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A method for the quantification of acoustophoretic separation and dispersionfor microparticle populations featuring continuously distributed physicalparameters is presented. The derivation of the method starts by (i)~consideringthe equation of motion for a particle ensemble in the coordinate+parameterspace, (ii)~performing moment analysis on the transport equation for theprobability density function (PDF), and (iii)~expanding up to the first-orderthe drift (and the diffusion coefficient) around the mean of the PDF. Followingthese steps, a system of ordinary differential equations for the evolution ofthe mean and the covariance in the coordinate+parameter space is derived. Thesedifferential equations enable for the approximation of the acoustophoreticseparation dynamics of particle ensembles by using a gaussian mixture for whichthe mean and the covariance of each gaussian evolve according to themean-and-covariance dynamics. The approximation property of this method isshown by comparison with direct numerical simulations of particle ensembles inthe cases of prototypical models of acoustophoretic and free-flowacoustophoretic separations for which the particle populations are distributedaccording to the radius. Furthermore, the indicators for quantifying free-flowacoustophoretic separation performance are introduced, and a method for theinference of particle-histogram parameters is illustrated.

Quantifying Acoustophoretic Separation of Microparticle Populations by Mean-and-Covariance Dynamics for Gaussians in Mixture Models