Nonlinear acoustic forces acting on inhomogeneous fluids at slow time-scales

Abstract

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.

Numerical simulation of micro-particle rotation by the acoustic viscous torque

“…The effects of thermal boundary layers are not considered in our model, but they could be included in analogy to recent publications of numerical thermo-viscoacoustics. 33,42,43 Clearly, an analytical treatment also has advantages over numerical simulations. For instance, it can provide closedform solutions, whereas the numerical solution has to be computed for every single parameter set and the discretization always has to stay within numerically feasible limits.…”