows or a valveless pump, and measure its output under different unsteady inputs using well-calibrated Particle Image Velocimetry (PIV).

The response is found to be more than linear with both amplitude and frequency. Irreversible diodic behavior, expressed in terms of effectiveness of the circuit increase with both amplitude and frequency. In addition, our steady characterization of the device allows us to predict the effectiveness based on steady assumption, which is then compared with the real effectiveness. Our findings confirm Tesla’s conjecture, the diodic behavior is boosted by unsteady effect. In another unexpected and counter-intuitive result, we found that the output DC flows are smoothened as the driving amplitude increases.

The scientific investigation of avian respiratory system has a long history, and dates back to V. Coitier in 1573. Among other aspects of the lung, the air flow dynamics remained controversial and unresolved despite much scientific scrutiny. In mammal’s lung, the air flow is inhaled into a tree-like structure ended in small sacs called aveola, and simply reverse direction when exhaled. In contrast, the bird lung, also known as the most efficient gas exchanger among living vertebrates, has a complex and unique structure: it contains closed loops in which uni-directional flow is sustained during both inhalation and exhalation. Early researchers speculated that the bird lung must possess valves that open and close at the right time, much like a circulatory system. In fact, extensive physiological studies have shown that the lung is rigid and has no valves, and the mechanism responsible for directed flow is deemed ’aerodynamic valving’. Subsequently, many aerodynamic mechanisms have been suggested, and each has been ruled out as either nonexistent, or not essential because it does not exhibit in all species, and the minimum ingredients required for directed flows remain a mystery for the last 100 years.

We simplified the airway network into simple loopy networks of tubes. The tubes are filled with water, and oscillatory flow (AC) is forced in one of the branches, and the resulted flows are measured in the “free" branch using PIV. Persistent DC flows emerge in the free branch for varying driving amplitude and frequency. Our finding demonstrates the minimum ingredients for DC flows are loops, which necessitate junctions (and for simplicity, we use T-junction), and the asymmetric connectivity of the junctions. Direct numerical simulation reproduced the qualitative phenomenon, and reveals that the valving mechanism is due to irreversibility. Flow separation and vortex shedding act to block a side branch of the T-junction only in half of the oscillation cycle, and with appropriate connectivity between partnered junction, DC flows emerge in loops. Chapter 1 reviews the physics relevant to macrofluidic networks, and flow rectification using static geometries. In Chapter 2, we take a pedagogical approach and draw on the electronic-hydraulic analogy to study Tesla’s valve and other asymmetric channel under steady conditions. Chapter 3 studies Tesla’s valve across dynamical regimes and under unsteady conditions. Chapter 4 presents our experiments and simulations on unidirectional flows in loopy network models of bird lungs. In Chapter 5, we propose a generalized modeling approach for flows in networks, and apply to an idealized network of a bird lung. Finally, Chapter 6 summarizes the findings and discusses further studies.

Indexing (document details)
Advisor: Ristroph, Leif, Zhang, Jun
Commitee: Chaikin, Paul M., Grosberg, Alexander Y., Zidovska, Alexandra
School: New York University
Department: Physics
School Location: United States -- New York
Source: DAI-B 82/9(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Fluid mechanics, Applied Mathematics, Biophysics
Keywords: Emergent flows, Irreversibility, Unsteady effects, Asymmetric geometries, Looped geometries
Publication Number: 28095508
ISBN: 9798582575887
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