Theory of acoustic fields and streaming with viscous boundary layers in microsystems

When a fluid oscillates acoustically, non-linear time-averaged 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 water-filled microsystems actuated by ultrasound frequencies. A central phenomenon in these devices is the micrometer-thin 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 so-called boundary-driven acoustic streaming. In this thesis, a theory for the viscous boundary layer is developed, which extends the current boundary-layer 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 well-known 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 so-called "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 3-dimensional simulations. Inspired by reported experimental observations of acoustic streaming in closed resonating cavities, the phenomenon of bulk-driven acoustic streaming is investigated theoretically. Bulk-driven acoustic streaming is often ignored in acoustofluidic devices having length scales comparable to the acoustic wavelength.

Here, it is found that bulk-driven 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 bulk-driven streaming should not be ignored neither in the understanding nor in the calculations of resonating acoustofluidic devices.

In this thesis, a general length-scale condition for ignoring bulk-driven 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 boundary-layer 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 sub-micron particles by use of acoustophoresis, and as such, this final result has promising perspectives for further experimental research.