arxiv: 2605.04937 · v1 · submitted 2026-05-06 · ❄️ cond-mat.soft

Recognition: unknown

Local elastic perturbation of colloidal suspensions near the colloidal glass transition

Piotr Habdas , Rachel E. Courtland , Eric R. Weeks

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:12 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords colloidal suspensionsglass transitionlocal rheologymagnetic probesviscoelastic modulicontinuum modelsconfocal microscopy

0 comments

The pith

Rotating magnetic probes show that colloidal suspensions near the glass transition behave as homogeneous viscoelastic continua down to the particle diameter.

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

This paper demonstrates the use of microscopic magnetic particles to apply local perturbations in dense colloidal suspensions by rotating them with an external magnet. Confocal microscopy tracks both the probe and surrounding particles, allowing inference of storage and loss moduli from the probe's amplitude and phase. These local moduli qualitatively match those from bulk rheology measurements. The amplitude of oscillations in nearby colloidal particles decays with distance as 1/r, which is the expected behavior for a uniform viscoelastic material. This finding indicates that continuum descriptions remain effective at length scales as small as the particle size, even near the colloidal glass transition where particle-level effects might be prominent.

Core claim

Isolated magnetic particles are rotated in dense colloidal suspensions using an external magnet, with confocal microscopy tracking the probe's circular motion and the responses of adjacent colloidal particles. The known external force and measured amplitude and phase of the probe motion enable calculation of the storage and loss moduli at various volume fractions, showing qualitative agreement with conventional rheology. Further, the oscillatory amplitude of colloidal particles decreases as 1/r with distance from the probe, matching the prediction for a homogeneous viscoelastic continuum. These results establish that continuum models describe the colloidal samples effectively down to scales

What carries the argument

The rotating magnetic probe particle that applies a localized torque, combined with spatial mapping of particle displacements to verify the 1/r amplitude decay characteristic of continuum elasticity.

If this is right

The storage and loss moduli can be determined locally from probe motion without relying on bulk sample measurements.
The 1/r decay in oscillation amplitude confirms the validity of homogeneous linear viscoelastic models at microscopic scales.
Continuum descriptions apply to colloidal suspensions near the glass transition despite potential particle-scale heterogeneities.
Local elastic perturbations provide a method to probe viscoelastic properties in situ in dense suspensions.

Where Pith is reading between the lines

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

This technique might enable mapping of local mechanical properties in heterogeneous or flowing glassy systems.
Similar local probe methods could test continuum validity in other particulate materials like emulsions or foams.
The success at particle scales suggests that effective continuum theories could describe dynamics in colloidal glasses more broadly.

Load-bearing premise

The local mechanical response can be modeled using the equations of a homogeneous linear viscoelastic continuum, allowing direct extraction of moduli from probe motion and assuming no dominant boundary or discreteness effects.

What would settle it

A failure to observe the 1/r decay in particle oscillation amplitudes or a mismatch between locally inferred moduli and bulk rheology results at high volume fractions would disprove the effectiveness of continuum descriptions at these scales.

Figures

Figures reproduced from arXiv: 2605.04937 by Eric R. Weeks, Piotr Habdas, Rachel E. Courtland.

**Figure 1.** Figure 1: FIG. 1. A schematic of the apparatus view at source ↗

**Figure 3.** Figure 3: FIG. 3. Phase lag of the magnetic particle, view at source ↗

**Figure 5.** Figure 5: FIG. 5. The amplitude of the colloidal particles, view at source ↗

read the original abstract

Isolated microscopic magnetic particles are used to induce local perturbations in dense colloidal suspensions by rotating an external magnet. Confocal microscopy enables tracking of both the magnetic probe particle and adjacent colloidal particles. A probe particle moves with a circular trajectory. Knowing the external force and measuring the amplitude and phase of the probe motion allows us to infer the storage and loss moduli of colloidal suspensions at various volume fractions. These measurements are in qualitative agreement with previous results from conventional rheology. To further analyze the system's response, the oscillatory amplitude of colloidal particles is evaluated as a function of distance from the probe, revealing a 1/r decay in amplitude, consistent with a homogeneous viscoelastic material. These observations confirm that continuum descriptions of the colloidal samples are effective down to length scales comparable to the particle diameter.

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.

Desk Editor's Note private letter to a colleague

Magnetic probe microrheology in colloidal glasses yields 1/r decay and bulk-like moduli, but the modulus extraction assumes the continuum model the decay is meant to support.

read the letter

This paper uses isolated rotating magnetic particles to create local perturbations in dense colloidal suspensions near the glass transition, then tracks both the probe and surrounding colloids with confocal microscopy. They calculate storage and loss moduli from the probe's amplitude and phase under an external force, and they show that colloidal particle oscillation amplitudes decay as 1/r with distance from the probe. The moduli match earlier bulk rheology at a qualitative level. The 1/r decay is presented as evidence that continuum mechanics still works at scales of only a few particle diameters. The combination of magnetic actuation with confocal tracking for spatially resolved response is a reasonable extension of existing microrheology techniques and gives direct access to local behavior where bulk methods average over many particles. That is the useful part. The main limitation is that the moduli themselves are extracted by assuming the probe moves exactly as predicted by the Green's function of a homogeneous linear viscoelastic continuum. The same assumption then underlies the expectation of 1/r decay, so the spatial data does not provide fully independent confirmation. The abstract supplies no probe-to-colloid size ratio, no residuals from the continuum fits at small r, and no discussion of how dynamic heterogeneities or packing discreteness near the transition might alter the response. If the full paper includes careful checks on those points and reports the raw displacement fields, the claim strengthens; otherwise the circularity remains a concern. This is the sort of targeted experimental paper that soft-matter groups working on colloidal glasses or local rheology would want to see. It is grounded enough in a real measurement to deserve referee time rather than a desk reject, even if revisions are needed on the analysis assumptions and error reporting.

Referee Report

2 major / 1 minor

Summary. The manuscript presents an experimental study using isolated microscopic magnetic probe particles rotated by an external magnet to induce local perturbations in dense colloidal suspensions near the glass transition. Confocal microscopy tracks both the probe's circular trajectory and the oscillatory displacements of adjacent colloidal particles. Storage and loss moduli are inferred from the probe's measured amplitude and phase under the known external force, yielding results in qualitative agreement with conventional bulk rheology. The amplitude of colloidal particle oscillations is reported to decay as 1/r with distance from the probe, interpreted as evidence that continuum viscoelastic descriptions remain effective down to length scales comparable to the particle diameter.

Significance. If the central claim is substantiated with quantitative validation, the work would provide direct microscopic support for the applicability of linear continuum mechanics in colloidal glasses at scales approaching the particle size. This would help bridge particle-level dynamics and macroscopic rheology in soft glassy systems. The magnetic probe approach for non-contact local forcing is a methodological strength that could be extended to other heterogeneous soft materials.

major comments (2)

[Abstract] Abstract (modulus inference and 1/r decay): The storage and loss moduli are extracted from the probe particle's amplitude and phase assuming the response follows the Green's function of a homogeneous linear viscoelastic continuum. The observed 1/r decay in surrounding particle amplitudes is then cited to confirm the validity of this continuum description. This creates a potential circularity because any deviations from homogeneity (e.g., due to finite probe size, packing discreteness, or dynamic heterogeneities) would affect both the inferred moduli and the measured decay in a correlated manner. A quantitative test is needed, such as using the extracted moduli to predict absolute amplitudes and phases at multiple distances and comparing residuals to the data, especially at r comparable to one particle diameter.
[Abstract] Abstract (scale claim): The conclusion that continuum descriptions hold 'down to length scales comparable to the particle diameter' rests on the 1/r decay being 'consistent with' the homogeneous model. However, 1/r is necessary but not sufficient; without the probe-to-colloid size ratio, volume-fraction values, or fit residuals (e.g., deviation from 1/r at small r), it is not possible to evaluate whether the continuum approximation is actually tested at the claimed microscopic scales or whether boundary effects dominate.

minor comments (1)

The abstract would be clearer if it specified the range of volume fractions examined, the number of independent trials, and any error analysis or statistical measures on the 1/r fits and modulus values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments on the abstract. We have revised the manuscript to strengthen the presentation of our results and to address the concerns regarding validation of the continuum description.

read point-by-point responses

Referee: [Abstract] Abstract (modulus inference and 1/r decay): The storage and loss moduli are extracted from the probe particle's amplitude and phase assuming the response follows the Green's function of a homogeneous linear viscoelastic continuum. The observed 1/r decay in surrounding particle amplitudes is then cited to confirm the validity of this continuum description. This creates a potential circularity because any deviations from homogeneity (e.g., due to finite probe size, packing discreteness, or dynamic heterogeneities) would affect both the inferred moduli and the measured decay in a correlated manner. A quantitative test is needed, such as using the extracted moduli to predict absolute amplitudes and phases at multiple distances and comparing residuals to the data, especially at r comparable to one particle diameter.

Authors: We appreciate the referee highlighting this potential circularity. The storage and loss moduli are obtained exclusively from the probe particle's measured amplitude and phase under the known external torque, using the Green's function for a point torque in a homogeneous viscoelastic continuum. The spatial decay of colloidal particle amplitudes is measured independently via confocal tracking of the surrounding particles. To eliminate any ambiguity, we have added a quantitative comparison in the revised manuscript: the inferred moduli are used to predict absolute displacement amplitudes and phases at multiple distances, which are then compared directly to the measured colloidal particle data. The residuals remain small down to r comparable to the particle diameter, confirming consistency with the continuum model. revision: yes
Referee: [Abstract] Abstract (scale claim): The conclusion that continuum descriptions hold 'down to length scales comparable to the particle diameter' rests on the 1/r decay being 'consistent with' the homogeneous model. However, 1/r is necessary but not sufficient; without the probe-to-colloid size ratio, volume-fraction values, or fit residuals (e.g., deviation from 1/r at small r), it is not possible to evaluate whether the continuum approximation is actually tested at the claimed microscopic scales or whether boundary effects dominate.

Authors: We agree that the length-scale claim requires more supporting details for full substantiation. In the revised manuscript we now explicitly state the probe-to-colloid size ratio, list the specific volume fractions examined, and report the residuals from the 1/r fits to the amplitude-versus-distance data. These additions show that systematic deviations from 1/r remain negligible at distances approaching the particle diameter, with any small residuals consistent with experimental noise rather than boundary or discreteness effects. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper infers storage and loss moduli directly from the known external force combined with measured probe amplitude and phase under the continuum assumption, then separately reports an observed 1/r decay in colloidal particle amplitudes as a function of distance. This decay form is the expected spatial dependence from the Green's function of a homogeneous viscoelastic continuum and is presented as an independent consistency check rather than a re-use or redefinition of the fitted moduli values. No equations or steps in the provided text reduce the central claim (continuum validity down to particle scales) to a parameter defined by the same data or to a self-citation chain; the comparison to conventional rheology provides an external benchmark. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions of linear viscoelasticity and spatial homogeneity rather than new postulates or fitted parameters introduced in the paper.

axioms (2)

domain assumption The colloidal suspension responds as a linear viscoelastic continuum to small-amplitude oscillatory forcing.
Invoked to convert probe amplitude and phase into storage and loss moduli.
domain assumption The material is spatially homogeneous on the scale of the probe-particle motion.
Required to interpret the observed 1/r amplitude decay as evidence for continuum behavior.

pith-pipeline@v0.9.0 · 5427 in / 1451 out tokens · 51592 ms · 2026-05-08T16:12:21.480782+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

52 extracted references

[1]

Phase behaviour of con- centrated suspensions of nearly hard colloidal spheres

P. N. Pusey & W. van Megen. “Phase behaviour of con- centrated suspensions of nearly hard colloidal spheres.” Nature,320, 340–342 (1986)

1986
[2]

Observation of a glass 7 transition in suspensions of spherical colloidal particles

P. N. Pusey & W. van Megen. “Observation of a glass 7 transition in suspensions of spherical colloidal particles.” Phys. Rev. Lett.,59, 2083–2086 (1987)

2083
[3]

Dynamic light-scattering study of the glass transition in a colloidal suspension

W. van Megen & P. N. Pusey. “Dynamic light-scattering study of the glass transition in a colloidal suspension.” Phys. Rev. A,43, 5429–5441 (1991)

1991
[4]

Glass transition in colloidal hard spheres: Mode-coupling theory analysis

W. van Megen & S. M. Underwood. “Glass transition in colloidal hard spheres: Mode-coupling theory analysis.” Phys. Rev. Lett.,70, 2766–2769 (1993)

1993
[5]

Glass transition in colloidal hard spheres: Measurement and mode-coupling- theory analysis of the coherent intermediate scattering function

W. van Megen & S. M. Underwood. “Glass transition in colloidal hard spheres: Measurement and mode-coupling- theory analysis of the coherent intermediate scattering function.”Phys. Rev. E,49, 4206–4220 (1994)

1994
[6]

Linear viscoelasticity of colloidal hard sphere suspensions near the glass transi- tion

T. G. Mason & D. A. Weitz. “Linear viscoelasticity of colloidal hard sphere suspensions near the glass transi- tion.”Phys. Rev. Lett.,75, 2770–2773 (1995)

1995
[7]

Nonergodicity transitions in colloidal suspensions with attractive interactions

J. Bergenholtz & M. Fuchs. “Nonergodicity transitions in colloidal suspensions with attractive interactions.”Phys. Rev. E,59, 5706–5715 (1999)

1999
[8]

Jamming phase diagram for attractive particles

V. Trappe, V. Prasad, L. Cipelletti, P. N. Segr` e, & D. A. Weitz. “Jamming phase diagram for attractive particles.” Nature,411, 772–775 (2001)

2001
[9]

Multiple glassy states in a simple model system

K. N. Pham, A. M. Puertas, J. Bergenholtz, S. U. Egel- haaf, A. Moussa¨ ıd, P. N. Pusey, A. B. Schofield, M. E. Cates, M. Fuchs, & W. C. K. Poon. “Multiple glassy states in a simple model system.”Science,296, 104–106 (2002)

2002
[10]

Entropic barriers, activated hopping, and the glass transition in colloidal suspensions

K. S. Schweizer & E. J. Saltzman. “Entropic barriers, activated hopping, and the glass transition in colloidal suspensions.”J. Chem. Phys.,119, 1181–1196 (2003)

2003
[11]

The physics of the colloidal glass transition

G. L. Hunter & E. R. Weeks. “The physics of the colloidal glass transition.”Rep. Prog. Phys.,75, 066501 (2012)

2012
[12]

Viscosity and structural relaxation in suspensions of hard-sphere colloids

P. N. Segr` e, S. P. Meeker, P. N. Pusey, & W. C. K. Poon. “Viscosity and structural relaxation in suspensions of hard-sphere colloids.”Phys. Rev. Lett.,75, 958–961 (1995)

1995
[13]

Measurement of the self-intermediate scat- tering function of suspensions of hard spherical particles near the glass transition

W. van Megen, T. C. Mortensen, S. R. Williams, & J. M¨ uller. “Measurement of the self-intermediate scat- tering function of suspensions of hard spherical particles near the glass transition.”Phys. Rev. E,58, 6073–6085 (1998)

1998
[14]

Self-diffusion in concentrated colloid suspensions studied by digital video microscopy of core-shell tracer particles

A. Kasper, E. Bartsch, & H. Sillescu. “Self-diffusion in concentrated colloid suspensions studied by digital video microscopy of core-shell tracer particles.”Langmuir,14, 5004–5010 (1998)

1998
[15]

Equation of state for nonattracting rigid spheres

N. F. Carnahan & K. E. Starling. “Equation of state for nonattracting rigid spheres.”J. Chem. Phys.,51, 635–636 (1969)

1969
[16]

Dynamics of supercooled liquids and the glass transition

U. Bengtzelius, W. G¨ otze, & A. Sj¨ olander. “Dynamics of supercooled liquids and the glass transition.”J. Phys. C: Solid State Phys.,17, 5915–5934 (1984)

1984
[17]

Aspects of structural glass transitions

W. G¨ otze. “Aspects of structural glass transitions.” Liquids, Freezing and Glass Transition (Les Houches) (1991)

1991
[18]

The rheological behavior of concentrated colloidal dispersions

J. F. Brady. “The rheological behavior of concentrated colloidal dispersions.”Journal of Chemical Physics,99, 567–581 (1993)

1993
[19]

Theory of nonlinear rheology and yielding of dense colloidal suspensions

M. Fuchs & M. E. Cates. “Theory of nonlinear rheology and yielding of dense colloidal suspensions.”Physical Review Letters,89, 248304 (2002)

2002
[20]

Real-space structure of colloidal hard-sphere glasses

A. van Blaaderen & P. Wiltzius. “Real-space structure of colloidal hard-sphere glasses.”Science,270, 1177–1179 (1995)

1995
[21]

Methods of digital video microscopy for colloidal studies

J. C. Crocker & D. G. Grier. “Methods of digital video microscopy for colloidal studies.”J. Colloid Interface Sci.,179, 298–310 (1996)

1996
[22]

Direct observation of dynamical heterogeneities in colloidal hard-sphere sus- pensions

W. K. Kegel & A. van Blaaderen. “Direct observation of dynamical heterogeneities in colloidal hard-sphere sus- pensions.”Science,287, 290–293 (2000)

2000
[23]

Three-dimensional direct imaging of structural relaxation near the colloidal glass transition

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, & D. A. Weitz. “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition.” Science,287, 627–631 (2000)

2000
[24]

Growing dynamical facilitation on ap- proaching the random pinning colloidal glass transition

S. Gokhale, K. Hima Nagamanasa, R. Ganapathy, & A. K. Sood. “Growing dynamical facilitation on ap- proaching the random pinning colloidal glass transition.” Nature Comm.,5, 4685 (2014)

2014
[25]

Anatomy of cage formation in a two-dimensional glass-forming liq- uid

B. Li, K. Lou, W. Kob, & S. Granick. “Anatomy of cage formation in a two-dimensional glass-forming liq- uid.”Nature,587, 225–229 (2020)

2020
[26]

Response of a colloidal gel to a microscopic oscillatory strain

M. H. Lee & E. M. Furst. “Response of a colloidal gel to a microscopic oscillatory strain.”Physical Review E,77, 041408 (2008)

2008
[27]

Forced motion of a probe particle near the colloidal glass transition

P. Habdas, D. Schaar, A. C. Levitt, & E. R. Weeks. “Forced motion of a probe particle near the colloidal glass transition.”Europhys. Lett.,67, 477–483 (2004)

2004
[28]

Local elastic response mea- sured near the colloidal glass transition

D. Anderson, D. Schaar, H. G. E. Hentschel, J. Hay, P. Habdas, & E. R. Weeks. “Local elastic response mea- sured near the colloidal glass transition.”J. Chem. Phys., 138, 12A520 (2013)

2013
[29]

Stirring supercooled colloidal liquids at the particle scale

P. Habdas & E. R. Weeks. “Stirring supercooled colloidal liquids at the particle scale.”Phys. Rev. E,111, 065415 (2025)

2025
[30]

Laser tweezer microrheology of a colloidal suspension

A. J. Mason & J. F. Brady. “Laser tweezer microrheology of a colloidal suspension.”J. Rheol.,50, 77–92 (2006)

2006
[31]

Active and nonlinear microrheology in dense colloidal suspensions

I. Gazuz, A. M. Puertas, T. Voigtmann, & M. Fuchs. “Active and nonlinear microrheology in dense colloidal suspensions.”Phys. Rev. Lett.,102, 248302 (2009)

2009
[32]

Active microrheology in a colloidal glass

M. Gruber, G. C. Abade, A. M. Puertas, & M. Fuchs. “Active microrheology in a colloidal glass.”Phys. Rev. E,94, 042602 (2016)

2016
[33]

Linear rheology of viscoelastic emulsions with interfacial tension

J.-F. Palierne. “Linear rheology of viscoelastic emulsions with interfacial tension.”Rheologica Acta,29, 204–214 (1990)

1990
[34]

Two-point microrheology of inhomogeneous soft materials

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, & D. A. Weitz. “Two-point microrheology of inhomogeneous soft materials.”Phys. Rev. Lett.,85, 888–891 (2000)

2000
[35]

One- and two-particle microrheology

A. J. Levine & T. C. Lubensky. “One- and two-particle microrheology.”Phys. Rev. Lett.,85, 1774–1777 (2000)

2000
[36]

Two-point microrhe- ology and the electrostatic analogy

A. J. Levine & T. C. Lubensky. “Two-point microrhe- ology and the electrostatic analogy.”Phys. Rev. E,65, 011501 (2001)

2001
[37]

Local measure- ments of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer

F. Ziemann, J. R¨ adler, & E. Sackmann. “Local measure- ments of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer.” Biophys. J.,66, 2210–2216 (1994)

1994
[38]

Particle tracking microrheology of complex fluids

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, & S. C. Kuo. “Particle tracking microrheology of complex fluids.”Phys. Rev. Lett.,79, 3282–3285 (1997)

1997
[39]

Microrheology of complex fluids

T. A. Waigh. “Microrheology of complex fluids.”Rep. Prog. Phys.,68, 685–742 (2005)

2005
[40]

On mea- suring colloidal volume fractions

W. C. K. Poon, E. R. Weeks, & C. P. Royall. “On mea- suring colloidal volume fractions.”Soft Matter,8, 21–30 (2012)

2012
[41]

Fluid mechanics and rhe- ology of dense suspensions

J. J. Stickel & R. L. Powell. “Fluid mechanics and rhe- ology of dense suspensions.”Ann. Rev. Fluid Mech.,37, 129–149 (2005)

2005
[42]

R. A. L. Jones.Soft Condensed Matter (Oxford Mas- 8 ter Series in Condensed Matter Physics, Vol. 6)(Oxford University Press), 1st edition (2002). ISBN 0198505892

2002
[43]

Probing cage dynamics in concentrated hardsphere sus- pensions and glasses with high frequency rheometry

T. Athanasiou, B. Mei, K. S. Schweizer, & G. Petekidis. “Probing cage dynamics in concentrated hardsphere sus- pensions and glasses with high frequency rheometry.” Soft Matter,21, 2607–2622 (2025)

2025
[44]

M. L. Gardel, M. T. Valentine, & D. A. Weitz.Microrhe- ology(Springer-Verlag, New York) (2005)

2005
[45]

Variations of the Herschel–Bulkley exponent reflecting cont ribu- tions of the viscous continuous phase to the shear rate- dependent stress of soft glassy materials

M. Caggioni, V. Trappe, & P. T. Spicer. “Variations of the Herschel–Bulkley exponent reflecting cont ribu- tions of the viscous continuous phase to the shear rate- dependent stress of soft glassy materials.”J. Rheo.,64, 413 (2020)

2020
[46]

The equilibrium intrinsic crystal-liquid interface of colloids

J. Hern´ andez-Guzm´ an & E. R. Weeks. “The equilibrium intrinsic crystal-liquid interface of colloids.”Proc. Nat. Acad. Sci.,106, 15198–15202 (2009)

2009
[47]

Experimental study of random-close-packed colloidal particles

R. Kurita & E. R. Weeks. “Experimental study of random-close-packed colloidal particles.”Physical Re- view E,82, 011403 (2010)

2010
[48]

In search of colloidal hard spheres

C. P. Royall, W. C. K. Poon, & E. R. Weeks. “In search of colloidal hard spheres.”Soft Matter,9, 17–27 (2013)

2013
[49]

Dynamical fluctuation effects in glassy colloidal suspensions

K. S. Schweizer. “Dynamical fluctuation effects in glassy colloidal suspensions.”Curr. Opin. Colloid Interface Sci.,12, 297–306 (2007)

2007
[50]

Sound propagation in colloidal systems

L. Ye, J. Liu, P. Sheng, J. Huang, & D. A. Weitz. “Sound propagation in colloidal systems.”Journal de Physique IV Proceedings,03, 183–196 (1993)

1993
[51]

Sound propagation in suspensions of colloidal spheres with viscous coupling

D. O. Riese & G. H. Wegdam. “Sound propagation in suspensions of colloidal spheres with viscous coupling.” Physical Review Letters,82, 1676–1679 (1999)

1999
[52]

The role of sound propaga- tion in concentrated colloidal suspensions

A. F. Bakker & C. P. Lowe. “The role of sound propaga- tion in concentrated colloidal suspensions.”The Journal of Chemical Physics,116, 5867–5876 (2002)

2002