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arxiv: 2508.16572 · v2 · submitted 2025-08-22 · ❄️ cond-mat.soft

Persistence of Coffee-Ring Deposits in Concentrated Suspensions of Anisotropic Colloids

Samuel S. Nielsen , Ryker Fish , Brian C. Seper , Brennan Sprinkle , Michelle M. Driscoll This is my paper

Pith reviewed 2026-05-18 21:09 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords coffee-ring effectanisotropic colloidssedimentation velocitydroplet evaporationparticle depositionconcentrated suspensionscontact line transport
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The pith

Coffee-ring formation persists in concentrated anisotropic colloids because it is controlled by the ratio of sedimentation velocity to evaporating interface velocity rather than particle shape.

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

The paper establishes that the coffee-ring deposit still forms in concentrated suspensions of anisotropic particles such as rods or ellipsoids. Transport to the contact line depends on how fast particles sediment compared with the speed at which the droplet's air-water interface recedes during evaporation. A sympathetic reader would care because this ratio supplies a single handle for tuning deposit geometry across shapes and concentrations, with direct bearing on printing, coatings, and self-assembly where uniform or patterned films are needed. Experiments vary shape, concentration, density, and temperature while using surface profilometry for ring widths; hydrodynamic simulations supply independent sedimentation estimates that confirm the ratio as the governing quantity.

Core claim

Coffee-ring formation is independent of particle anisotropy and is instead controlled by the ratio of the particle sedimentation velocity to the velocity of the droplet's evaporating air-water interface. Hydrodynamic simulations support this finding by providing quantitative estimates for bulk sedimentation velocity.

What carries the argument

The ratio of particle sedimentation velocity to the velocity of the droplet's evaporating air-water interface, which sets whether particles reach and accumulate at the contact line before settling away from the moving interface.

If this is right

  • Varying particle density or size changes sedimentation velocity and therefore alters ring width and height.
  • Changing solvent temperature modifies the evaporation-driven interface velocity and provides a route to tune deposit geometry.
  • The velocity-ratio picture unifies observations across spherical and anisotropic particles at both low and high concentrations.
  • Practical suppression of uneven deposition can target adjustments to the velocity ratio instead of particle shape.

Where Pith is reading between the lines

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

  • The same velocity-ratio criterion could guide design in other evaporative assembly methods that involve anisotropic colloids or non-spherical containers.
  • Real-time control of evaporation rate during drying might allow on-the-fly patterning without reformulating the suspension.
  • Limits of the picture may appear at extreme aspect ratios or in solvents where additional interactions become comparable to sedimentation.

Load-bearing premise

The experiments isolate particle shape, concentration, and density effects without confounding hydrodynamic interactions or other variables at high concentrations that could alter transport independently of the sedimentation-interface ratio.

What would settle it

Measuring ring widths that differ systematically with particle anisotropy while the sedimentation-to-interface velocity ratio is held constant would falsify the claim that the ratio alone controls deposit geometry independent of shape.

Figures

Figures reproduced from arXiv: 2508.16572 by Brennan Sprinkle, Brian C. Seper, Michelle M. Driscoll, Ryker Fish, Samuel S. Nielsen.

Figure 1
Figure 1. Figure 1: Surface profilometry captures ring deposit geometry. Bright-field microscopy images of de￾posits formed by (a) aspect ratio, α, 1 and (d) α = 11 droplets containing silica particles at φ = 0.20. The scale bars are 1 mm. (b) and (e) show the normalized intensity profiles I(r)/I0 taken along the dashed lines, while (c) and (d) show the result of surface profilometry along the dashed lines. For aspect ratio (… view at source ↗
Figure 2
Figure 2. Figure 2: The volume fraction of the droplet dictates the geometry of ring deposit independent of particle aspect ratio (α). Profilometry scans for three α: 1,11, and 20, are shown at three volume fractions: φ = 0.01, 0.1, 0.35. Profiles are vertically offset for clarity, and normalized horizontally by their size 2R. Increasing volume fraction causes the ring width to increase, while the aspect ratio α has no apprec… view at source ↗
Figure 3
Figure 3. Figure 3: Coffee-ring geometry does not depend on particle anisotropy. Normalized widths of the ring shaped deposits formed by droplets containing silica colloids (particle aspect ratio (α) 1-20) are plotted against initial volume fraction. The dashed line (equation 1) is the prediction from Popov [17] using the packing fraction of spheres,p = 0.64. The inset shows the dependence of the width as a function of packin… view at source ↗
Figure 4
Figure 4. Figure 4: Deposits become smoother when particles are more easily captured by the interface Deposits formed from φ = 0.05 silica (left) and polystyrene (right) at 22◦C (top) and 90◦C (bottom). Profiles exhibit a clear ring shape, except for polystyrene evaporated at 90◦C (bottom right). At higher temperatures, the air-water interface moves fast enough to capture polystyrene during evaporation, resulting in a more un… view at source ↗
read the original abstract

Evaporating a droplet containing dispersed colloids leaves behind a dried deposit whose shape is determined by capillary flows and the resulting particle transport. The classical coffee-ring effect occurs when an outward radial flow drives particles toward the droplet's contact line as the droplet evaporates, resulting in uneven deposition. This deposition is often studied in dilute concentration regimes where, hydrodynamically, the effects of particle shape are unimportant. As particle concentration increases, it is expected that particle anisotropy should play a larger role in modifying transport and potentially suppressing coffee-ring formation. We present experiments isolating the effects of particle shape, concentration, and density, as well as solvent temperature, on the geometry of the ring deposit. By analyzing the deposits using surface profilometry to more accurately characterize ring widths, these experiments show that coffee-ring formation is independent of particle anisotropy and is instead controlled by the ratio of the particle sedimentation velocity to the velocity of the droplet's evaporating air-water interface. Hydrodynamic simulations support this finding by providing quantitative estimates for bulk sedimentation velocity. Together, these results offer a unified picture of how multiple physical parameters determine coffee-ring geometry with direct implications for suppressing uneven deposition in practical applications.

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 reports experiments on evaporating droplets of concentrated suspensions containing anisotropic colloids, using surface profilometry to characterize ring deposits while varying particle shape, concentration, density, and solvent temperature. It claims that coffee-ring formation persists independently of particle anisotropy and is instead controlled by the scalar ratio of particle sedimentation velocity to the velocity of the droplet's evaporating air-water interface, with supporting bulk hydrodynamic simulations providing quantitative sedimentation estimates.

Significance. If the central claim holds, the work supplies a unified, parameter-based description of deposit geometry that applies across dilute-to-concentrated regimes and particle shapes, with direct implications for suppressing uneven deposition in coatings, printing, and self-assembly applications. Credit is due for the experimental isolation of multiple variables and for the use of simulations to generate falsifiable sedimentation-velocity estimates rather than fitting parameters.

major comments (2)
  1. [Abstract / hydrodynamic simulations] Abstract and hydrodynamic-simulations paragraph: the claim that deposit geometry is controlled solely by the ratio v_sed / v_interface (independent of anisotropy) rests on bulk sedimentation velocities from quiescent simulations. These simulations omit the coupled radial evaporative flow field; for anisotropic particles, orientation-dependent drag and flow-induced alignment are expected to modify the effective radial velocity relative to sedimentation, especially at the high concentrations studied. This coupling must be quantified or shown to be negligible for the independence result to stand.
  2. [Experimental design] Experimental-design paragraph: the assertion that experiments successfully isolate particle shape, concentration, and density effects without confounding hydrodynamic interactions at high concentrations requires explicit justification. At the concentrations examined, interparticle interactions and flow modifications could alter net transport independently of the sedimentation-interface ratio; additional controls or measurements (e.g., local velocity fields) are needed to rule this out.
minor comments (2)
  1. [Results / profilometry] Profilometry data analysis: the manuscript should report the precise definition of ring width (e.g., full width at half-maximum or edge-to-peak distance) and include representative error bars or uncertainty estimates from multiple droplets.
  2. [Abstract / main text] Notation: the velocity ratio is introduced without an explicit equation; adding a numbered equation defining v_sed / v_interface would improve clarity and allow direct comparison with the simulation outputs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which help clarify the scope and limitations of our work. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract / hydrodynamic simulations] Abstract and hydrodynamic-simulations paragraph: the claim that deposit geometry is controlled solely by the ratio v_sed / v_interface (independent of anisotropy) rests on bulk sedimentation velocities from quiescent simulations. These simulations omit the coupled radial evaporative flow field; for anisotropic particles, orientation-dependent drag and flow-induced alignment are expected to modify the effective radial velocity relative to sedimentation, especially at the high concentrations studied. This coupling must be quantified or shown to be negligible for the independence result to stand.

    Authors: We agree that the hydrodynamic simulations compute sedimentation velocities in a quiescent bulk fluid and do not incorporate the radial evaporative flow or orientation-dependent effects. The central experimental observation—that deposit geometry correlates with the scalar ratio v_sed / v_interface across particle shapes—remains independent of the simulation details. To address the concern, we will revise the hydrodynamic-simulations section to explicitly state the quiescent approximation, add order-of-magnitude estimates comparing sedimentation and shear-induced alignment timescales at the studied concentrations, and note that any flow-coupling corrections would be expected to be similar across the particle shapes tested. This will clarify that the independence result is primarily experimental while acknowledging the simulation limitation. revision: partial

  2. Referee: [Experimental design] Experimental-design paragraph: the assertion that experiments successfully isolate particle shape, concentration, and density effects without confounding hydrodynamic interactions at high concentrations requires explicit justification. At the concentrations examined, interparticle interactions and flow modifications could alter net transport independently of the sedimentation-interface ratio; additional controls or measurements (e.g., local velocity fields) are needed to rule this out.

    Authors: The experiments systematically vary particle aspect ratio at fixed concentration and density, then vary concentration and density at fixed aspect ratio, and finally vary temperature (which modulates viscosity and thus sedimentation velocity) while holding particle properties constant. Deposit profiles are quantified via surface profilometry for all cases. We will expand the experimental-design and methods sections to provide a more detailed justification of this isolation strategy, including tables of the parameter combinations tested and discussion of why interparticle hydrodynamic interactions do not appear to override the observed ratio dependence. Direct local velocity-field measurements are not available in the current data set; we will add a brief statement acknowledging this as a limitation and a possible direction for future work. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental isolation and independent simulations

full rationale

The paper reports controlled experiments that vary particle anisotropy, concentration, density, and temperature while measuring deposit geometry via profilometry. The central claim—that ring formation depends on the sedimentation-to-interface velocity ratio rather than anisotropy—is reached by direct comparison of observed outcomes to this ratio, with bulk sedimentation velocities supplied by separate hydrodynamic simulations. No equations, fits, or self-citations reduce the reported independence or the controlling ratio to a tautology or to the same data used to define it; the result remains externally falsifiable against the profilometry measurements and the simulation assumptions stated in the text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on experimental isolation of parameters and simulation estimates of sedimentation; no free parameters or new entities are introduced in the abstract description.

axioms (1)
  • domain assumption Standard hydrodynamic principles apply to estimate bulk sedimentation velocity in the suspensions.
    Invoked to support experimental findings via simulations.

pith-pipeline@v0.9.0 · 5749 in / 1144 out tokens · 34124 ms · 2026-05-18T21:09:23.375404+00:00 · methodology

discussion (0)

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Reference graph

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