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Abstract
When a fluid oscillates acoustically, nonlinear timeaveraged forces are exerted both on a given particle suspended in the fluid and on the fluid itself. The latter effect gives rise to a steady motion of the fluid, called acoustic streaming, which causes an additional force on the suspended particle in the form of viscous drag. The resulting particle motion due to an acoustic field is called acoustophoresis, and it is extensively exploited in the field of acoustofluidics for controlled handling of biological microparticles in waterfilled microsystems actuated by ultrasound frequencies. A central phenomenon in these devices
is the micrometerthin viscous boundary layer forming close to a solid wall, where the fluid motion adapts to the solid motion. This boundary layer play an essential role for both viscous dissipation and for the generation of the socalled boundarydriven acoustic streaming.
In this thesis, a theory for the viscous boundary layer is developed, which extends the current boundarylayer theories of the literature in two major perspectives: First, a boundary condition on the oscillating acoustic pressure is derived, which take into account the viscous dissipation in the boundary layer. Second, the wellknown slip condition on the acoustic streaming is extended to apply for a curved wall that oscillates in any direction. The derived boundary conditions constitute the socalled "effective model" for calculations of acoustic fields and streaming in arbitrary geometries where the boundary layer is taken into account analytically. From a numerical point of view, the effective model leads to drastic reductions in the memory requirements thus facilitating larger 3dimensional simulations.
Inspired by reported experimental observations of acoustic streaming in closed resonating cavities, the phenomenon of bulkdriven acoustic streaming is investigated theoretically. Bulkdriven acoustic streaming is often ignored in acoustofluidic devices having length scales comparable to the acoustic wavelength. Here, it is found that bulkdriven streaming can play an essential role in such systems if the acoustic motion is rotating. Remarkably, this rotation may be induced unexpectedly even though the actuation is not rotating. Therefore, a central message of this thesis is, that bulkdriven streaming should not be ignored neither in the understanding nor in the calculations of resonating acoustofluidic devices. In this thesis, a general lengthscale condition for ignoring bulkdriven streaming is provided, which is rarely satisfied in acoustofluidic systems.
Acoustic trapping in capillary tubes is a promising application of acoustofludics which has mainly been studied experimentally. Using the effective boundary conditions for the viscous boundary layer, the acoustic fields and radiation force in long straight capillary tubes of arbitrary cross section are calculated. The analysis leads to an analytical expression for the axial radiation force and an optimal axial actuation length for the acoustic trap.
Finally, due to the effective boundarylayer model, it is possible to calculate the acoustic streaming sufficiently fast so that many different channel shapes can be examined. This advantage is exploited in an iterative algorithm that optimizes the channel shape in order to suppress acoustic streaming. The resulting optimized shape is shown on the front page of this thesis, and the corresponding streaming is suppressed by two orders of magnitude relative to conventional rectangular channels. The numerically proposed shape may allow for controlled handling of submicron particles by use of acoustophoresis, and as such, this
final result has promising perspectives for further experimental research.
is the micrometerthin viscous boundary layer forming close to a solid wall, where the fluid motion adapts to the solid motion. This boundary layer play an essential role for both viscous dissipation and for the generation of the socalled boundarydriven acoustic streaming.
In this thesis, a theory for the viscous boundary layer is developed, which extends the current boundarylayer theories of the literature in two major perspectives: First, a boundary condition on the oscillating acoustic pressure is derived, which take into account the viscous dissipation in the boundary layer. Second, the wellknown slip condition on the acoustic streaming is extended to apply for a curved wall that oscillates in any direction. The derived boundary conditions constitute the socalled "effective model" for calculations of acoustic fields and streaming in arbitrary geometries where the boundary layer is taken into account analytically. From a numerical point of view, the effective model leads to drastic reductions in the memory requirements thus facilitating larger 3dimensional simulations.
Inspired by reported experimental observations of acoustic streaming in closed resonating cavities, the phenomenon of bulkdriven acoustic streaming is investigated theoretically. Bulkdriven acoustic streaming is often ignored in acoustofluidic devices having length scales comparable to the acoustic wavelength. Here, it is found that bulkdriven streaming can play an essential role in such systems if the acoustic motion is rotating. Remarkably, this rotation may be induced unexpectedly even though the actuation is not rotating. Therefore, a central message of this thesis is, that bulkdriven streaming should not be ignored neither in the understanding nor in the calculations of resonating acoustofluidic devices. In this thesis, a general lengthscale condition for ignoring bulkdriven streaming is provided, which is rarely satisfied in acoustofluidic systems.
Acoustic trapping in capillary tubes is a promising application of acoustofludics which has mainly been studied experimentally. Using the effective boundary conditions for the viscous boundary layer, the acoustic fields and radiation force in long straight capillary tubes of arbitrary cross section are calculated. The analysis leads to an analytical expression for the axial radiation force and an optimal axial actuation length for the acoustic trap.
Finally, due to the effective boundarylayer model, it is possible to calculate the acoustic streaming sufficiently fast so that many different channel shapes can be examined. This advantage is exploited in an iterative algorithm that optimizes the channel shape in order to suppress acoustic streaming. The resulting optimized shape is shown on the front page of this thesis, and the corresponding streaming is suppressed by two orders of magnitude relative to conventional rectangular channels. The numerically proposed shape may allow for controlled handling of submicron particles by use of acoustophoresis, and as such, this
final result has promising perspectives for further experimental research.
Original language  English 

Publisher  Department of Physics, Technical University of Denmark 

Number of pages  175 
Publication status  Published  2020 
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 1 Finished

Theory and modeling of acoustic streaming in microfluidic devices
Bach, J. S., Bruus, H., Bohr, T., Thomsen, E. V., Thomas, J. & Viklund, M.
Technical University of Denmark
01/03/2017 → 13/05/2020
Project: PhD