We present a theoretical analysis of the acoustic radiation force on a single small spherical particle, either a thermoviscous fluid droplet or a thermoelastic solid particle, suspended in a viscous and heat-conducting fluid medium. Within the perturbation assumptions, our analysis places no restrictions on the length scales of the viscous and thermal boundary-layer thicknesses δ(s) and δ(t) relative to the particle radius a, but it assumes the particle to be small in comparison to the acoustic wavelength λ. This is the limit relevant to scattering of ultrasound waves from nanometer- and micrometer-sized particles. For particles of size comparable to or smaller than the boundary layers, the thermoviscous theory leads to profound consequences for the acoustic radiation force. Not only do we predict forces orders of magnitude larger than expected from ideal-fluid theory, but for certain relevant choices of materials, we also find a sign change in the acoustic radiation force on different-sized but otherwise identical particles. These findings lead to the concept of a particle-size-dependent acoustophoretic contrast factor, highly relevant to acoustic separation of microparticles in gases, as well as to handling of nanoparticles in lab-on-a-chip systems.

Mechanical phenotyping of single cells is an emerging tool for cell classification, enabling assessment of effective parameters relating to cells' interior molecular content and structure. Here, we present iso-acoustic focusing, an equilibrium method to analyze the effective acoustic impedance of single cells in continuous flow. While flowing through a microchannel, cells migrate sideways, influenced by an acoustic field, into streams of increasing acoustic impedance, until reaching their cell-type specific point of zero acoustic contrast. We establish an experimental procedure and provide theoretical justifications and models for iso-acoustic focusing. We describe a method for providing a suitable acoustic contrast gradient in a cell-friendly medium, and use acoustic forces to maintain that gradient in the presence of destabilizing forces. Applying this method we demonstrate iso-acoustic focusing of cell lines and leukocytes, showing that acoustic properties provide phenotypic information independent of size.

We present a theory for the acoustic force density acting on inhomogeneous fluids in acoustic fields on time scales that are slow compared to the acoustic oscillation period. The acoustic force density depends on gradients in the density and compressibility of the fluid. For microfluidic systems, the theory predicts a relocation of the inhomogeneities into stable field-dependent configurations, which are qualitatively different from the horizontally layered configurations due to gravity. Experimental validation is obtained by confocal imaging of aqueous solutions in a glass-silicon microchip.

We present a theoretical and experimental study of boundary-driven acoustic streaming in an inhomogeneous fluid with variations in density and compressibility. In a homogeneous fluid this streaming results from dissipation in the boundary layers (Rayleigh streaming). We show that in an inhomogeneous fluid, an additional nondissipative force density acts on the fluid to stabilize particular inhomogeneity configurations, which markedly alters and even suppresses the streaming flows. Our theoretical and numerical analysis of the phenomenon is supported by ultrasound experiments performed with inhomogeneous aqueous iodixanol solutions in a glass-silicon microchip.

Suppression of boundary-driven Rayleigh streaming has recently been demonstrated for fluids of spatial inhomogeneity in density and compressibility owing to the competition between the boundary-layer-induced streaming stress and the inhomogeneity-induced acoustic body force. Here we characterize acoustic streaming by general defocusing particle tracking inside a half-wavelength acoustic resonator filled with two miscible aqueous solutions of different density and speed of sound controlled by the mass fraction of solute molecules. We follow the temporal evolution of the system as the solute molecules become homogenized by diffusion and advection. Acoustic streaming rolls is suppressed in the bulk of the microchannel for 70-200 seconds dependent on the choice of inhomogeneous solutions. From confocal measurements of the concentration field of fluorescently labelled Ficoll solute molecules, we conclude that the temporal evolution of the acoustic streaming depends on the diffusivity and the initial distribution of these molecules. Suppression and deformation of the streaming rolls are observed for inhomogeneities in the solute mass fraction down to 0.1 %.

We demonstrate theoretically that acoustic forces acting on inhomogeneous fluids can be used to pattern and manipulate solute concentration fields into spatiotemporally controllable configurations stabilized against gravity. A theoretical framework describing the dynamics of concentration fields that weakly perturb the fluid density and speed of sound is presented and applied to study manipulation of concentration fields in rectangular-channel acoustic eigenmodes and in Bessel-function acoustic vortices. In the first example, methods to obtain horizontal and vertical multilayer stratification of the concentration field at the end of a flow-through channel are presented. In the second example, we demonstrate acoustic tweezing and spatiotemporal manipulation of a local high-concentration region in a lower-concentration medium, thereby extending the realm of acoustic tweezing to include concentration fields.

Acoustofluidics relying on acoustic forces to handle fluids and particles in microfluidic systems has emerged as a useful tool for characterizing, focusing, separating, and sorting cells based on their acousto-mechanical properties. Here, we present recent advances in the theoretical understanding of acoustic forces on particles and fluids. In particular, we address the effects of thermoviscous boundary layers on acoustic scattering off sub-micron particles or droplets. Re-examining the far-field method of calculating acoustic radiation forces and torques, we show that exact non-perturbative expressions can be derived regardless of boundary layer dissipation. The necessary condition for moving the surface of integration from the particle surface to the far field, is the time-periodicity of the system rather than negligible boundary-layer dissipation. In the long-wavelength limit, this approach leads to particularly simple expressions for the force and torque acting on a particle in a thermoviscous fluid. Finally, relaxing the requirement of having two immiscible phases (particle/fluid or droplet/fluid), we generalize the theory to include acoustic forces acting on continuous density and compressibility distributions of inhomogeneous fluids, such as aqueous salt solutions.

We present a novel theory describing the nonlinear acoustic force density acting on a fluid of inhomogeneous density and compressibility, for example, due to an added salt concentration. We derive an expression for the time-averaged acoustic force density acting on an inhomogeneous fluid, which depends on the gradients of the fluid density and compressibility. This smeared-out force density can be interpreted as a generalization of the well-known acoustic forces acting on a particle or an immiscible-fluid interface. The special case where the speed of sound in the solution is independent of the salt concentration, which is a good approximation for many actual salt solutions, leads to a particularly simple theoretical description. The theory predicts that in microfluidic channels, the nonlinear acoustic forces act to relocate density distributions into field-dependent configurations, which are stabilized against gravitational collapse driven by hydrostatic pressure gradients. We show the first experimental confirmations of these predictions obtained by confocal imaging in glass-silicon microchips.