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 Title: Quantifying microbubble streaming and its applications Author(s): Rallabandi, Venkatarama Bhargav Director of Research: Hilgenfeldt, Sascha Doctoral Committee Chair(s): Hilgenfeldt, Sascha Doctoral Committee Member(s): Freund, Jonathan B.; Ewoldt, Randy H.; Bodony, Daniel J. Department / Program: Mechanical Sci & Engineering Discipline: Theoretical & Applied Mechans Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Microfluidics Acoustics Microbubbles Streaming Bubble dynamics Micromixing Boundary layers Low-Reynolds-number hydrodynamics Abstract: The growing interest in microfluidics in the last two decades has resulted in new and exciting ways in which to drive microfluidic flows. A simple and powerful flow actuation method involves the use of acoustically excited microbubbles. For ease of manufacture and flow control, setups have largely focused on microbubbles of semi-cylindrical shape, attached to a wall of the microchannel. The application of an ultrasound field drives oscillations of the bubble interface, which then become rectified into strong secondary steady currents in the fluid, termed streaming''. While several researchers have used such setups in experiments, a theoretical quantification of the bubble streaming flows, crucial for the systematic design of practical microfluidics applications, has lagged behind. In the first part of the dissertation, we resolve both the primary oscillatory and secondary steady flow components. We begin by developing an asymptotic theory describing the oscillatory response of the bubble to the applied acoustic field. We show that the presence of viscous boundary layers and pinned contact lines at the walls (i) strongly couples volume oscillations of the bubble to shape oscillations of the interface, and (ii) results in much wider surface-mode frequency resonance peaks than is nominally predicted by potential flow theory. The oscillatory dynamics then feed into a calculation of the secondary flow, which rigorously accounts for boundary layers over the bubble and the wall. We show that the two-dimensional steady vortical streaming flows observed in experiment are governed at low frequencies by surface mode dynamics, but undergo a reversal of orientation at higher frequencies, where volume oscillations dominate. The theory therefore connects the oscillatory dynamics to the steady streaming, reproducing the entire spectrum of steady flow patterns observed in experiments, with no adjustable parameters. The 2D theory is then modified to include 3D flow effects, in the light of recent collaborative experimental measurements. We show that these flows arise due to the axial confinement of the bubble by no-slip walls, and can be modeled by a perturbation of the 2D streaming solutions by additional (axial) Stokes solutions. The 3D theory explains the experimentally observed flow kinematics over a wide range of time scales, showing that the 2D trajectories typically observed in experiments are in fact sections of a higher three-dimensional flow structure that becomes apparent only on much longer time scales. We then develop a Hamiltonian formalism that governs the long time 3D motion and is applicable to any perturbed 2D flow under confinement. Having now systematically developed a theoretical description of the flow field, the second part of the dissertation deals with its application to practically useful situations in microfluidics. We first analyze the micromixing between two fluid streams continuously transported through the channel by a Poiseuille flow, whose mixing properties are enhanced by an array of acoustically excited bubbles located at the channel walls. We argue that in order to achieve exponentially fast fluid mixing, it is necessary to introduce a temporal modulation in the flow field, achieved here through a duty cycling of the streaming flow (i.e., of the driving ultrasound). It is then shown using numerical simulations that the mixing is optimized at specific duty cycles that can be understood from global transport properties of the Poiseuille flow and the streaming vortices, thus forming the first protocol for open-flow mixing that is optimized from first principles. Finally, we analyze the motion of rigid spherical microparticles within streaming flows, with the intention of designing a size-sensitive sorting device. We show that assuming a short-range hard-core interaction to prevent penetration of particle and bubble surfaces is sufficient to explain a drift of particles across streamlines close to the bubble. This drift ultimately results in the size-dependent sorting behavior observed in experiments, provided that 3D flow effects are properly accounted for. Issue Date: 2015-07-17 Type: Thesis URI: http://hdl.handle.net/2142/88198 Rights Information: Copyright 2015 Venkatarama Bhargav Rallabandi Date Available in IDEALS: 2015-09-292017-09-29 Date Deposited: August 201
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