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arxiv: 2604.25353 · v1 · submitted 2026-04-28 · ⚛️ physics.flu-dyn

Inertial focusing of neutrally buoyant spherical particle in shallow microchannels

Guiquan Wang , Willem Van Roy , Chengxun Liu , Tim Stakenborg , Benjamin Jones This is my paper

Pith reviewed 2026-05-07 15:09 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords inertial lift forcemicrofluidic channelsparticle focusingPoiseuille flowimmersed boundary methodneutrally buoyant particlesslip boundary conditions
0
0 comments X

The pith

An explicit formula predicts the inertial lift force on neutrally buoyant spherical particles up to 35 percent of channel height at low Reynolds numbers.

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

This paper calculates the lift force on finite-size spherical particles flowing through shallow channels using numerical simulations of planar Poiseuille flow. It derives a simple explicit formula that remains accurate for particle sizes as large as one-third the channel height and for particle Reynolds numbers up to one, even though the near-wall component of the force decreases at the upper end of that range. The work also shows that slip at the channel walls lowers the near-wall lift and moves the stable particle position closer to the wall. Trajectory predictions based on the formula agree with existing experimental measurements of particle migration. The result supplies a practical way to estimate how large particles will move in microfluidic devices without needing case-by-case simulations.

Core claim

Using immersed boundary method simulations of 2D planar Poiseuille flow, the study derives an explicit formula for the lift force that accurately predicts the force for particle radius to height ratios from 0.03 to 0.35 and particle Reynolds numbers up to 1. The formula remains valid even as near-wall lift forces decrease at higher Reynolds numbers within this range. Predictions of particle trajectories using this model match published experimental observations.

What carries the argument

The explicit formula for the lift force obtained from immersed boundary method calculations in planar Poiseuille flow.

If this is right

  • The formula enables direct estimation of particle migration paths in microfluidic devices without repeated simulations.
  • Increased wall slip length reduces near-wall lift force and shifts particle equilibrium positions closer to the walls.
  • The model applies to particles up to 35 percent of channel height, expanding the usable size range beyond earlier limits.
  • Trajectory predictions from the derived model align with experimental data on particle migration.

Where Pith is reading between the lines

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

  • If the formula holds in three-dimensional rectangular channels, it could simplify design of inertial focusing devices for separating particles by size.
  • The observed drop in near-wall lift at higher Reynolds numbers within the stated range indicates that inertial corrections become necessary even at nominally low Reynolds numbers.
  • The same simulation approach could be tested on non-spherical particles or different flow profiles to check whether a similar explicit formula emerges.

Load-bearing premise

The two-dimensional immersed boundary method simulations accurately represent the three-dimensional lift forces experienced by particles in actual microchannels.

What would settle it

Experimental measurements of equilibrium positions or lift forces for particles with radius-to-height ratio 0.35 at particle Reynolds number 1 that differ substantially from the formula's predictions.

Figures

Figures reproduced from arXiv: 2604.25353 by Benjamin Jones, Chengxun Liu, Guiquan Wang, Tim Stakenborg, Willem Van Roy.

Figure 1
Figure 1. Figure 1: FIG. 1: Particle migration in the presence of walls as a funct view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The top panel shows a contour plot of the wall-normal v view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Mesh-convergence study of the lift coefficient view at source ↗
Figure 4
Figure 4. Figure 4: (a), the present results align well with the model predictions of Asmolov et al. [35], which are theoretically valid for a/H ≪ 1 and Rep ≪ 1, while remaining applicable for channel Reynolds number up to Re . 20. Compared to the simulation results of Gupta et al. [51] at Re = 13 and 38, the present lift force is smaller near the wall (zp/H < 0.3) but becomes higher toward the channel center (0.3 < zp/H < 0.… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Lift force under different scaling laws for particle view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Lift coefficient view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Equilibrium positions as a function of particle size view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Effect of Reynolds number on the lift coefficient view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (a) Comparison of single-phase flow profiles between n view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Comparison of the simulated Segré-Silberberg effe view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Comparison of particle lateral migration velociti view at source ↗
read the original abstract

This study investigates the lift force acting on a finite-size, neutrally buoyant spherical particle suspended in a liquid while flowing through a shallow channel at low Reynolds numbers. Using an immersed boundary method, we calculate the lift force for particle radius-to-channel height ratios spanning \(0.03 \leq a/H \leq 0.35\) in 2D planar Poiseuille flows. We propose an explicit formula that accurately predicts the lift force for particles as large as \(a/H = 0.35\) and remains valid for particle Reynolds number \(Re_p \leq 1\), despite a reduction in near-wall lift force at higher \(Re_p\). The influence of slip boundary conditions is also explored, demonstrating that increased slip length reduces near-wall lift force and shifts the particle equilibrium position closer to the wall. Predictions of the particle trajectory from the derived model are in good agreement to the published experimental data. These findings offer a practical framework for estimating the migration of large particles in microfluidic devices.(This article has been accepted for publication in Physics of Fluids. After publication, it will be available via the AIP Publishing website.)

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 manuscript uses 2D immersed-boundary simulations of planar Poiseuille flow to compute the lift force on neutrally buoyant spheres for 0.03 ≤ a/H ≤ 0.35. It proposes an explicit formula asserted to remain accurate up to a/H = 0.35 and Re_p ≤ 1 (despite near-wall lift reduction at higher Re_p), examines the effect of slip boundary conditions on equilibrium position, and reports that integrated trajectories agree with published experimental data.

Significance. If the 2D reduction is shown to be quantitatively reliable, the explicit formula would provide a practical, ready-to-use expression for inertial migration of large particles in shallow microfluidic channels. The reported experimental agreement is a strength, but the absence of 3D benchmarks leaves the central predictive claim dependent on an unverified dimensional approximation.

major comments (2)
  1. [Simulation method and results sections] The central claim rests on 2D IBM results in planar Poiseuille flow being representative of 3D spherical particles. For a/H = 0.35 the particle nearly spans the channel height; 3D flow around the equator will modify both pressure and viscous contributions to lift. No comparison to 3D simulations, to the small-a/H asymptotic lift expressions of Ho & Leal or Schonberg & Hinch, or to any 3D benchmark is described, making the validity range a/H ≤ 0.35 load-bearing and unverified.
  2. [Derivation of the explicit lift-force formula] The explicit formula is stated to be 'derived from simulations.' The manuscript must clarify whether its coefficients were obtained by least-squares fit to the same IBM data later used for validation; if so, the formula is a correlation rather than an independent prediction, and the reported accuracy must be re-evaluated on held-out cases or independent 3D data.
minor comments (2)
  1. [Abstract and validation section] The abstract states 'good agreement' with experiments; quantitative metrics (RMS error in equilibrium position or lift coefficient) should be reported in the main text or a table.
  2. [Results] Notation for the proposed formula (e.g., definition of all non-dimensional groups and the precise functional form) should be collected in one place for reproducibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed and constructive review. We address the two major comments point by point below. Revisions have been made to clarify the nature of the explicit formula and to discuss the limitations of the 2D approximation, while acknowledging that direct 3D validation lies outside the present study.

read point-by-point responses

  1. Referee: The central claim rests on 2D IBM results in planar Poiseuille flow being representative of 3D spherical particles. For a/H = 0.35 the particle nearly spans the channel height; 3D flow around the equator will modify both pressure and viscous contributions to lift. No comparison to 3D simulations, to the small-a/H asymptotic lift expressions of Ho & Leal or Schonberg & Hinch, or to any 3D benchmark is described, making the validity range a/H ≤ 0.35 load-bearing and unverified.

    Authors: We agree that the 2D planar simulations cannot fully capture three-dimensional flow features around the particle equator, particularly when a/H approaches 0.35. The 2D model is motivated by the shallow-channel limit (height ≪ width) in which the mid-plane flow is approximately planar; however, we recognize that this approximation becomes less accurate for large particles. In the revised manuscript we have added an explicit limitations paragraph that (i) cites the Ho & Leal and Schonberg & Hinch asymptotics for small a/H, (ii) notes the absence of 3D benchmarks, and (iii) qualifies the stated validity range accordingly. The experimental trajectory agreement remains the primary external check, but we do not claim it substitutes for 3D lift-force validation. revision: partial

  2. Referee: The explicit formula is stated to be 'derived from simulations.' The manuscript must clarify whether its coefficients were obtained by least-squares fit to the same IBM data later used for validation; if so, the formula is a correlation rather than an independent prediction, and the reported accuracy must be re-evaluated on held-out cases or independent 3D data.

    Authors: The coefficients were obtained by a least-squares fit to the full set of 2D IBM lift-force data. We have revised the text to state explicitly that the formula is an empirical correlation fitted to the simulated cases. No held-out subset was reserved; instead, the independent validation we provide is the integration of the fitted force into particle trajectories that are compared against published experimental data. We have added a sentence noting that the accuracy figures therefore reflect in-sample performance of the correlation within the 2D parameter space. revision: yes

standing simulated objections not resolved
  • Direct three-dimensional simulation benchmarks or comparisons to 3D asymptotic lift expressions for a/H up to 0.35

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external experimental validation

full rationale

The paper computes lift forces via 2D immersed-boundary simulations across the stated a/H range, constructs an explicit formula from those results, and validates resulting trajectory predictions against independent published experimental data. No load-bearing self-citations, self-definitional reductions, or fitted inputs called predictions on the same dataset appear in the abstract or described chain. The central claim is therefore self-contained against an external benchmark rather than tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on numerical simulation results and the assumption that an explicit fit to those results constitutes a general predictive model; full details of any fitted coefficients are not visible in the abstract.

free parameters (1)
  • coefficients in the proposed explicit lift-force formula
    Any closed-form expression fitted to simulation data necessarily introduces free parameters whose values are determined by the numerical results.
axioms (2)
  • domain assumption The flow is two-dimensional planar Poiseuille flow.
    Explicitly stated as the setting for all lift-force calculations.
  • domain assumption The particle is neutrally buoyant, rigid, and spherical.
    Stated in the problem definition and required for the lift-force symmetry.

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Reference graph

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