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Focusing patterns of spherical particles in a viscoelastic flow through square channels

Published online by Cambridge University Press:  06 November 2025

Hiroshi Yamashita Open the ORCID record for Hiroshi Yamashita [Opens in a new window] ,
Yuta Miki ,
Daisuke Yoneyama ,
Kento Higashi ,
Takuma Tsukasa ,
Yoshiyuki Tagawa Open the ORCID record for Yoshiyuki Tagawa [Opens in a new window] ,
Naoto Yokoyama Open the ORCID record for Naoto Yokoyama [Opens in a new window] ,
Tomoaki Itano Open the ORCID record for Tomoaki Itano [Opens in a new window]  and
Masako Sugihara-Seki Open the ORCID record for Masako Sugihara-Seki [Opens in a new window]
Hiroshi Yamashita*
Affiliation:
Graduate School of Integrated Sciences for Life, Hiroshima University , Higashihiroshima, Hiroshima 739-8521, Japan
Yuta Miki
Affiliation:
Department of Pure and Applied Physics, Kansai University, Suita, Osaka 564-8680, Japan
Daisuke Yoneyama
Affiliation:
Department of Pure and Applied Physics, Kansai University, Suita, Osaka 564-8680, Japan
Kento Higashi
Affiliation:
Department of Pure and Applied Physics, Kansai University, Suita, Osaka 564-8680, Japan
Takuma Tsukasa
Affiliation:
Department of Pure and Applied Physics, Kansai University, Suita, Osaka 564-8680, Japan
Yoshiyuki Tagawa
Affiliation:
Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan
Naoto Yokoyama
Affiliation:
Department of Mechanical Engineering, Tokyo Denki University, Adachi, Tokyo 120-8551, Japan
Tomoaki Itano
Affiliation:
Department of Pure and Applied Physics, Kansai University, Suita, Osaka 564-8680, Japan
Masako Sugihara-Seki
Affiliation:
Department of Pure and Applied Physics, Kansai University, Suita, Osaka 564-8680, Japan
*
Corresponding author: Hiroshi Yamashita, hyamashi@hiroshima-u.ac.jp
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Abstract

The inertial migration of neutrally buoyant spherical particles in viscoelastic fluids flowing through square channels is experimentally and numerically studied. In the experiments, using dilute aqueous solutions of polymers with various concentrations that have nearly constant viscosities, we measured the distribution of suspended particles in downstream cross-sections for the Reynolds number ($\textit{Re}$) up to 100 and the elasticity number ($El$) up to 0.07. There are several focusing patterns of the particles, such as four-point focusing near the centre of the channel faces on the midlines for low $\textit{El}$ and/or high $\textit{Re}$, four-point focusing on the diagonals for medium $\textit{El}$, single-point focusing at the channel centre for relatively high $\textit{El}$ and low $\textit{Re}$, and five-point focusing near the four corners and the channel centre for high $\textit{El}$ and very low $\textit{Re}$. Among these focusing patterns, various types of particle distributions suggesting the presence of a new equilibrium position located between the midline and the diagonal, and multistable states of different equilibrium positions were observed. In general, as $\textit{El}$ increases from 0 at a constant $\textit{Re}$, the particle focusing positions shift from the midline to the diagonal in the azimuthal direction first, and then inward in the radial direction to the channel centre. These focusing patterns and their transitions were numerically well reproduced based on a FENE-P model with measured values of viscosity and relaxation time. Using the numerical results, the experimentally observed focusing patterns of particles are elucidated in terms of the fluid elasticity-induced lift and the wall-induced elastic lift.

JFM classification

Non-Newtonian Flows: Viscoelasticity Micro-/Nano-fluid dynamics: Microfluidics

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JFM Papers
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Journal of Fluid Mechanics , Volume 1022 , 10 November 2025 , A44
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© The Author(s), 2025. Published by Cambridge University Press

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