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arxiv: 2605.08906 · v1 · submitted 2026-05-09 · ⚛️ physics.flu-dyn

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Viscoelastic control of acoustic particle migration and trapping in microchannels

A. K. Sen, T. Sujith

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:22 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords viscoelastic fluidsacoustofluidicsparticle trappingacoustic streamingOldroyd-B modelDeborah numbermicrochannelradiation force
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The pith

Viscoelastic fluids reduce the critical particle size for acoustic trapping in microchannels below Newtonian limits.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates how viscoelasticity alters particle migration and trapping under ultrasound in microchannels. The authors solve the continuity, momentum, and Oldroyd-B constitutive equations via perturbation to obtain the acoustic field and steady streaming, then incorporate a semi-analytical radiation force to track particle force balance. They demonstrate that the Deborah number De and viscous diffusion number Dv govern trajectory shifts and equilibrium locations, with high Dv causing traps to move from bulk to wall, nodal line, center, or symmetry line as De rises. The central result is that the critical particle size separating radiation-dominated from streaming-dominated regimes shrinks with increasing De, permitting control of submicron particles. This establishes viscoelasticity as a tunable mechanism for acoustophoretic transport in complex fluids.

Core claim

In an ultrasonically actuated microchannel filled with an Oldroyd-B fluid, the steady streaming and acoustic radiation forces compete to set particle trajectories, with the transition size between streaming-dominated and radiation-dominated regimes becoming a decreasing function of the Deborah number De at fixed viscous diffusion number Dv; above a threshold De the critical radius falls below its Newtonian value, enabling effective trapping and migration of submicron particles.

What carries the argument

Perturbation expansion of the Oldroyd-B constitutive equations to compute oscillatory flow and steady streaming, combined with a semi-analytical acoustic radiation force model that enters the particle force balance to determine equilibrium locations as functions of De and Dv.

If this is right

  • At high Dv, raising De moves equilibrium trapping from the bulk region successively to the channel wall, pressure nodal line, channel center, or ultrasound symmetry line.
  • The critical particle size for radiation dominance decreases with De, becoming significantly smaller than the Newtonian value.
  • Particle trajectories are controlled primarily by the two dimensionless groups De and Dv.
  • Viscoelasticity supplies new tunable mechanisms for migration and trapping that are absent in Newtonian acoustofluidics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Viscoelastic sample media could be used directly in acoustofluidic chips to manipulate submicron biological particles without dilution or stronger transducers.
  • The De–Dv parameter map supplies a design rule for choosing polymer concentration or frequency to place traps at desired positions for a given particle size.
  • Similar reductions in critical size may occur in other viscoelastic or shear-thinning fluids, suggesting broader non-Newtonian acoustofluidic applications.

Load-bearing premise

The perturbation solution of the Oldroyd-B equations together with the semi-analytical radiation force model accurately captures the steady streaming flows and the net force balance on particles inside the microchannel geometry.

What would settle it

An experiment in which the measured critical particle radius or the observed trapping location remains unchanged as the fluid relaxation time (hence Deborah number) is increased at fixed viscous diffusion number would falsify the predicted dependence.

Figures

Figures reproduced from arXiv: 2605.08906 by A. K. Sen, T. Sujith.

Figure 1
Figure 1. Figure 1: (a) Schematic of the domain of study, corresponding to the cross section of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Schematic of the experimental setup. Inset shows the cross section of the [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Schematic of the microchannel illustrating the top (T), center (C), and bottom [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Schematic representation of the distribution of 5 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Schematic of the microchannel illustrating the different perspectives used [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Schematic of the microchannel illustrating the top (T), center (C), and bottom [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Schematic of the microchannel illustrating the different perspectives used [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Theoretically predicted trajectories of a 4 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Theoretical results showing the variation of dimensionless particle velocity [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a) Spatial variation of the dimensionless i. acoustic radiation force and ii. [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Early- and late-time analysis of particle migration in the acoustic streaming [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Early- and late-time analysis of particle migration at [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: (a) Early- and late-time analysis of particle migration in the pressure-nodal-line [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Early- and late-time analysis of particle migration in the pressure-nodal-line [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: (a) Early- and late-time analysis of particle migration in the pressure-nodal [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: (a) Early- and late-time analysis of particle migration in the center-point (CP) [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: (a) Early- and late-time analysis of particle migration in the ultrasound symmetry [PITH_FULL_IMAGE:figures/full_fig_p028_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: (a) Variation of the normalized critical particle diameter [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Variation of the dimensionless streaming-induced drag force, [PITH_FULL_IMAGE:figures/full_fig_p030_19.png] view at source ↗
read the original abstract

Particle migration and trapping in ultrasonically actuated microscale flows arise from the competition between acoustic radiation forces and streaming-induced drag. While these mechanisms are well understood in Newtonian fluids, the role of fluid viscoelasticity in governing particle dynamics remains largely unexplored. Here, we investigate particle transport and trapping in a viscoelastic fluid within an ultrasonically excited microchannel under the combined action of acoustic streaming and radiation forces. Using a perturbation framework, we solve the continuity, momentum and constitutive equations for an Oldroyd-B fluid to obtain the oscillatory acoustic field and the resulting steady streaming flows in the bulk and near-wall boundary layers. Acoustic radiation forces, incorporated through a semi-analytical model, drives particle migration, while streaming-induced drag can oppose, alter or suppress trapping. We show that particle trajectories and equilibrium trapping locations are governed primarily by the Deborah number ($De$) and viscous diffusion number ($Dv$). At high $Dv$, increasing $De$ shifts the trapping location from the bulk region to the channel wall, pressure nodal line, channel centre or ultrasound symmetry line. We further determine the critical particle size governing the transition between radiation-dominated and streaming-dominated regimes as a function of $De$ and $Dv$. The critical particle size can become significantly smaller than that in a Newtonian fluid, enabling effective manipulation of submicron particles and overcoming a key limitation of conventional acoustofluidics. These results demonstrate how viscoelasticity fundamentally modifies acoustophoretic transport and establish new mechanisms for tunable particle migration and trapping in complex fluids.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a perturbation solution for the Oldroyd-B constitutive equations in an ultrasonically actuated microchannel to obtain the oscillatory acoustic field and steady streaming flows. It then couples these to a semi-analytical (Newtonian-derived) acoustic radiation force model to predict particle trajectories, equilibrium trapping locations, and the critical particle radius separating radiation-dominated and streaming-dominated regimes as functions of the Deborah number De and viscous diffusion number Dv. The central claim is that increasing De at fixed Dv can shift trapping locations and substantially reduce the critical particle size relative to Newtonian fluids, enabling submicron particle manipulation.

Significance. If the hybrid fluid–force model is accurate, the work identifies a new viscoelastic mechanism for lowering the size threshold in acoustophoretic trapping, which would be a notable advance for handling submicron particles in complex fluids. The parametric exploration of De and Dv and the boundary-layer treatment of streaming are technically interesting contributions, but the absence of any validation data or full derivation details limits immediate impact.

major comments (2)
  1. [Acoustic radiation force incorporation and particle force balance] The acoustic radiation force is incorporated via a semi-analytical model taken from the Newtonian literature (Gor'kov-type or equivalent). No re-derivation of the time-averaged Maxwell stress or particle–fluid interaction terms is provided under the Oldroyd-B constitutive relation. This omission is load-bearing for the headline result that the critical radius decreases significantly with De, because any De-dependent correction to the force integral would alter the radiation-versus-streaming balance precisely in the regime De ≳ 1 where the reduction is claimed.
  2. [Results on critical particle size and trapping locations] The manuscript provides no experimental validation, numerical benchmarks, or comparison against fully resolved simulations for either the streaming velocity field or the predicted critical particle sizes. Without such checks, it is impossible to assess whether the perturbation framework plus the hybrid force model quantitatively captures the steady-state particle equilibrium.
minor comments (2)
  1. The abstract and text refer to “semi-analytical model” for radiation forces without citing the specific Newtonian expression or stating the assumptions under which it remains valid for viscoelastic fluids.
  2. Notation for the viscous diffusion number Dv should be defined explicitly at first use and distinguished from the usual viscous penetration depth scaling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments highlight important aspects of our modeling approach and the need for clarity on its assumptions. We address each major comment below and have made targeted revisions to improve the manuscript, including additional discussion of model limitations and expanded benchmarking against known limits.

read point-by-point responses

  1. Referee: The acoustic radiation force is incorporated via a semi-analytical model taken from the Newtonian literature (Gor'kov-type or equivalent). No re-derivation of the time-averaged Maxwell stress or particle–fluid interaction terms is provided under the Oldroyd-B constitutive relation. This omission is load-bearing for the headline result that the critical radius decreases significantly with De, because any De-dependent correction to the force integral would alter the radiation-versus-streaming balance precisely in the regime De ≳ 1 where the reduction is claimed.

    Authors: We acknowledge that the acoustic radiation force is implemented using the established Newtonian Gor'kov framework applied to the viscoelastic acoustic fields obtained from our perturbation solution. A complete re-derivation of the time-averaged force including Oldroyd-B stress contributions to the particle-fluid interaction would require a separate asymptotic analysis of the scattered field around the particle and is outside the scope of the present work, which centers on the modification of the background flow by viscoelasticity. In the regime of interest (particle radius much smaller than the acoustic wavelength), the leading-order radiation force is governed by the far-field oscillatory pressure and velocity, which are directly provided by our Oldroyd-B solution. The reported reduction in critical radius with increasing De arises principally from the viscoelastic enhancement of the steady streaming velocity (and thus the opposing drag), rather than from changes to the radiation force itself. We have added a dedicated paragraph in the revised manuscript justifying this hybrid modeling choice, discussing its expected validity for De ≲ O(1), and explicitly noting that De-dependent corrections to the force could be explored in future extensions. revision: partial

  2. Referee: The manuscript provides no experimental validation, numerical benchmarks, or comparison against fully resolved simulations for either the streaming velocity field or the predicted critical particle sizes. Without such checks, it is impossible to assess whether the perturbation framework plus the hybrid force model quantitatively captures the steady-state particle equilibrium.

    Authors: We agree that quantitative validation against experiments or fully resolved simulations would increase confidence in the predicted critical sizes and equilibrium locations. The present study is a theoretical investigation that derives a perturbation solution for the Oldroyd-B acoustic and streaming fields and couples it to an existing radiation-force expression. We have benchmarked the model by recovering the Newtonian (De = 0) limits for both the streaming velocity and the critical radius, as well as by verifying consistency with known asymptotic expressions for boundary-layer streaming. These checks are reported in the results and discussion sections. We have expanded the manuscript with additional analytical comparisons and a clearer statement of the model's assumptions and range of applicability. Full experimental validation or direct numerical simulations of the coupled viscoelastic-particle problem lie beyond the scope of this work and are identified as directions for future research. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper solves the Oldroyd-B continuity, momentum and constitutive equations via a perturbation expansion to obtain the oscillatory acoustic field and steady streaming velocity (bulk and boundary layers). Particle motion is then obtained by balancing this streaming drag against a semi-analytical radiation force taken from the Newtonian literature. The critical particle size is computed directly from that force balance as a function of the independent dimensionless groups De and Dv; no parameter is fitted to the target quantity and then re-used as a prediction. No self-citation is invoked as a uniqueness theorem or load-bearing premise, and the radiation-force model is not re-derived inside the paper, so the result is not equivalent to its inputs by construction. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the Oldroyd-B constitutive model under small-amplitude acoustic perturbation and on the accuracy of the semi-analytical radiation-force expression; no new entities are postulated.

axioms (2)
  • domain assumption Oldroyd-B constitutive relation for viscoelastic fluid
    Invoked to close the momentum and constitutive equations in the perturbation expansion for the oscillatory acoustic field and steady streaming.
  • domain assumption Semi-analytical model for acoustic radiation force
    Used to drive particle migration; its form is taken from prior Newtonian literature and assumed to remain valid in the viscoelastic case.

pith-pipeline@v0.9.0 · 5568 in / 1435 out tokens · 41064 ms · 2026-05-12T02:22:08.820414+00:00 · methodology

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