Focusing in a quadrupole acoustic channel

We investigate analytically and numerically focusing of aerosol micron-and-submicron size particles in the incompressible laminar flow in a three-dimensional quadrupole acoustic channel of hyperbolic cross-section. The fluid–particle interaction of micron-size non-diffusive particles is described by a linear drag force. Considering motion of diffusive submicron particles, we account for their random displacements. Focusing efficiency is investigated for variety of flow and particle parameters, expressed in terms of dimensionless groups, namely acoustic strength parameter β = 2 p s / ρ f ( ω r 0 ) 2 , where p s is the amplitude of pressure oscillations generated at channel walls, ω is the circular frequency of the oscillations, r 0 is the channel cross-sectional half-size, ρ f is the fluid density; axial flow velocity parameter Π U = U / ω r 0 , where U is the maximal velocity of the axial flow; and frequency parameter ω τ , where τ is Stokes relaxation time. It is shown that acoustic oscillations with frequency of about 1 kHz focus micron size particles on axial distance comparable to channel cross-sectional size. Submicron diffusive particles cannot be focused exactly at the channel axis owing to the adverse effect of Brownian motion leading to the diffusion broadening. It is shown that the achievable focusing width decreases with increasing the acoustic strength parameter.