Analytical characterization of particle kinematics and transverse dispersion in free-flow acoustophoretic devices

Abstract

The overdamped dynamics of particles dragged by a parallel flow in a straight micro-channel in the presence of a transverse acoustophoretic force is investigated. Analytical solutions are presented in the case of plug, shear, or Poiseuille flow velocity profile. Two regimes of particle dynamics are observed, namely an early regime dominated by the local stream-wise velocity and a later regime governed by the local transverse flow at the stable nodes of the acoustophoretic force. The crossover time between these regimes is analyzed as a function of the particle position at the channel inlet. The impact of Brownian fluctuations on particle dynamics is also addressed, both in terms of average velocity and dispersion. Specific attention is focused on the dynamics of the cross-sectional marginal distribution, and a simplified model able to capture quantitatively the dynamics of the first and second moments is developed. Qualitatively different behaviors of the scalar variance dynamics are observed depending on whether the particle position at the channel entrance is located at the channel core or in the near-wall region, giving rise to a monotonic or non-monotonic trend, respectively. The implications of these results on the design of acoustofluidic devices are addressed.