Evaporation-induced freezing dynamics of droplets levitated in acoustic field

Koji Hasegawa; Misaki Mitsuno; Xiao Ma

REVIEW 4 major objections 4 minor 1 references

Evaporation-induced freezing dynamics of droplets levitated in acoustic field

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A simple energy balance predicts when an evaporating levitated droplet freezes.

desk verdict Solid experimental observation of evaporation-induced freezing in pure cyclohexane, but the freezing-onset model Eq. (14) is not an independent prediction and needs revision. read the letter →

arxiv 2505.22001 v2 pith:K2SZZVKE submitted 2025-05-28 physics.flu-dyn

Misaki Mitsuno , Xiao Ma , Koji Hasegawa This is my paper · ORCID

classification physics.flu-dyn

keywords acousticlevitationdropletevaporationevaporation-inducedfreezingcyclohexaneheattransfercoefficientsupercoolingenergybalanceNusseltnumber

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports that a droplet of pure cyclohexane levitated in an acoustic standing wave freezes in mid-air because evaporation cools its surface below the freezing point. The authors measured the evaporation rate, surface temperature, and freezing time with high-speed and infrared cameras, and they show that the measured heat transfer coefficient matches the standard Nusselt-number correlation for a sphere in an external flow driven by acoustic streaming. They then build a simple energy-balance model, Eq. (14), that predicts the freezing-onset time from the droplet volume, surface temperature, and heat transfer coefficient, and they find that the predicted times agree with experiments within uncertainty. If correct, this establishes that containerless evaporation-induced freezing in an acoustic field can be described by a steady energy balance without invoking detailed nucleation theory.

What carries the argument

The load-bearing object is the energy-balance equation (14) for the freezing-onset time, combined with the heat transfer coefficient $h$ obtained by equating evaporative heat loss, $\rho_l L_e \, \mathrm{d}V/\mathrm{d}t$, with convective loss, $hS(T_s-T_\infty)$. The coefficient is validated against the standard forced-convection correlation $Nu=2+0.6Re^{1/2}Pr^{1/3}$ with the acoustic streaming velocity measured at 232 ± 31 mm/s, and against the acoustic boundary-layer Nusselt number of Eq. (10). The model's working assumption is that the droplet volume at minimum surface temperature, $V'$, is entirely evaporated during the freezing time, so that $\mathrm{d}V/\mathrm{d}t = -V'/t_{fr}$, and that the relevant latent heat is the latent heat of evaporation $L_e$.

What would settle it

Record the droplet volume with high-speed imaging continuously through the freezing interval, and detect the first appearance of solid phase from the space-time diagram. If the volume actually evaporated during the measured freezing time is substantially smaller than $V'$, or if the evaporation rate is not approximately constant, then Eq. (14) is not an energy-balance prediction but a curve fit with a calibrated volume.

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Extended reading notes

Core claim

The central claim is that evaporation-induced freezing of an acoustically levitated pure cyclohexane droplet is governed by the balance between sensible heat carried by the evaporating mass and the heat losses from the droplet, and that this balance gives an accurate freezing-onset time. In the experiments, the droplet surface cools below the cyclohexane freezing point of 6.5 °C within a few seconds, remains supercooled, then freezes rapidly. The model is Eq. (14), $$t_{fr} = \frac{\rho_l V' (L_e + c_p(T_s-T_\infty))}{h S'(T_s-T_\infty) + k_a S'(T_s-T_\infty)/\delta_T},$$ where $V'$ and $S'$ are the volume and surface area at the moment of lowest surface temperature, $\delta_T$ is the thermal boundary-layer thickness, and $h$ is the heat transfer coefficient determined from the evaporation rate. The authors report that the experimentally measured freezing times agree with the model within uncertainties, verifying Eq. (14) as a way to estimate the freezing time of a levitated droplet in an acoustic field.

Load-bearing premise

The model assumes that the entire droplet volume measured at the coldest surface temperature evaporates at a steady rate during the freezing time, and that the heat of evaporation, not the heat of fusion, is the latent heat in the energy balance; if that volume-balance shortcut is wrong, the agreement of Eq. (14) with the experiments could be coincidental.

Editorial extensions

If this is right

A steady energy balance, not detailed nucleation kinetics, is enough to estimate when a levitated volatile droplet begins to freeze, making the onset time accessible to engineering calculation.
The measured heat transfer coefficients for acoustically levitated droplets follow the standard sphere correlation, so acoustic streaming can be represented as an equivalent uniform flow with a measured velocity.
Pure fluids with high vapor pressure and low heat of evaporation, such as cyclohexane, can be used as model systems for evaporation-induced phase change without water-condensation interference.
The same volume-temperature-heat-transfer recipe could be applied to other volatile levitated droplets in lab-in-a-drop applications once the heat transfer coefficient is known.
Acoustic levitation maintains a wall-free supercooled state long enough for freezing onset to be observed and timed, which is difficult in container-based experiments.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct test would be to measure the droplet volume continuously during the freezing interval instead of assuming $\mathrm{d}V/\mathrm{d}t = -V'/t_{fr}$; this would separate the energy-balance structure from the volume-average shortcut.
The paper defines freezing time by the droplet no longer transmitting backlight, which is closer to complete solidification than to nucleation onset; the model may therefore be predicting total freezing time rather than true onset, a distinction worth pinning down.
Applying the same model to other pure volatile fluids with different vapor pressures would show whether the agreement is specific to cyclohexane or generic to evaporation-driven freezing.
The energy balance omits the latent heat of fusion, which becomes nonzero when freezing occurs; including it could change the predicted times and would clarify how much of the solidification heat is balanced by evaporation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the experimental observation is real and the heat-transfer characterization is worth having, but the freezing-onset model in Eq. (14) does not work as a prediction. It assumes the full droplet volume evaporates during the freezing interval, uses the latent heat of evaporation where the latent heat of fusion should matter, and is validated using the same measured h_exp that went into it. The agreement in Fig. 7 is therefore a consistency check, not a predictive test.

What's new: this is, as far as I know, the first clean report of evaporation-induced freezing of a pure cyclohexane droplet in an acoustic levitator. The simultaneous high-speed and IR imaging gives a clear picture: surface temperature drops below the freezing point, stays supercooled, then recovers as freezing starts. That's a solid experimental result. The extraction of h_exp from dV/dt and ΔT via Eq. (5) is straightforward, and the comparison with the Ranz-Marshall correlation and the boundary-layer streaming model (Eq. 10) is honest and shows the expected enhancement. The acoustic streaming velocity measurement is useful too.

The soft spot is Sec. III.C. Equations (11)-(13) set up an energy balance that mixes the heat needed to warm the evaporating vapor with the surface heat loss, and then Eq. (14) replaces dV/dt with -V'/t_fr. That asserts that the whole volume V' evaporates during the freezing time. But the images show freezing starts while most of the droplet is still liquid. The L_e term is also in the numerator, so a larger latent heat predicts a longer freezing time, which is the opposite of the physical intuition that faster evaporation cools the droplet faster. The validation uses the maximum measured h_exp, not an independently predicted h_RM. A real predictive test would use h_RM from Eq. (8). The authors themselves concede in the Conclusions that the discrepancy between experiment and prediction remains to be elucidated. Given that, I would treat Eq. (14) as an empirical fit, not a validated model.

Who this is for: people working on containerless phase change or lab-in-a-drop applications. The experimental data and the heat-transfer analysis are useful; the freezing model needs reworking. I would send it to peer review because the experiments are solid and the model can be fixed with a proper energy balance and an independent h. The paper is honest about its limits, which is a point in its favor.

Referee Report

4 major / 4 minor

Summary. The paper investigates evaporation-induced freezing of pure cyclohexane droplets levitated in an acoustic levitator. High-speed and infrared cameras capture the droplet size and surface temperature over time, showing rapid evaporative cooling, supercooling, and freezing. The authors extract an experimental heat transfer coefficient from the evaporation rate and surface temperature, compare it with the Ranz-Marshall correlation, and then propose an energy-balance model, Eq. (14), for the freezing time. They claim the model predictions agree with experimental freezing times within uncertainties, verifying its applicability. The main body also includes supporting observations of the freezing process, a space-time diagram, and a discussion of acoustic-streaming-enhanced heat transfer.

Significance. If the freezing-time model were physically grounded and independently validated, the paper would provide a simple predictive tool for evaporation-induced freezing in containerless droplet processing, with implications for lab-in-a-drop technologies and phase-change studies. The experimental dataset is valuable: simultaneous high-speed imaging and infrared thermography of a pure, well-characterized fluid in an acoustic levitator, plus heat-transfer coefficients that agree with Ranz-Marshall predictions, are useful contributions. However, the central predictive claim rests on an energy balance that is not physically justified, and the validation is not independent of the inputs used to construct the model. The paper's own conclusions acknowledge that the discrepancy between experiment and prediction remains unexplained, which further weakens the verification claim. The experimental core is sound, but the model and its validation need substantial reworking before the paper can be accepted.

major comments (4)

[§III.C, Eqs. (11)–(14)] The derivation of Eq. (14) implicitly replaces the instantaneous evaporation rate dV/dt with -V'/t_fr, thereby assuming that the entire remaining volume V' evaporates during the freezing time. This is not consistent with the observations in Figs. 2–4, where freezing begins while the droplet is still mostly liquid; only a small fraction of V' has evaporated by the time freezing is initiated. Consequently, the term L_e ρ_l V' in the numerator represents the latent heat of complete evaporation, not the energy removed before freezing onset. The latent heat of fusion is entirely absent from the model, even though freezing is the phase transition being predicted. Additionally, Eq. (14) predicts that a larger latent heat of evaporation L_e gives a longer freezing time for fixed V', S', and ΔT, which is physically counterintuitive: a larger L_e means each unit of evaporated mass removes more heat, so the droplet should cool faster and freeze sooner. These issues indicate that the energy balance in Eqs. (11)-(13) is not the correct description of freezing onset.
[§III.C, Fig. 7 and Eq. (5)] The validation shown in Fig. 7 is not an independent test of Eq. (14). The calculation uses the maximum experimental heat transfer coefficient h_exp from Eq. (5), which is itself derived from the same droplet's measured evaporation rate dV/dt and surface temperature difference (T_s - T_inf), together with the same droplet's V' and S'. The agreement in Fig. 7 is therefore a consistency check between different algebraic combinations of the same measured quantities, not a predictive verification. The authors should present a genuine prediction using h_RM from Eq. (8) or a model calibrated on one subset of droplets and tested on another. They should also propagate uncertainties from T_s, d', and dV/dt into the predicted freezing time and show the prediction band rather than comparing point values.
[§III.C, Eq. (11)] Eq. (11) defines the internal energy term as Q_in = ρ_l (dV/dt) c_p (T_s - T_inf), which has units of watts but is not the sensible-heat storage rate of the droplet. The unsteady thermal energy of a lumped droplet should involve ρ_l V c_p dT_s/dt, and the role of the mass-loss term dV/dt in the energy balance needs to be justified from the full enthalpy equation. The sign conventions in Eqs. (11)-(13) are also confusing: Q_in is written as positive for a negative dV/dt during evaporation, while Q_out contains negative and positive contributions, and equating them in Eq. (13) does not follow from a clean control-volume energy balance. The derivation should be restarted from an explicitly stated control-volume energy equation with clearly defined sign conventions.
[§III.C and §IV] The term 'onset of freezing time' is used for the model, but the experimental freezing time in Fig. 7 is defined as the moment when the backlight is no longer transmitted, i.e., complete freezing. These are different events: the observations show that freezing starts at the surface while the droplet is largely liquid and then propagates within about one second. Comparing a model for onset with data for completion is inconsistent and may explain part of the reported discrepancy. The Conclusions also state that 'the discrepancy between the experiment and the prediction remains to be elucidated,' which directly contradicts the earlier claim in §III.C that the predictions 'agreed well' and 'verifying the applicability of Eq. (14).' The authors need to resolve this inconsistency, either by defining and modeling the same observable or by removing the verification claim.

minor comments (4)

[§III.A, Fig. 4(c)] Fig. 4(c) lists 'simultaneous water condensation' as part of step (1) of the freezing process, but the paper repeatedly emphasizes that pure cyclohexane is immiscible with water and does not absorb ambient moisture. This appears internally inconsistent and should be clarified or corrected.
[§III.B, Eq. (5)] The heat transfer coefficient extraction in Eq. (5) assumes that all heat loss is due to evaporation. Radiative heat loss and sensible heat transfer to the surrounding air are neglected. Given that the surface temperature is measured by IR thermometry and the ambient temperature is only specified as 20 ± 5 °C, the impact of these neglected terms on h_exp should be estimated or at least discussed.
[§III.A, Fig. 3(b)] The text states that the surface temperature increased at approximately 25 s, while Fig. 2(a) shows the droplet darkening at 26 s. Please ensure the freezing-onset time is consistently reported across figures and text, or explain the difference.
[Eq. (10)] The expression for the average Nusselt number in Eq. (10) is introduced without derivation or citation to the specific theoretical treatment; a reference or a brief explanation of its origin would help the reader assess its applicability to the present acoustic levitator geometry.

Circularity Check

2 steps flagged · score 6.0 of 10

Eq. (14) reduces to a rearrangement of measured evaporation data: t_fr is defined as the time to evaporate the measured volume V', and the validation reuses the same fitted h_exp.

self definitional [Section III C, Eqs. (11)-(14)]
"𝜌𝑙 𝑑𝑉/𝑑𝑡 𝑐𝑝(𝑇𝑠 − 𝑇∞) = −ℎ𝑆′(𝑇𝑠 − 𝑇∞) − 𝑘𝑎𝑆′ (𝑇𝑠 − 𝑇∞)/𝛿𝑇 − 𝐿𝑒𝜌𝑙 𝑑𝑉/𝑑𝑡, (13) ... The onset of freezing time (𝑡𝑓𝑟) for levitated droplets can be estimated using the following equation: 𝑡𝑓𝑟 = 𝜌𝑙𝑉′ (𝐿𝑒 + 𝑐𝑝(𝑇𝑠 − 𝑇∞))/(ℎ𝑆′(𝑇𝑠 − 𝑇∞) + 𝑘𝑎𝑆′ (𝑇𝑠 − 𝑇∞)/𝛿𝑇). (14)"

Equation (14) follows from Eq. (13) only if the instantaneous evaporation rate dV/dt is replaced by the average -V'/t_fr. That substitution makes t_fr, by construction, the time required to evaporate the entire measured volume V'. No freezing-specific physics (e.g., latent heat of fusion or a nucleation criterion) enters; the predicted t_fr is simply the measured volume divided by the measured evaporation rate. Comparing this with the experimentally observed freezing time is a consistency check of the evaporation data, not an independent prediction of freezing onset.
fitted input called prediction [Section III C, Fig. 7 paragraph]
"Fig. 7 presents a comparison between the experimentally obtained freezing times and those calculated using Eq. (14) by substituting the maximum heat transfer coefficient."

The heat transfer coefficient substituted into Eq. (14) is h_exp from Eq. (5), which is computed from the same droplets' measured dV/dt and surface-temperature difference used to determine the freezing-time data. Thus the 'model prediction' reuses the very experimental inputs it claims to verify. The agreement in Fig. 7 is therefore partly forced by construction; an independent test would require a parameter-free h (e.g., h_RM from the Ranz-Marshall correlation) or a freezing-onset criterion not derived from the measured V'/t_fr.

full rationale

The paper's heat-transfer characterization in Section III B is not circular: h_exp from Eq. (5) is benchmarked against the external Ranz-Marshall correlation (Eqs. (6)-(8)), which provides independent support. The circularity is concentrated in the freezing-onset 'prediction' of Section III C. Equation (14) is obtained from Eq. (13) by implicitly setting dV/dt = -V'/t_fr, so the predicted freezing time is, by construction, the time for the measured volume V' to evaporate at the measured rate. The validation then substitutes h_exp, which is fitted from the same dV/dt and ΔT data, into Eq. (14). The apparent agreement in Fig. 7 is thus a consistency check rather than a parameter-free prediction. The conclusion's admission that 'the discrepancy between the experiment and the prediction remains to be elucidated' further indicates that the model has not independently captured the freezing mechanism. Because an external benchmark exists for the heat-transfer coefficient, the circularity is partial rather than total, giving a score of 6.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The model relies on several literature correlations and two empirically chosen inputs: the constant temperature difference ΔT = 15.3 °C and the maximum measured heat transfer coefficient. The most fragile entry is the ad hoc assumption that freezing time equals the time to evaporate the remaining volume V', with L_e used instead of the latent heat of fusion.

free parameters (2)

Temperature difference ΔT = 15.3 °C
Adopted as a constant from the measured maximum temperature differences (Fig. 5) and used in Eqs. (13)-(14).
Maximum heat transfer coefficient h_max = Maximum of h_exp from Eq. (5) per droplet
Used in Eq. (14) for freezing time; chosen as the maximum measured value, not independently predicted.

assumptions (5)

domain assumption Evaporation follows the d-squared-law model of Eq. (1) from Refs. [45,48], assuming a spherical droplet and diffusion-limited quasi-steady evaporation.
Used in Fig. 2(c) to compare with measured evaporation; the model underestimates cyclohexane evaporation, motivating the heat transfer analysis.
domain assumption The Ranz-Marshall correlation (Eq. (6)) is applicable to the acoustically levitated droplet with a uniform external flow velocity U_a = 232 ± 31 mm/s measured from water mist displacement.
Used to validate h_exp in Fig. 6(a); the actual flow around the droplet includes vortices, acknowledged by the authors.
ad hoc to paper The droplet is treated as a lumped thermal system with uniform surface temperature T_s and a constant temperature difference ΔT = 15.3 °C throughout freezing.
Fig. 5 shows ΔT is approximately constant across diameters, but assuming it stays constant during freezing is an idealization.
ad hoc to paper The freezing time equals the time to evaporate the remaining droplet volume V' at the measured evaporation rate, i.e., dV/dt ≈ -V'/t_fr, and the latent heat of evaporation L_e governs the energy balance, not the latent heat of fusion.
This is the load-bearing assumption in Eq. (14) and is not derived or justified physically.
domain assumption Infrared emissivity of cyclohexane is 0.96 as cited from Ref. [45].
Used to convert IR radiance to surface temperature; no in-situ calibration is reported.

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Pith. "Pith review of Evaporation-induced freezing dynamics of droplets levitated in acoustic field." pith.science (2026). https://pith.science/paper/K2SZZVKE

@misc{pith2026250522001,
  author       = {Pith},
  title        = {Pith review of: Evaporation-induced freezing dynamics of droplets levitated in acoustic field},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K2SZZVKE}},
  note         = {Machine review of arXiv:2505.22001}
}

read the original abstract

This paper presents the evaporation-induced freezing dynamics of pure cyclohexane droplets levitated via acoustic levitation. Acoustic levitation has attracted considerable attention across various fields owing to its potential to create lab-in-a-drop systems. While droplet evaporation is a fundamental physicochemical process in such a platform, the freezing of droplets induced by evaporation has been sparsely explored experimentally. For pure cyclohexane, the rapid evaporation of levitated droplets initiated freezing at the droplet surface. To better understand this evaporation-induced freezing process, the evaporation behavior of the levitated cyclohexane droplets was visualized and quantified using a high-speed camera and an infrared camera. According to the obtained experimental data, the evaporative heat transfer characteristics of the droplets were identified with theoretical models. Using the derived heat transfer coefficient, a mathematical prediction method for the onset of freezing was proposed and validated with the experimental data. These experimental findings offer valuable insights into the phase transition process and its potential physicochemical applications in a containerless environment.

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Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing,

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work page 2006

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Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing,

1 J. Park and J. Moon, “Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing,” Langmuir 22, 3506 (2006). 2 A. Ahsan, “Two phase flow, phase change and numerical modeling,” BoD –Books on Demand Ch. 13 (2012). 3 C. Bae and J. Kim, “Alternative fuels for internal combustion engines,” Proc. Combust. Inst. 36(3),...

work page 2006