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

## TL;DR

This paper bridges kinematic and statistical methods for assessing parameter impacts in acoustophoretic separation, enhancing understanding of particle dispersion through a unified dynamical framework.

## Contribution

It reinterprets the kinematic method in terms of tangent space dynamics and links it to the covariance-based statistical approach, clarifying their relationship.

## Key findings

- Unified the kinematic and statistical methods through tangent space dynamics.
- Demonstrated the connection using numerical simulations of acoustophoretic separation.
- Highlighted differences and similarities between the two approaches.

## Abstract

In this communication I reconcile the kinematic method illustrated by some authors~\cite{yang2018,vitali2018} in studying the impact of system and suspension parameters on acoustophoretic separations with the statistical method formerly proposed by Garofalo~\cite{garofalo2014,garofalo2014_2} and lately extended to particle populations by the same author~\cite{garofalo2017,garofalo2018}. The connection between these two methods is established by (i)~reinterpreting the kinematic method in terms of tangent space dynamics, and (ii)~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 auuthor are illustrated and discussed in the light of the numerical results for a prototypical model of acoustophoretic separation. \keywords{Acoustofl