Evaporative thermo-fluidics and deposition patterns in surface-active droplets

A R Harikrishnan; Purbarun Dhar; Randeep Ravesh

arxiv: 2604.14380 · v1 · submitted 2026-04-15 · ⚛️ physics.flu-dyn · cond-mat.soft· physics.app-ph

Evaporative thermo-fluidics and deposition patterns in surface-active droplets

Randeep Ravesh , A R Harikrishnan , Purbarun Dhar This is my paper

Pith reviewed 2026-05-10 11:44 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cond-mat.softphysics.app-ph

keywords evaporating dropletssurfactantMarangoni flowsolutal advectiondeposition patternssessile dropletevaporation ratecontact line motion

0 comments

The pith

Marangoni solutal advection dominates internal flows in evaporating surfactant-laden droplets and sets evaporation rates according to concentration and surface type.

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

The paper examines thermo-solutal transport and resulting deposit patterns when surfactant-laden droplets evaporate on solid surfaces. Experiments track temperature fields with infrared imaging and internal velocities with particle image velocimetry while varying surfactant concentration and substrate wettability. Scaling analysis shows that surface-tension gradients created by uneven surfactant distribution drive the strongest flows, outpacing temperature-driven Marangoni motion and buoyancy. These flows explain the observed rise in evaporation rate with added surfactant on hydrophobic surfaces, the peak at half the critical micelle concentration on hydrophilic surfaces, and the later slowdown caused by crowding and higher viscosity. The work also records stick-slip motion of the contact line during drying.

Core claim

In sessile droplets containing sodium dodecyl sulphate, advection driven by surfactant-concentration gradients at the free surface dominates over thermal Marangoni advection and buoyancy-driven flow. Particle-image-velocimetry velocities match the scaling predictions for solutal Marangoni flow, and the evaporation rate computed from shadowgraphy rises monotonically with surfactant concentration on hydrophobic substrates but reaches a maximum at 0.5 CMC and then declines on hydrophilic substrates. Surfactant crowding together with the measured rise in bulk viscosity damps the advection at higher concentrations, while contact-line speed records abrupt jumps consistent with stick-slip pinning.

What carries the argument

Marangoni solutal advection, the interfacial flow produced by surface-tension gradients that arise from non-uniform surfactant concentration along the droplet surface.

Load-bearing premise

The scaling estimates and PIV velocity comparisons fully identify the dominant transport mechanism without important unmeasured contributions from substrate interactions or experimental artifacts.

What would settle it

If repeated PIV measurements on the same droplets showed thermal or buoyancy velocities exceeding the solutal Marangoni values, or if evaporation rates failed to follow the reported non-monotonic dependence on surfactant concentration for each substrate.

Figures

Figures reproduced from arXiv: 2604.14380 by A R Harikrishnan, Purbarun Dhar, Randeep Ravesh.

**Figure 4.** Figure 4: Temporally averaged velocity contours (from analyses of PIV experiments data) for SDS solution droplets on hydrophilic surface at: a) 0.25 CMC, b) 0.5 CMC, and c) 1 CMC concentrations. The spatio-temporally averaged velocity values have been shown in part d) for both hydrophilic (ph) and superhydrophobic (SH) cases (see Figure A3 in appendix for the velocity contours on superhydrophobic substrate) [PITH_F… view at source ↗

**Figure 7.** Figure 7: (a) Variation of thermal Marangoni number (MaT) against Rayleigh number (Ra) for both hydrophilic (ph) and superhydrophbic surfaces (shs) with variation in concentration; (b) Variation of solutal marangoni number (Mas) against thermal Marangoni number (MaT) [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗

**Figure 8.** Figure 8: Comparison between experimentally obtained average velocities (expt) and predicted Marangoni solutal velocities (theo) for superhydrophobic (SHS) and hydrophilic surfaces (Philic). The comparisons between velocities is demonstrated with variation in SDS concentration as a fraction of critical micelle concentration (CMC) [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗

**Figure 10.** Figure 10: Variation of rim width for SDS and CTAB surfactants with the change in concentration [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗

**Figure 11.** Figure 11: Morphology of the deposition pattern of the aqueous SDS solution droplet. (a,b) [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗

read the original abstract

We investigate the thermo solutal transport phenomena and deposition patterns during the evaporation of surfactant laden droplets experimentally and through theoretical scaling based analysis. Experiments were conducted using the sessile droplet configuration in the acrylic chamber for both hydrophilic and hydrophobic substrates. Infrared thermography and particle image velocimetry measurements were conducted during evaporation to illustrate the temperature and velocity distributions, respectively. Sodium dodecyl sulphate SDS surfactant molecules enhanced the evaporation rate with an increase in concentration for the hydrophobic surface. In contrast, the evaporation rate increased up to 0.5 CMC and then decreased for droplets on a hydrophilic substrate. The evaporation rates computed from the shadowgraphy imaging were explained using the average velocities obtained from the PIV analysis. It was found that advection within the droplet is strongly dependent on surfactant concentration and wettability. Further, the theoretically obtained Marangoni velocities were in close agreement with the experimental values. It was found that Marangoni solutal advection dominates other advection mechanisms, such as Marangoni thermal advection and buoyancy driven flow. However, surfactant crowding and viscous resistance with increasing surfactant concentration can dampen the increase in solutal advection. The surface tension and viscosity measurements were also conducted with variation in surfactant concentration to understand the suppression of advection by viscous forces. The computation of contact line velocities showed sudden fluctuations, illustrating stick slip behaviour during droplet drying, complementing microscopic visual observations.

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

Experiments track how SDS concentration reverses evaporation trends on hydrophilic surfaces and ties internal flows to solutal Marangoni, but the dominance claim rests on scaling without shown order-of-magnitude checks on the other terms.

read the letter

The main thing here is new data on surfactant-laden droplets: evaporation rate rises then falls with SDS concentration on hydrophilic substrates while it keeps rising on hydrophobic ones, and PIV velocities line up with a solutal Marangoni scaling that they say beats thermal Marangoni and buoyancy. They also note stick-slip at the contact line from velocity jumps and link high-concentration damping to crowding plus measured viscosity rise. That combination of IR, PIV, shadowgraphy, and separate tension/viscosity runs gives a coherent picture of how wettability and concentration shift the advection inside the drop. The experiments look careful and the observations are independent of the scaling, so the reversal and the velocity trends stand on their own. The soft spot is exactly where the stress test flagged it. The paper states solutal advection dominates and gets damped at high concentration, yet the description gives no tabulated comparison of the three velocity scales across the full concentration range or both substrates, no explicit Marangoni numbers, and no bound on how much the neglected terms could grow when viscosity increases. Without those numbers the dominance statement stays qualitative even though the measured velocities are reported. If the full manuscript has the derivations and the side-by-side estimates, that gap closes; from the abstract and summary it does not. This is useful for people modeling evaporative deposition or surfactant-driven flows in printing and coating applications. A reader already deep in droplet evaporation will find the substrate-specific reversal and the damping mechanism worth citing for data, but it is not a mechanism overhaul. The work is grounded enough and the experiments targeted enough that it deserves referee time rather than a desk reject; the experimental core is solid even if the scaling section needs tightening.

Referee Report

3 major / 3 minor

Summary. The manuscript investigates thermo-solutal transport and deposition patterns in evaporating surfactant-laden (SDS) droplets on hydrophilic and hydrophobic substrates. Experiments employ IR thermography for temperature fields, PIV for internal velocities, and shadowgraphy for evaporation rates and contact-line dynamics. Scaling analysis is used to compare advection mechanisms. Key claims are that solutal Marangoni advection dominates thermal Marangoni and buoyancy-driven flows, that evaporation rates depend non-monotonically on concentration (increasing to 0.5 CMC then decreasing on hydrophilic surfaces), that measured velocities agree with theoretical Marangoni scales, and that crowding/viscous resistance damps advection at high concentrations. Stick-slip contact-line motion is also reported.

Significance. If the dominance claim can be placed on a quantitative footing, the work would add useful experimental and scaling insight into how surfactants modulate internal advection and evaporation in sessile droplets. The combination of multiple optical diagnostics with surface-tension and viscosity measurements is a strength, and the wettability-dependent trends are of practical interest for coating and printing applications. However, the current lack of explicit order-of-magnitude bounds and tabulated comparisons limits the strength of the central mechanistic conclusion.

major comments (3)

[Abstract and scaling analysis] Abstract and scaling analysis: the assertion that solutal Marangoni advection dominates thermal Marangoni and buoyancy flows is not supported by tabulated order-of-magnitude comparisons of the three velocity scales across the full SDS concentration range. No solutal Marangoni number, explicit bounds on the neglected terms, or values of dσ/dc and surface-concentration gradients are provided, so the dominance statement cannot be verified independently, especially at high concentrations where viscous damping is invoked.
[Results (PIV and scaling comparison)] Results section on velocity comparison: the statement of 'close agreement' between theoretically obtained Marangoni velocities and PIV measurements lacks quantitative metrics (error bars, percentage deviation, or R² values) and does not address how the comparison holds when viscosity rises with concentration. This weakens the validation of the scaling and the damping mechanism.
[Evaporation rate and advection dependence] Evaporation-rate discussion: the non-monotonic evaporation behavior on hydrophilic substrates is attributed to concentration-dependent advection, yet no explicit derivation linking the measured average velocities to the observed rates (or to the shadowgraphy data) is shown, leaving the explanation qualitative rather than predictive.

minor comments (3)

[Abstract] The abstract refers to 'theoretically obtained Marangoni velocities' without stating the key assumptions or the explicit scaling expressions used.
[Methods and supplementary measurements] Surface-tension and viscosity data are mentioned as supporting the viscous-resistance argument, but the manuscript would benefit from a dedicated figure or table showing these measurements versus concentration alongside the velocity trends.
[Figures] Figure captions and axis labels for PIV and IR images should explicitly note the surfactant concentrations and substrate types shown, to aid direct comparison with the scaling claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the insightful comments, which have helped us identify areas where the manuscript can be strengthened with additional quantitative details. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

Referee: [Abstract and scaling analysis] Abstract and scaling analysis: the assertion that solutal Marangoni advection dominates thermal Marangoni and buoyancy flows is not supported by tabulated order-of-magnitude comparisons of the three velocity scales across the full SDS concentration range. No solutal Marangoni number, explicit bounds on the neglected terms, or values of dσ/dc and surface-concentration gradients are provided, so the dominance statement cannot be verified independently, especially at high concentrations where viscous damping is invoked.

Authors: We agree that providing explicit order-of-magnitude comparisons would make the dominance claim more verifiable. In the revised manuscript, we will add a table in the scaling analysis section that compares the three velocity scales (solutal Marangoni, thermal Marangoni, and buoyancy) for the full range of SDS concentrations. We will include the solutal Marangoni number, our measured dσ/dc values, estimated surface concentration gradients, and bounds on neglected terms. This will also clarify the viscous damping at high concentrations. revision: yes
Referee: [Results (PIV and scaling comparison)] Results section on velocity comparison: the statement of 'close agreement' between theoretically obtained Marangoni velocities and PIV measurements lacks quantitative metrics (error bars, percentage deviation, or R² values) and does not address how the comparison holds when viscosity rises with concentration. This weakens the validation of the scaling and the damping mechanism.

Authors: We acknowledge the need for quantitative metrics to support the 'close agreement'. We will update the results section to include error bars on the experimental PIV data, compute percentage deviations and R² values for the comparison between theoretical Marangoni velocities and measurements. We will also explicitly discuss the effect of increasing viscosity with concentration on this agreement, using our viscosity data to substantiate the damping mechanism. revision: yes
Referee: [Evaporation rate and advection dependence] Evaporation-rate discussion: the non-monotonic evaporation behavior on hydrophilic substrates is attributed to concentration-dependent advection, yet no explicit derivation linking the measured average velocities to the observed rates (or to the shadowgraphy data) is shown, leaving the explanation qualitative rather than predictive.

Authors: We agree that the connection between advection velocities and evaporation rates could be presented more rigorously. In the revision, we will include an explicit scaling derivation or analysis that links the PIV-measured average velocities to the evaporation rates obtained from shadowgraphy. This will demonstrate how concentration-dependent advection modulates the evaporation, making the explanation more quantitative and predictive. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scaling validated against independent experiments

full rationale

The paper grounds its claims in direct experimental measurements (PIV velocities, IR thermography, shadowgraphy evaporation rates, surface tension, and viscosity) that are independent of the scaling analysis. Theoretical Marangoni velocity scales are computed from measured dσ/dc and estimated gradients, then compared to PIV data for agreement rather than fitted to it. No equations reduce a prediction to an input parameter by construction, no self-citations are load-bearing for the dominance claim, and no ansatz or uniqueness theorem is smuggled in. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; scaling analysis is mentioned but without equations or assumptions detailed.

pith-pipeline@v0.9.0 · 5553 in / 1069 out tokens · 37137 ms · 2026-05-10T11:44:12.556179+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

Evaporation characteristics of cis-1,1,1,4,4,4-hexafluoro-2-butene (R1336mzz(Z)) droplet in high pressure and temperature environments,

1 J. Yin, Q. Di Wang, L.F. Zhang, L.K. Norvihoho, B. Liu, and Z.F. Zhou, “Evaporation characteristics of cis-1,1,1,4,4,4-hexafluoro-2-butene (R1336mzz(Z)) droplet in high pressure and temperature environments,” Phys. Fluids 36(2), (2024). 2 J. Yin, B.J. Rong, Y. Liu, X.G. Zhu, Y.P. Li, Z.L. He, and Z.F. Zhou, “Comparative investigation on the droplet evap...

work page 2024
[2]

Crystallisation of sodium dodecyl sulfate and the corresponding effect of 1-dodecanol addition,

Nonlinear, Soft Matter Phys. 71(3), 1–17 (2005). 43 E. Summerton, G. Zimbitas, M. Britton, and S. Bakalis, “Crystallisation of sodium dodecyl sulfate and the corresponding effect of 1-dodecanol addition,” J. Cryst. Growth 455(April), 111–116 (2016). 44 C. Vautier-Giongo, and B.L. Bales, “Estimate of the ionization degree of ionic micelles based on Krafft ...

work page 2005

[1] [1]

Evaporation characteristics of cis-1,1,1,4,4,4-hexafluoro-2-butene (R1336mzz(Z)) droplet in high pressure and temperature environments,

1 J. Yin, Q. Di Wang, L.F. Zhang, L.K. Norvihoho, B. Liu, and Z.F. Zhou, “Evaporation characteristics of cis-1,1,1,4,4,4-hexafluoro-2-butene (R1336mzz(Z)) droplet in high pressure and temperature environments,” Phys. Fluids 36(2), (2024). 2 J. Yin, B.J. Rong, Y. Liu, X.G. Zhu, Y.P. Li, Z.L. He, and Z.F. Zhou, “Comparative investigation on the droplet evap...

work page 2024

[2] [2]

Crystallisation of sodium dodecyl sulfate and the corresponding effect of 1-dodecanol addition,

Nonlinear, Soft Matter Phys. 71(3), 1–17 (2005). 43 E. Summerton, G. Zimbitas, M. Britton, and S. Bakalis, “Crystallisation of sodium dodecyl sulfate and the corresponding effect of 1-dodecanol addition,” J. Cryst. Growth 455(April), 111–116 (2016). 44 C. Vautier-Giongo, and B.L. Bales, “Estimate of the ionization degree of ionic micelles based on Krafft ...

work page 2005