Microacoustofluidics: An Arbitrary Lagrangian-Eulerian Framewor

The lab-on-a-chip concept refers to the quest of integrating numerous functionalities onto a single microchip for applications within medicine and biotechnology. To achieve precise fluid and particle handling capabilities required for such applications, microacoustofluidics (i.e. the merger of acoustics and microfluidics) has shown great potential.;The primary motivation of this dissertation is to revisit the formulation of the governing equations for microacoustofluidics in an fluid-structure interaction (FSI) context to develop a numerical formulation that is transparent with regards to the reference frames as well as the time-scale separation. In this context, we present a generalized Lagrangian formulation by posing our governing equations over a convenient mean configuration that does not coincide with the current configurations. The formulation stems from an explicit separation of time-scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidics.;We also present a comparison of the generalized Lagrangian formulation with the typically employed Eulerian formulation and highlight the superior numerical performance of our formulation to aid easier comparison with the experimental observations.;Next, we describe the fluid and particle motion in acoustically-actuated, confined, leaky systems. The investigated model system is a microchip typically used for biomedical analyses; a liquid-filled polydimethylsiloxane microchannel driven acoustically by inter-digital transducers. Through a combination of quantitative experimental measurements and numerical results, we reveal the full three dimensional motion of the fluids and suspended particles. By varying the size of suspended particles, we capture the two limits for which the particle motion is dominated by the acoustic streaming drag to which it is dominated by the acoustic radiation force. The observed fluid and particle motion is captured numerically without any fitting parameter by a reduced-fluid model based on a thermoviscous, Lagrangian velocity-based formulation. Through a combination of experimental observations and precise numerical boundary conditions, we remove the existing ambiguity in the literature concerning the acoustic streaming direction as well as the critical particle size for which the particle motion switches between the aforementioned two limits. Further, combining experimental and numerical results, we indirectly determine the first-order acoustic field of the vertically-propagating pseudo-standing wave as well as give an estimate of the actual displacement on the piezoelectric substrate. Through a combination of a simplified analytical model and our numerical results, we demonstrate that these "pseudo-standing" waves owe their origin to the small yet significant reflections from the fluid and channel wall interface and are the primary reason for the vertical focusing of particles. We present numerical results for the vertical focusing of both positive as well as negative contrast neutrally-buoyant particles and provide the design criteria for the microchannels to achieve desired vertical focusing locations. We also demonstrate the ability to tune the focusing locations of particles in both horizontal as well as vertical direction by tuning the phase difference between the incoming surface acoustic waves (SAWs) and the applied acoustic power.;Further, we outline the extension of the presented generalized Lagrangian formulation for FSI problems in microacoustofluidics. To this end, we present "proofof- concept" results concerning the tracking of a fluid sub-domain inside a microacoustofluidic device.