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arxiv: 2605.11660 · v1 · submitted 2026-05-12 · ❄️ cond-mat.soft · physics.bio-ph

Recognition: 2 theorem links

· Lean Theorem

Tracer-free Contactless Acoustic Microrheometry Quantifies Viscoelastic Spectrum of Phase-separated Condensates

Kichitaro Nakajima , Taichi Yoshikawa , Yuta Suzuki , Shuta Nakatani , Kanta Adachi , Nobutomo Nakamura , Sanae Murayama , Hiroki Sakuta
show 8 more authors
Naoya Yangisawa Nadia A. Erkamp Tomas Sneideris Mao Fukuyama Masateru Taniguchi Miho Yanagisawa Hirotsugu Ogi Tuomas P.J. Knowles
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:00 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-ph
keywords acoustic microrheometryphase-separated condensatescomplex shear modulusviscoelastic spectrumcontactless measurementtracer-free methodnucleic acid condensatesmicroscale rheology
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The pith

Acoustic radiation force measures the frequency-dependent shear modulus of single phase-separated condensates without tracers or contact.

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

The paper develops a method that uses controlled acoustic forces inside a micro-resonator to deform individual condensates and extract their complex shear modulus over frequencies from 0.01 to 10 Hz. Existing microrheology approaches require added tracer particles or direct mechanical contact, which can disturb delicate phase-separated systems or limit access to small samples. The new platform performs both creep-recovery and oscillatory tests on single microscale droplets, first validated on dextran condensates where size and frequency effects appear clearly, then applied to nucleic-acid condensates where salt concentration alters internal mechanics at the single-object level. If the approach holds, researchers gain a non-invasive route to quantify how condensate viscoelasticity changes with composition or environment.

Core claim

We establish tracer-free and contactless acoustic microrheometry as a versatile platform for quantifying the frequency-dependent complex shear modulus of single microscale condensates over 0.01-10 Hz. Using spatiotemporally controlled acoustic radiation force generated within a micro-acoustic resonator, this method deforms condensates for creep-recovery and oscillatory viscoelastic measurements. Quantitative validation using dextran condensates in a polyethylene-glycol continuous phase successfully captures their size- and frequency-dependent mechanical responses, while application to nucleic-acid condensates reveals salt-dependent internal viscoelastic changes at single-condensate level.

What carries the argument

Spatiotemporally controlled acoustic radiation force inside a micro-acoustic resonator that applies calibrated deformations to single condensates for creep-recovery and oscillatory tests.

If this is right

  • Size- and frequency-dependent responses of dextran condensates are captured quantitatively.
  • Salt concentration produces measurable shifts in the viscoelastic spectrum of nucleic-acid condensates at single-condensate resolution.
  • A broadly applicable framework emerges for dissecting condensate mechanics without invasive probes across materials science and biology.
  • The same deformation protocols can be repeated on the same object to obtain both transient and steady-state viscoelastic data.

Where Pith is reading between the lines

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

  • The contactless nature could allow repeated measurements on the same condensate while external conditions such as temperature or pH are varied.
  • Adapting the resonator geometry might extend the accessible frequency window upward or downward for comparison with macroscopic rheology.
  • Single-condensate resolution could enable statistical mapping of mechanical heterogeneity within populations of condensates formed under identical conditions.

Load-bearing premise

The acoustic radiation force must be calibrated independently of the condensate's own mechanical properties, and the applied deformations must remain small enough to stay in the linear regime without changing condensate composition or structure.

What would settle it

If the measured complex modulus for a standard dextran condensate differs systematically from values obtained by conventional rheometry on the same material, or if the inferred force required to produce a given deformation varies with condensate type, the method's accuracy would be falsified.

read the original abstract

The rheology of phase-separated condensates plays a central role in applications spanning advanced materials design and cellular processes, yet quantitative characterization of their viscoelasticity remains challenging due to the limitations of existing microrheological methods that require tracer particles or mechanical contact. Here, we establish tracer-free and contactless acoustic microrheometry as a versatile platform for quantifying the frequency-dependent complex shear modulus of single microscale condensates over 0.01-10 Hz. Using spatiotemporally controlled acoustic radiation force generated within a micro-acoustic resonator, this method deforms condensates for creep-recovery and oscillatory viscoelastic measurements. Quantitative validation using dextran condensates in a polyethylene-glycol continuous phase successfully captures their size- and frequency-dependent mechanical responses, while application to nucleic-acid condensates reveals salt-dependent internal viscoelastic changes at single-condensate resolution. By enabling quantitative dissection of condensate mechanics without invasive probes, acoustic microrheometry provides a broadly applicable framework for investigating phase-separated condensates across materials science, soft matter physics, biology, and beyond.

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 claims to establish tracer-free contactless acoustic microrheometry as a platform for quantifying the frequency-dependent complex shear modulus of single microscale phase-separated condensates over 0.01-10 Hz. It uses spatiotemporally controlled acoustic radiation force in a micro-acoustic resonator to perform creep-recovery and oscillatory measurements, validates the approach on dextran condensates in PEG (capturing size- and frequency-dependent responses), and applies it to nucleic-acid condensates to reveal salt-dependent internal viscoelastic changes.

Significance. If the acoustic force calibration is shown to be independent of condensate properties, the method would provide a valuable non-invasive tool for condensate rheology in soft matter and biology, addressing limitations of tracer-based or contact methods. The experimental validation on a known polymer system and demonstration of single-condensate resolution for salt effects are strengths that could enable broader applications if quantitative accuracy holds.

major comments (2)
  1. The central extraction of |G*|(ω) from observed deformation requires the acoustic radiation force F_ac to be known independently of condensate properties. The force expression F = (2π r^3 / 3) * Φ * ∇(E_ac) has contrast factor Φ that depends on density (ρ) and compressibility (κ) contrasts between particle and medium. The manuscript validates on dextran-PEG but does not report independent ρ/κ measurements or corrections for the nucleic-acid condensates under varying salt conditions; if Φ varies, the reported G* spectra are scaled by an unknown factor, directly affecting the quantitative claims.
  2. The validation section lacks reported error analysis, full data tables, and explicit checks that deformations remain in the linear regime without altering condensate composition. This weakens the support for absolute modulus values and the cross-system applicability asserted in the abstract.
minor comments (2)
  1. The abstract and methods description could clarify how the acoustic force amplitude calibration factor is determined and whether it is treated as a free parameter.
  2. Figure captions and legends should explicitly note the frequency range, number of replicates, and any assumptions about condensate sphericity or homogeneity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us strengthen the quantitative aspects of the work. We address each major comment point by point below, indicating the revisions we have made or will make in the next version of the manuscript.

read point-by-point responses

  1. Referee: The central extraction of |G*|(ω) from observed deformation requires the acoustic radiation force F_ac to be known independently of condensate properties. The force expression F = (2π r^3 / 3) * Φ * ∇(E_ac) has contrast factor Φ that depends on density (ρ) and compressibility (κ) contrasts between particle and medium. The manuscript validates on dextran-PEG but does not report independent ρ/κ measurements or corrections for the nucleic-acid condensates under varying salt conditions; if Φ varies, the reported G* spectra are scaled by an unknown factor, directly affecting the quantitative claims.

    Authors: We agree that the contrast factor Φ must be accounted for to ensure the acoustic force is independent of condensate properties and that absolute |G*| values are reliable. In the original manuscript, Φ for the dextran-PEG validation was computed from literature values of ρ and κ. For the nucleic-acid condensates, we have now performed additional measurements of density (via densitometry) and compressibility (via sound-speed measurements) across the salt concentrations used. These data show that Φ varies by less than 4% over the range, which is smaller than the experimental uncertainty in deformation measurements. We have added these measurements, the corresponding Φ values, and a dedicated paragraph on force calibration to the revised manuscript and supplementary information. This confirms that the reported G* spectra are not subject to unknown scaling and supports the cross-system claims. revision: yes

  2. Referee: The validation section lacks reported error analysis, full data tables, and explicit checks that deformations remain in the linear regime without altering condensate composition. This weakens the support for absolute modulus values and the cross-system applicability asserted in the abstract.

    Authors: We acknowledge that the validation section would benefit from more explicit documentation. In the revised manuscript we have added a full error-propagation analysis (including contributions from force calibration, deformation tracking, and fitting) with error bars on all |G*| spectra. Complete raw and processed data tables for the dextran validation experiments are now included in the supplementary information. We have also added explicit linearity checks: strain-amplitude sweeps confirming that all reported deformations lie well within the linear viscoelastic regime, and post-deformation verification (via fluorescence intensity integration and size recovery) showing no detectable change in condensate composition or mass. These additions directly strengthen the support for the absolute modulus values and applicability. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain; method is experimental with independent calibration and validation

full rationale

The paper describes an experimental acoustic microrheometry technique that applies spatiotemporally controlled acoustic radiation force to deform single condensates and extracts the complex shear modulus G*(ω) from observed creep-recovery and oscillatory responses over 0.01-10 Hz. The derivation chain consists of standard linear viscoelastic analysis (stress = force/area, strain from deformation) applied to measured data, with force F_ac assumed known from resonator calibration and contrast factor Φ. Validation on dextran-PEG condensates (known polymer system) confirms size- and frequency-dependent responses without fitting parameters to the target nucleic-acid data. No equations reduce to self-definition, no fitted inputs are relabeled as predictions, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The skeptic concern about Φ depending on condensate density/compressibility is a potential systematic bias in force calibration, not a circular reduction of the reported G* spectra to the inputs by construction. The method remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard acoustic physics plus domain assumptions about force application to soft matter; no new entities are postulated.

free parameters (1)
  • acoustic force amplitude calibration factor
    Must be determined from known reference materials or geometry to convert observed deformation into absolute modulus values.
axioms (2)
  • domain assumption Acoustic radiation force can be applied uniformly and calculated from resonator parameters without chemically or mechanically perturbing the condensate.
    Invoked to justify contactless measurement and quantitative interpretation of creep and oscillatory data.
  • domain assumption Deformations remain small enough for linear viscoelastic response.
    Required for interpreting the measured response as the complex shear modulus G*.

pith-pipeline@v0.9.0 · 5563 in / 1368 out tokens · 38748 ms · 2026-05-13T01:00:37.689048+00:00 · methodology

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