On the methodologies for the assessment of the impact of parameters in acoustophoretic separation devices

In this communication, we reconcile the kinematic method illustrated by some authors (Yang et al. in Microfluid Nanofluid 22:44–56, 2018; Vitali et al. in RSC Adv 8:38955, 2018) in studying the impact of system and suspension parameters on acoustophoretic separations with the statistical method formerly proposed by Garofalo (Microfluid Nanofluid 18(3):367–382, 2014a; ASME 2014 3rd global congress on nanoengineering for medicine and biology NEMB2014-93092, 2014b. https://www.researchgate.net/publication/259962346_Free-flow_acoustofluidic_devices_kinematics_cross-sectional_dispersion_and_particle_ensemble_correlations_Presentation ) and lately extended to particle populations by the same author (Garofalo in CBMS the 14th conference on acoustofluidics, San Diego (CA), August 28–29, 2017, 2017. https://www.researchgate.net/publication/259962346_Free-flow_acoustofluidic_devices_kinematics_cross-sectional_dispersion_and_particle_ensemble_correlations_Presentation ; Quantifying acoustophoretic separation of microparticle populations by mean-and-covariance dynamics for Gaussians in mixture models, 2018. arXiv:1802.09790 ). The connection between these two methods is established by (1) reinterpreting the kinematic method in terms of tangent space dynamics, and (2) transforming the dynamics in the tangent space into the dynamics of the area elements. The dynamics of the area elements is equivalent to the dynamics of the covariance matrix derived by moment analysis and associated with the dispersion problem during microparticle acoustophoresis. The similarities and the differences between the kinematic based method and the stochastic method proposed by the present author are illustrated and discussed in the light of the numerical results for a prototypical model of acoustophoretic separation.