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Three-dimensional numerical simulation of particle acoustophoresis: COMSOL implementation and case studies

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Abstract

As a microfluidic-based noncontact manipulation and separation technique, acoustophoresis is the motion of the particles or cells within a host fluid under the effect of acoustic waves. Wave scattering off the particle surface generates both acoustic radiation forces and interparticle interaction forces that move the particles relative to the host fluid and each other, respectively. In this paper, an implementation in the commercial finite element software COMSOL Multiphysics for three-dimensional simulations of particle acoustophoresis is presented. Case studies with various particle types including rigid, compressible, elastic, core–shell and different particle geometries including spherical and spheroidal particles as well as pair-particle are simulated. The simulation results are verified by comparing the scattered velocity potential around the particle and the acoustic forces on the particle, against the existing analytical solutions. Furthermore, the COMSOL Livelink for MATLAB is utilized to implement an incremental simulation algorithm for the particle migration under the effect of a standing wave in a microchannel, based on the Stokes drag formula. The acoustophoretic motion simulations are performed for single particle and pair-particle case studies to demonstrate the presented implementation capabilities in modeling multi-particle tracking in real applications.

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source particle distance from the wave node, for different interparticle distances of a , b, and c

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source and probe particles, over simulation time

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Abbreviations

\(A\) :

Particle cross-section (μm2)

\(a:\) :

Particle outer radius (μm)

\(b:\) :

Inner radius of core–shell particle (μm)

\({c}_{f}:\) :

Sound wave speed in fluid (m/s)

\({c}_{c}:\) :

Compressional wave speed in elastic particle material (m/s)

\({c}_{s}:\) :

Shear wave speed in elastic particle material (m/s)

\(E:\) :

Young’s modulus (MPa)

\({E}_{ac}:\) :

Acoustic energy density (N/m2)

\({F}^{rad}:\) :

Acoustic radiation force (N)

\(f:\) :

Stimulation frequency (MHz)

\({f}_{m}:\) :

Monopole scattering coefficient

\({f}_{d}:\) :

Dipole scattering coefficient

\(H:\) :

Channel height (μm)

\(h:\) :

Particle distance from anti-node (μm)

\({h}_{s}:\) :

Distance between the source particle and the first wave node (μm)

\(i:\) :

Complex variable equal to \(\sqrt{-1}\)

\({\varvec{I}}\) :

Second-order identity tensor

\(k:\) :

Wave number (1/m)

\({k}_{\perp }:\) :

Added mass coefficient of spheroid in the perpendicular direction

\({k}_{\parallel }:\) :

Added mass coefficient of spheroid in the parallel direction

\(L:\) :

Inter-particle distance (μm)

\({\varvec{n}}:\) :

Surface normal outgoing vector

\(p:\) :

Fluid pressure (Pa)

\({p}_{in}:\) :

Incident wave pressure (Pa)

\({P}_{sc}:\) :

Scattered wave pressure (Pa)

\({\varvec{r}}:\) :

Surface element vector from the center of particle

\(r:\) :

Position relative to the center of particle (μm)

\({r}_{a}:\) :

Wave-perpendicular spheroidal radius (μm)

\({r}_{b}:\) :

Wave-parallel spheroidal radius (μm)

\({r}_{p}:\) :

Position relative to the center of probe particle (μm)

\({r}_{s}:\) :

Position relative to the center of source particle (μm)

\({r}_{sp}:\) :

Distance between source and probe particles (μm)

\(S:\) :

Surface area (μm2)

\({T}_{rad}:\) :

Radiation torque (Nm)

\(U\left({r}_{p}|{r}_{s}\right):\) :

Potential energy of the pair interaction (μJ)

\(V\) :

Particle volume (μm3)

\({v}_{p}:\) :

Particle speed (m/s)

\({\varvec{v}}:\) :

Fluid velocity (m/s)

\({v}_{in}:\) :

First-order incident velocity (m/s)

\({v}_{sc}:\) :

Scattered wave velocity (m/s)

\({Y}_{st}:\) :

Acoustic radiation force function

\(\delta :\) :

Viscous boundary-layer thickness (μm)

\(\varepsilon\) :

Ellipsoidal eccentricity

\({\epsilon }_{p}\) :

Dimensionless scattering parameter

\(\theta\) :

Angular distraction of ellipsoidal particle relative to wave propagation direction (rad)

\({\kappa }_{f}\) :

Fluid compressibility (Pa−1)

\(\stackrel{\sim }{\kappa }\) :

Particle relative compressibility

\({\kappa }_{p}\) :

Particle compressibility (Pa−1)

\(\lambda\) :

Wave length (μm)

\(\mu\) :

Fluid viscosity (Pa s)

\(\upsilon\) :

Poisson’s ratio

\(\rho\) :

Fluid density field (Kg/m3)

\({\rho }_{f}\) :

Fluid unperturbed density (Kg/m3)

\(\stackrel{\sim }{\rho }\) :

Particle relative density

\({\rho }_{p}\) :

Particle density (Kg/m3)

\({\rho }_{in}\) :

First-order incident density (kg/m3)

\(\sigma\) :

Stress (N/m2)

\(\Psi\) :

Acoustic contrast factor

\(\phi\) :

Fluid velocity potential (m2/s)

\({\phi }_{in}\) :

Incident wave velocity potential (m2/s)

\({\phi }_{sc}\) :

Scattered wave potential (m2/s)

\({\phi }_{ext}\) :

External incident wave potential (m2/s)

\({\phi }_{sc}(\left({r}_{p}|{r}_{s}\right))\) :

Scattered potential of the source particle at the probe position (m2/s)

\(\omega\) :

Angular frequency of the acoustic field (rad/s)

0:

Unperturbed state

1:

First-order perturbed state

2:

Second-order perturbed state

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    S. M. Zareei & S. Ziaei-Rad

  2. National University of Singapore, 9 Engineering Drive 1, Singapore, 117575, Singapore

    S. Sepehrirahnama

  3. Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, #16-16 Connexis, Singapore, 138632, Singapore

    M. Jamshidian

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  1. S. M. Zareei
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Zareei, S.M., Sepehrirahnama, S., Jamshidian, M. et al. Three-dimensional numerical simulation of particle acoustophoresis: COMSOL implementation and case studies. Engineering with Computers 39, 735–750 (2023). https://doi.org/10.1007/s00366-022-01663-0

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