Aerogel-based Leidenfrost vapor percolator for ultra-fast thermal cooling

Domain: physics
Published: 2025-12-29
Editorial outcome: major_revision

Abstract
The Leidenfrost effect—where liquid droplets levitate on superheated surfaces—hinders efficient heat transfer. Conventional mitigation strategies typically rely on rigid materials with complex surface engineering, but their applicability is limited by stringent weight requirements, especially in aerospace systems where every gram counts. Here, through controlled tuning of the drying stress field and targeted welding of hollow nanofibers, we construct an aerogel-based Leidenfrost vapor percolator featuring directed nano/micro tunnels for efficient vapor evacuation and flow-topology reconstruction. This ultralight (7 mg cm−3) permeator robustly suppresses the Leidenfrost effect up to 1000 °C and achieves a high heat flux of 110.43 W cm−2. Moreover, the permeator delivers a temperature drop of 760 °C under multi-flow injection, corresponding to a density-normalized Leidenfrost temperature reaching 142.9 °C cm3 mg−1. This two-order-of-magnitude enhancement over conventional materials highlights the pivotal roles of hierarchical structuring and vapor-channel regulation in overcoming the Leidenfrost barrier.

Introduction
Effective cooling of overheated surfaces is of paramount importance in diverse fields, from everyday technologies to high-demand industrial sectors such as steel manufacturing, aerospace, and nuclear power generation1–7. Active cooling methods, including spray and jet cooling, are highly favored due to their efficiency and reliability. However, their performances are often limited under extreme temperatures. When surface temperatures exceed the Leidenfrost temperature (LFT, typically 250 °C for water in metal surface), a continuous vapor film (λ vapor=0.026 Wm−1 K−1 @ 100 °C) forms, leading to thin film boiling, which increases thermal resistance and diminishes heat transfer efficiency2,3,8. Therefore, the phenomenon of interest primarily manifests within the thermal regime spans from the boiling point of water (100 °C at 1 atm) to the LFT, implying that elevating the LFT is a key strategic approach to sustaining efficient thermal transport3,9.

Current research for improving the LFT has primarily focused on rigid materials combined with complex surface engineering techniques2,6,9, including thermally conductive micropillars7,10–12, tailored surface roughness13–15, and porous structures16. These designs enhance solid-liquid interfacial contact and facilitate phase change10,17,18, while the incorporation of thermally conductive surface textures further reduces interfacial thermal resistance, thereby elevating the LFT to approximately 453–570 °C8,17. Nevertheless, most of these techniques rely on dense substrates with high intrinsic mass and limited structural adaptability, which constrain their applicability in weight-sensitive and thermally extreme environments such as spacecraft thermal protection systems. The challenge, therefore, is to design a lightweight and mechanically compliant cooling architecture that concurrently mitigates the Leidenfrost effect and fulfills the stringent mass requirements of advanced thermal protection systems.

Ultra-low-density ceramic nanofiber aerogels are promising for high-temperature thermal protection due to their high porosity, excellent chemical and thermal stability, and pronounced elasticity19–21. Critically, the highly cross-linked three-dimensional (3D) nanofibrous porous network in these aerogels provides optimized pathways for heat and mass transfer while maintaining structural integrity under extreme conditions19,20,22. Building on these features, we propose an LFT-enhancement design: a ceramic nanofiber aerogel-based vapor permeator (NAVP), in which the nanofibers are hollow, thereby facilitating the efficient removal of vapor induced by the Leidenfrost effect and elevating the LFT. Nevertheless, the proposed design presents considerable challenges, particularly in ensuring the structural integrity of the nanofiber tunnels during the drying process of hollow ceramic nanofibers (HCNFs) fabrication and in avoiding pore blockages during aerogel preparation.

To overcome these challenges, we present a compositional-structural engineering strategy that integrates solution exchange during HCNF preparation with congener-targeted welding of the resulting aerogels, thereby facilitating the advancement of ultralight vapor permeator. By leveraging the cavitation effect of low-surface-energy solvents to alleviate drying stress and employing confined welding to optimize interfacial coupling—crucial for preventing excessive crosslinking within the aerogel network—our NAVPs exhibit integrated nanoscale (nanofiber pores) and microscale (aerogel pores) tunnel architectures that facilitate efficient vapor evacuation during the Leidenfrost effect. Consequently, the ultralight (7 mg cm−3) NAVPs effectively suppress the Leidenfrost effect at temperatures up to 1000 °C with a heat flux of 110.43 W cm−2, performing comparably to the best-in-class thermal cooling materials3. Moreover, they can reduce the surface temperatures to about 240 °C (T initial=1000 °C, ΔT=760 °C) under a cumulative water droplet cooling rate of 9.5 mL min−1. More importantly, unlike traditional cooling systems that rely on structural stability, the failure threshold of NAVP materials is determined by the intrinsic melting point of the ceramic nanofibers, marking the conceptual shift in thermal management technology from structural defense to material intrinsic defense.

Results
Design and principle of aerogel-based Leidenfrost vapor percolator
Thermal cooling technology in extreme environments, such as advanced electronics cooling, high-performance computing systems, and aerospace applications, requires cooling materials capable of withstanding heat fluxes that often exceed 100 W cm−2 3,23. In this context, phase-change cooling techniques attract considerable attention due to their exceptionally high heat flux (q) and heat transfer coefficients (HTC) (Fig. 1a)23–25. The heat transfer curve of phase-change cooling is typically depicted in Fig. 1b9,26. An appeared trend is observed where the q increases with the superheat T w, particularly in the nucleate boiling regime (regions ii in Fig. 1b). However, once the T w surpasses the LFT, the Leidenfrost effect occurs due to the film boiling (Regions iii and iv in Fig. 1b), causing a rapid decline in q and often resulting in device burnout or catastrophic system failure2,9,26.

These results were further elucidated using the experimental setup shown in Supplementary Fig. 1, designed to capture the dynamic behaviors of water droplets on extremely superheated surfaces (T w=1000 °C). Notably, the droplets (~16 μL) were deposited in a controlled quasi-static manner (velocity of ~18 cm s−1), which corresponds to the standard conditions for the defining LFT, rather than being subjected to high-impact dynamic contact. Concretely, upon impact with a superheated bare metal surface (SUS 304 stainless steel, surface roughness Ra<0.1 μm), the droplet rapidly rebounded, remaining within the Leidenfrost regime throughout its duration (τ) of around 41 s due to the stable vapor layer characteristic of the Leidenfrost regime (Fig. 1c). Distinctly, the developed NAVP surface, characterized by honeycomb-like micro networks with aligned pore walls, strengthened capillary action of liquids and accelerated the evacuation of vapors (Fig. 1d). Thus, the droplet lifetime τ was drastically reduced to 0.417 s—approximately 98 times shorter than that on the bare metal surface, demonstrating a pronounced suppression of the Leidenfrost effect and an improvement in cooling performance. Notably, these phenomena were similarly demonstrated with liquid nitrogen, whose boiling point is about 300 °C lower than that of water. As shown in the Supplementary Fig. 2, the liquid nitrogen spread evenly over the NAVPs at 1100 °C, resulting in a sub-second lifetime. By contrast, when liquid nitrogen droplets impact bare metal surfaces, they exhibit vigorous bouncing, incomplete wetting, and persistent vapor films, consistent with the classical Leidenfrost phenomenon (Supplementary Fig. 3).

3D laser scanning microscopy was employed to characterize the surface microstructure of NAVP. As shown in Fig. 1e, the surface exhibits a randomly distributed rough morphology, with an arithmetic average height (Sa) of 17.58 μm. More crucially, the distinctive surface morphology of the NAVP establishes a strong coupling with the escaping vapor flow, thereby regulating the interfacial thermodynamic and hydrodynamic processes through three synergistic mechanisms. First, the micro/nano-scale asperities induce localized turbulence within the vapor layer, which enhances momentum exchange at the solid-vapor interface. Simultaneously, the recoil forces generated by these asperities disrupt the continuity of the vapor film, reducing interfacial thermal resistance9,10,27,28. Second, capillary-driven liquid spreading maintains intimate liquid-solid contact and effectively suppresses the formation of a continuous insulating vapor layer, ensuring robust thermal coupling while providing interconnected pathways for vapor evacuation15,27,28. Third, the hierarchical porous architecture facilitates boundary-slip–enhanced vapor transport, which significantly lowers viscous resistance and enables rapid radial drainage of vapor beneath the droplet (Fig. 1f)15,27,28.

Furthermore, to gain a comprehensive understanding of the heat-transfer characteristics across different surfaces, we systematically investigated the constitutive relationship between the evaporation lifetime τ and the surface temperature T w. As shown in Fig. 1g, the bare metal surface shows a typical two-phase heat transfer behavior: as T w rises from 100 °C to 200 °C, τ decreases from 50.2 s to 1.644 s (a 96.7% reduction) due to enhanced thermal convection and increased Nusselt number. Once T w exceeds the critical transition temperature (LTF of bare metal surface is 250 °C), however, τ sharply increases to 71.92 s (about 43.8 times higher), corresponding to the formation of a stable Leidenfrost vapor film (with a thickness > 500 μm, measured via high-speed imaging). Remarkably, the NAVP surface maintains ultra-low τ values (0.417–5.124 s) across a broad temperature range of 100–1000 °C, which is lower than that of the bare metal surface, and no CHT transition point is observed.

Moreover, the regulation of aerogel density (D) is crucial for enabling efficient evacuation of the vapor generated in substantial quantities. Notably, the density D can be readily tuned by altering the concentrations of HCNFs and ceramic sol, allowing D to be varied over the range of 4–12 mg cm−3 19. As shown in Fig. 1h, we observe a non-monotonic dependence of droplet lifetime τ on material density D, reflecting the distinct failure modes at both low- and high-density limits. Specifically, at low densities (D<7 mg cm−3), the droplet exhibits a short τ (with an average of 0.519 s), primarily due to mechanical collapse of the nanofiber scaffold rather than efficient cooling. Cracks formed during impact accelerate local phase change and rapid evaporation, yet the overall structural failure of NAVP renders it unsuitable for practical applications. Conversely, at high densities (D>9 mg cm−3), excessive fiber packing leads to pore clogging, delaying vapor evacuation and promoting the reformation of a continuous vapor film, thereby prolonging τ (averaging 2.532 s) and reducing the heat flux. These two failure modes collectively define a well-defined bounded operational regime for NAVP functionality, with the optimal density window (~7–8 mg cm−3) enabling complete droplet spreading, stable contact, and rapid phase-change cooling, with τ around 0.4 s at 1000 °C.

We further investigated the evolutionary pattern of the heat flux (q). As shown in Fig. 1i, the q exhibits a distinct stage-by-stage variation with increasing surface temperature (T w). In the sub-Leidenfrost region (T w<250 °C), both the bare metal and NAVP systems display a similar linear enhancement in q. However, once T w exceeds the LFT of the metal (i.e. T w ≥ 250 °C), a pronounced divergence emerges between the two samples. Concretely, the NAVP system maintains an average heat flux of 72.22 W cm−2 across the supercritical temperature range (300–1000 °C), which attributed to the unique capillary structure and the associated specific surface area multiplication effect. In contrast, the metallic system experiences a sharp decline in q from 40.024 W cm−2 at 200 °C to 3.037 W cm−2 at 300 °C —nearly an order of magnitude reduction— attributable to the continuous formation of an insulating vapor film with a low thermal conductivity of 0.026 W m−1 K−1.

Formation of the HCNFs
The NAVPs manufacturing process began with the formation of flexible, SiO2 HCNFs by combing coaxial electrospinning29, low-surface-energy solvent exchange technology, and a precisely controlled calcination process30,31. As illustrated in Fig. 2a, two injection syringes containing distinct electrospinning fluids were connected to the coaxial spinneret, which were mounted on an electrospinning apparatus31. Notably, the selection of spinning fluids were tailored based on the desired functional properties of the final material32. In the context of developing a thermal cooling material, it was of paramount importance to consider the flexibility, mechanical strength, and thermal stability of the sheath material. Additionally, the incorporation of an inert, immiscible (or poorly miscible) liquid as the core was essential for attaining the desired hollow structure. Such liquids serve as versatile and adaptive hollow nanofiber templates that obviate the need for molecular-level assembly.

In this work, a silica precursor (SP) sol was employed as the sheath spinning fluid, while paraffin oil (PO) was used as the core spinning fluid33. Mechanistically, the gelation of the SP sheath prior to the electrically driven breakup of the coaxial PO nanojet promoted the formation of a core–sheath architecture with a PO-filled core, which acting as a liquid template. This process was meticulously optimized by controlling the cross-sectional dimensions of the sheath and core spinnerets and applying distinct feeding rates for the SP sol and PO solutions to ensure a uniform flow of both components. Under these optimized conditions, precursor fibers were successfully fabricated29,31–33. A metallic plate, serving as the counter-electrode or collector, was positioned at a short distance—typically several centimeters—from the spinning nozzle.

Essentially, upon the evaporation of the core solution in drying process, the resulting nanofiber structure has undergone a morphological transition from a liquid-filled template to air-filled nanofibrous architecture, culminating in the desired hollow form. However, HCNFs often experienced substantial deformations during the evaporation process, which was attributable to capillarity-produced pressure within nanoscale pores. A crucial step, therefore, is the precise exchange of the core PO liquid with low-surface-energy solvents before drying (Fig. 2b). The evaporation of liquid contained in porous materials is typically governed via the following three distinct process: the liquid-vapor interface recession, the shrinkage due to drying, and the cavitation effect (Supplementary Fig. 4)34. In our work, the cavitation effect emerges as a pivotal factor in the drying process of core solutions (standard atmospheric pressure), beyond the scope of the two commonly recognized evaporation processes35. Mechanistically, cavitation occurs when the liquid confined within nanoscale pores is subjected to a capillary-induced tensile stress that exceeds its cohesive strength, triggering vapor-bubble nucleation within the gel matrix. This phenomenon is particularly pronounced when low–surface-energy solvents (e.g. n-hexane, n-octane) are involved, as the free energy barrier for cavitation scales strongly with the liquid’s surface tension (γ3) under constant pressure34, making higher-γ liquids significantly more resistant to cavitation. Moreover, the inherent surface chemistry characteristics of silica ceramic network contribute to the cavitation process. The presence of surface defects, such as residual silanol groups from inadequate sialylation, facilitates heterogeneous nucleation of vapor/air bubbles. This process requires less energy compared to homogeneous nucleation, thereby promoting the preservation of the nanofibrous pore architecture34,36,37. Consequently, n-hexane was selected as the exchange bath to replace PO prior to the drying of the precursor fibers. In short, through cavitation-induced stress release, this approach efficiently mitigated drying stress and maintained the integrity of the hollow structure. In contrast, direct drying and calcination led to pronounced structural collapse (Supplementary Fig. 5), emphasizing the vital importance of solvent exchange and cavitation control in preserving structural integrity of the HCNFs.

Further morphological and structural characterization of the as-synthesized HCNFs were conducted using High-Resolution Transmission Electron Microscopy (HRTEM) imaging. Fig. 2b and Supplementary Fig. 6 show representative low-magnification HRTEM images of HCNFs, clearly revealing their hollow configuration. To determine the chemical composition of the HCNFs, energy-dispersive X-ray spectroscopy (HRTEM-EDS) mapping was performed on a single nanofiber. As shown in Fig. 2c, Si and O signals were homogeneously distributed along the hollow framework, confirming that the HCNFs are hollow nanofibers with amorphous Si-O-Si walls38.

We further evaluated the mechanical flexibility of individual HCNFs by quantifying the radius of curvature (R c) at the critical bending points, where extreme deformations occur. Particularly, one end of each HCNF was secured to a substrate, while the other was connected to a movable probe (Fig. 2d and Supplementary Fig. 7). This setup allowed the fiber to be bent until fracture, which facilitated the calculation of R c 39,40. As illustrated in Fig. 2e, the R c for HCNFs is determined to be ~1.82 μm (HCNF-1) and ~1.14 μm (HCNF-2), a value that aligns with that of solid SiO 2 ceramic nanofibers (SCNF) with a R c of ~1.11 μm. The lower R c value indicates enhanced flexibility, reflecting a more pronounced angular velocity of the tangential direction in relation to the arc40. This characteristic is pivotal for materials that are subjected to bending stress, as it implies a greater capacity for deformation without structural failure.

Fabrication of NAVPs
The fabrication of NAVPs was guided by two key design principles: (i) constructing a hierarchically interconnected HCNF aerogel with well-controlled tunneling orientation, and (ii) establishing a robust interfacial bonding network that integrates elastic deformability with thermal stability while preserving the integrity of the multiscale pore architecture. To fulfill the first principle, an oriented freezing-assisted molding approach was developed to precisely regulate the 3D assembly and directional alignment of HCNFs. To satisfy the second, a directed interfacial welding strategy was employed, wherein Methyltrimethoxysilane (MTMS)-derived silica sols (Supplementary Fig. 8) were introduced to modulate interfacial coupling and enable controlled bonding among HCNFs. This strategy features three key innovations: (i) the intrinsic chemical compatibility between the MTMS-derived silica precursor and the HCNF matrix ensures thermally stable interfacial adhesion; (ii) the tunable sol-gel transition kinetics enable molecular-scale gradient bonding across the fiber junctions; and (iii) the spatial domain-confinement effect reinforces interfacial connectivity without compromising the aerogel’s framework topology or the hollow microstructure of HCNFs.

As presented in Fig. 3a, b, a straightforward method that integrated directional freezing-induced assembly and confinement targeted welding was developed to fabricate the NAVPs. Initially, short-chain n-alkane–filled (e.g., n-octane, n-hexane) HCNFs were selected to engineer targeted interfacial welding sites. The n-hexane–filled HCNFs were used as a model system, uniformly mixed with an MTMS-derived ceramic sol, and subsequently frozen directly in liquid nitrogen, enabling confined phase transition and localized interfacial welding during the subsequent sol-gel solidification process. As expected, a honeycomb-like micro network characterized by aligned pore walls was produced (Fig. 3h–l). To further increase the structural stability of the NAVPs, a high-temperature calcination process (in air) was performed. This procedure succeeded in removing the organic constituents within the NAVPs and facilitating transformed hydrolyzed ceramic sol (Supplementary Fig. 9) into a durable inorganic network, thereby strengthening the structural integrity of the NAVPs19,40.

To gain molecular-level insight into the interfacial coupling mechanism, molecular dynamics (MD) simulations were subsequently conducted by shearing the MTMS sol confined between HCNF walls and n-hexane at the nanoscale (Supplementary Note 2)41–43. Specifically, the Lennard-Jones potential was employed to describe the interfacial interactions. A cut-off distance of 12.5 Å was applied, with van der Waals and Coulomb interactions calculated using atomistic and Ewald methods, respectively. After energy minimization, the sandwich structure was subjected to shear along the z-axis after 50 ps, 200 ps and 400 ps with a displacement rate of 0.05 Å ps−1 in the NVT ensemble regulated by Nosé thermostat. Periodic boundary conditions were alternately applied in two directions to minimize edge effects (Supplementary Fig. 10). The dynamic trajectory was recorded every 5 ps. As shown in the simulation snapshots (Fig. 3g), in sharp contrast to n-hexane, the ceramic sol exhibited a strong interfacial attraction to the HCNF walls, consequently forming a distinctive wall-induced layering configuration that is characteristic of confined sol–surface interactions42,44. The calculated interfacial interaction energy (E in) for the Si sol/HCNF system reached −284.98 kcal mol−1, which is nearly an order of magnitude more negative than that of the Si sol/n-hexane system (−29.24 kcal mol−1), clearly indicating that the HCNF surface preferentially binds to the MTMS-derived Si sol rather than to n-hexane (Fig. 3e)45. This strong interfacial affinity can be primarily attributed to two dominant non-covalent interactions—hydrogen bonding (−15.34 kcal mol−1) and van der Waals forces (−222.61 kcal mol−1)—while the electrostatic contribution remains negligibly small (Fig. 3e and Supplementary Table 1).

Moreover, the electrostatic potential (ESP) distribution of the Si sol/HCNF system further confirmed the presence of hydrogen bonding, as evidenced by the positive ESP regions (red) localized on hydrogen atoms and the negative ESP regions (blue) on oxygen atoms (Fig. 3f)46. This electrostatic attraction between oppositely charged sites promotes the formation of stable hydrogen bonds at the interface. Inversely, the nonpolar nature of n-hexane limits both physical adsorption and chemical bonding with the Si sol, consistent with the weak interfacial adhesion observed in the simulation. In short, the stronger affinity of the silica sol for HCNFs, compared with n-hexane, provides a unique strategy for engineering anchored and confined welding sites. By filling the HCNFs hollow channels with nonpolar n-hexane, the inner spaces are effectively occupied, and the highly diluted concentration of the ceramic sol prevents excessive infiltration into the hollow channels and framework, thereby avoiding clogging or the formation of an uneven silica layer (Fig. 3c, d).

Encouraged by the above results, the NAVPs were further examined using SEM. As shown in Supplementary Fig. 11, the top-view SEM images reveal that the ceramic sol forms a continuous and uniform interconnecting layer among the HCNFs, effectively filling the interstitial regions after welding. Notably, no pore blockage was observed within the HCNFs, suggesting that the ceramic sol exhibits excellent chemical affinity and structural compatibility with the HCNFs47. These findings collectively demonstrate that the intrinsic hollow architecture of the HCNFs is well preserved throughout the NAVP fabrication process.

Mechanical property of the NAVP material
During spray cooling, the kinetic impact of atomized droplets imposes stringent requirements on the high-strain-rate mechanical properties of the cooling medium (Fig. 4a–c). To elucidate this impact resistance, the dynamic mechanical behavior of NAVPs were systematically characterized via dynamic mechanical analysis (DMA). As shown in Fig. 4d, the NAVPs exhibit remarkable mechanical resilience, maintaining structural integrity under compressive strains (ε) as high as 80%. The corresponding stress (σ) reached 19.8 kPa, reflecting a load-bearing capability exceeding 10,000 times their own weight—an exceptional mechanical robustness rarely achieved in other porous materials. Furthermore, hysteresis curves from 1,000 loading–unloading compressive cycles at ε=50% revealed negligible plastic deformation (Fig. 4e and Supplementary Fig. 12), and the NAVPs retained more than 50% of their maximum stress and initial Young’s modulus after cycling (Fig. 4f), confirming their remarkable structural robustness and cyclic durability. Dynamic compressive tests conducted via DMA further revealed that both the storage modulus and loss modulus remained nearly constant and independent of angular frequency across three orders of magnitude (0.01–100 Hz) (Fig. 4g). The measured damping ratio (~0.15) over the entire frequency range indicates that the elastic response predominates in the NAVPs, which can be attributed to their robust and viscoelastic nanofibrous network.

In addition, the dynamic deformation process of the NAVP under impact loading was captured by an imaging system. The real-time image sequence demonstrates that the NAVP can rebound a 6 mm diameter bearing steel ball twice (Fig. 4h), clearly confirming its exceptional dynamic elasticity.

The mechanical response of the NAVP was comprehensively investigated through multi-physics field-coupled finite element analysis (Supplementary Note 3). A 3D network model was developed and discretized using tetrahedral meshing, and vertical compression was simulated within the framework of a linear-elastic eigenstructure model. The simulation results reveal a pronounced structure-oriented stress distribution within the 20% strain range (Fig. 4i, j). Most of the applied stress is transmitted along the primary axis of the honeycomb tubular network, while the stress concentration factor (K t) at the fiber junctions ranges from 1.15 to 1.28—significantly lower than that of conventional foam materials (K t>2.5). This enhanced stress homogenization capability arises from three synergistic mechanisms: (i) the bionic honeycomb architecture guides multi-direction load diversion; (ii) the confined welding strengthens inter-fiber coupling and prevents interfacial debonding, and (iii) the controlled elastic buckling within the hollow tubular cells dissipates strain energy reversibly. Consequently, the octahedral topology at HCNF cross-nodes stabilizes the stress anisotropy index (AI) within 1.8–2.3—far below that of disordered porous networks (AI>5)—thereby ensuring homogeneous stress transfer and effectively mitigating brittle fracture48,49.

Thermal cooling applications of the NAVP material
We finally carried out a systematic investigation into the performance challenges of spacecraft thermal protection systems (TPS) under extreme multi-physics field-coupled environments. As depicted in Fig. 5a, the spacecraft experiences cyclic temperature fluctuations ranging from −120 °C to 100 °C during orbital operation; in the re-entry phase, the TPS is exposed to: (i) The initial high-thermal-shock phase, characterized by a transient temperature surge exceeding 3000 °C with a duration of less than 120 s. (ii) This is subsequently followed by a low-temperature vacuum phase, during which the surface temperature drops to −90 °C. (iii) Finally, in the terminal extreme re-entry phase, the TPS encounters a secondary atmospheric entry, during which it is subjected to ultra-high-temperature plasma flow (≈1900 °C) accompanied by intense aerodynamic shear stress exceeding 12 kPa. The thermal-mechanical coupling boundary conditions have been rigorously validated through high-enthalpy wind-tunnel simulations and multi-scale fluid–structure interaction analyses (Fig. 5b and Supplementary Fig. 13).

To address the thermal management limitations of conventional cooling materials, we designed and constructed a multimodal extreme thermal environment experimental platform, integrating a gradient heat-flux loading module, a high-speed infrared thermography system, and an active spray cooling unit (Supplementary Note 4 and Supplementary Fig. 1). The gradient heat-flux module employs a 15-kW electromagnetic induction heater coupled with a water-cooling circuit, enabling precise control of heat-flux density within 300–1300 °C. Notably, for low-temperature experiments (100–200 °C), a precision-controlled heating stage was employed to maintain uniform thermal boundary conditions. The high-speed infrared camera continuously recorded real-time surface temperature distributions (Supplementary Fig. 14), providing synchronized thermal field data for transient analyses. Meanwhile, the active spray cooling unit enabled dynamic regulation of the coolant flow rate (0.5–9.5 mL min−1) and impact frequency via pressure modulation, allowing accurate reproduction of the transient liquid–vapor interaction during re-entry.

As shown in Fig. 5c, droplets were continuously released at a flow rate (Q) of 0.5 mL min−1 from a vertical height of 6 mm, with the release interval carefully set to exceed the surface thermal relaxation time, ensuring that the temperature recovered to its initial equilibrium state between successive impacts3. The experimental results reveal that the temperature fluctuation on the bare metal surface after a single droplet impact is negligible, as the Leidenfrost effect induces a stable vapor cushion that prevents direct liquid-solid contact and severely limits transient heat exchange. In sharp contrast, the NAVP surface exhibits a temperature reduction of about 250 °C following a single droplet impact, driven by rapid liquid imbibition and efficient vapor evacuation through its multiscale porous network (Supplementary Fig. 15). This superwetting-mediated cooling behavior remains highly stable, with the cooling-efficiency decay rate below 20% even after 17 successive impact cycles, confirming the exceptional thermal durability and impact-resilient heat dissipation capability of the NAVP material.

Moreover, the NAVP material exhibits a cooling enhancement under repeated droplet impacts. As shown in Fig. 5d, e, at a flow rate of Q=4 mL min−1 and an initial surface temperature of 1000 °C, the temperature drop (ΔT) increases to approximately 691 °C. This reduction reflects a cumulative cooling effect arising from sequential liquid replenishment, intensified capillary infiltration, and accelerated vapor evacuation within the hierarchical porous framework of the NAVP, thereby enabling efficient and sustainable heat dissipation even under extreme high-enthalpy conditions. To quantitatively elucidate this cumulative cooling enhancement, the time-dependent evolution of the interfacial heat transfer can be analyzed using a transient thermal resistance model (Eq. 1). The progressive reduction in R th(t) originates from persistent thin-film evaporation and continuous improvement of interfacial heat transport at the droplet-substrate interface:

R th(t) = 1 / (k eff * sqrt(π * α eff * t)) * (1 + B i(t))

where the time-dependent Biot number is defined as:

B i(t) = h eff * sqrt(π * α eff * t) / k eff

Here, k eff and α eff represent the effective thermal conductivity and thermal diffusivity of the porous NAVP substrate, reflecting internal heat conduction. The interfacial heat transfer coefficient h eff accounts for phase-change-induced evaporation and vapor-phase transport at the droplet–surface interface. As repeated impacts increase the thermal penetration depth L(t) = sqrt(α eff * t), the Biot number correspondingly rises, indicating a transition from conduction-dominated to interface-limited heat transfer. This dynamic shift produces a non-linear yet asymptotic reduction in R th(t), thereby maintaining enhanced and self-sustaining cooling performance. In addition, the nanoscale surface features of the NAVP promote asymmetric contact-line pinning, effectively suppressing the Leidenfrost effect and preserving efficient heat exchange even at ultra high temperatures.

Flow-dependent studies further underscore the active thermal management capability of NAVP system (Fig. 5f, g). Increasing the flow rate to Q=9.5 mL min−1, corresponding to the jet cooling mode, the surface temperature undergoes an exponential decay from 1000 °C to 240 °C (ΔT=760 °C) over a period of 30 s (Supplementary Fig. 16). Such a rapid and monotonic temperature drop demonstrates that the NAVP responds sensitively to both flow rate and thermal load, exhibiting a quasi-linear flow-temperature coupling behavior that enables adaptive regulation under dynamic heat flux conditions. More strikingly, NAVP demonstrates the synergistic advantages of ultra-lightweight properties and high LFT compared to conventional active cooling materials (Fig. 5h and Supplementary Table 2)3,17,18,47,48, offering a promising potential for spacecraft re-entry thermal protection and the heat dissipation of high-power density electronics.

Discussion
In summary, a compositional-structural engineering strategy was proposed, which integrates solution exchange in the nanofiber preparation process with targeted inter-fiber welding of the resulting aerogel, achieving the synergistic construction of NAVP. Remarkably, leveraging low–surface-energy solvent cavitation to relieve drying stress and confined welding to enhance interfacial coupling yields NAVPs with hierarchically integrated tunnel architectures, enabling efficient vapor evacuation under Leidenfrost conditions. Importantly, the developed NAVPs effectively suppress the Leidenfrost effect even at temperatures approaching 1000 °C, while maintaining an ultra low density of 7 mg cm−3. The proposed percolator provides a potential approach to mitigate the Leidenfrost effect for efficient heat transfer.

Methods
Materials
Tetraethylorthosilicate (TEOS, Si(OC 2H 5) 4, 98%, Greagent), Methyltrimethoxysilane (MTMS, Shanghai energy chemical Co. Ltd.), Phosphoric acid (H 3PO 4, 85 wt%, Aladdin), Oxalic acid (H 2C 2O 4, 99%, Aladdin), n-hexane (C 6H 14, >99%, Greagent), Paraffin oil (CP, Greagent), Ethanol (EtOH, 99.7%, Greagent), Poly (vinyl alcohol) 1788 (PVA1788, Aladdin). Deionized water (resistivity > 18.2 MΩ cm) was used throughout all experiments.

Experimental methods
Preparation of silica precursor sol. The silica precursor sol was synthesized via the sol-gel method50. In a typical procedure, TEOS was subjected to hydrolyzed in the presence of H 3PO 4 as a catalyst for 8–10 hours, maintaining a mass ratio of MTMS: H 2O: H 3PO 4 at 100:100:1.1. After complete hydrolysis, a 13–14 wt% aqueous solution of PVA1788 was introduced into the silica sol at a mass ratio of 1:1. The resulting mixture was further stirred for an additional 3 h at ambient temperature to ensure full homogenization, yielding the SiO 2 precursor (SP) sol.

Preparation of HCNFs. Hollow SiO 2 ceramic nanofibers (HCNFs) were fabricated via a synergistic approach combining coaxial electrospinning and solvent exchange technology, followed by a calcination process. Initially, SP sol and paraffin oil (PO) were simultaneously processed using a coaxial electrospinning setup at a voltage of 14 kV. The collection distance was 12-15 cm, while flow rates for sheath/core fluids were 1 mL h−1/0.2 mL h−1. The operations were conducted under controlled environmental conditions (humidity 28 ± 3%; temperature 25 ± 3 °C). Subsequently, the as-spun nanofibers were immersed in n-hexane for 1–4 hours to enable sufficient diffusion and complete replacement of the PO phase by n-hexane, producing h-nanofibers. Finally, the h-nanofibers were air-dried at room temperature for 12 h and then calcined at 800 °C for 1 h to obtain HCNFs with well-defined hollow structure.

Preparation of NAVPs. NAVPs were fabricated via a directional freeze-drying method. Specifically, 0.4 g of MTMS with 0.003 g of oxalic acid were dissolved into 80 g water and stirred for at least 40 min to prepare MTMS silica ceramic sol42. Furtherly, 0.14 g of solid SiO 2 ceramic nanofibers (SCNF) (Supporting Methods) were introduced to the 40 g MTMS sol and uniformly dispersed to yield SCNF/MTMS dispersion. To achieve NAVPs with a target density (7 mg cm−3), another 0.14 g of HCNFs were uniformly dispersed in n-hexane and stirred for 5 h to allow the solvent to penetrate the hollow channels of HCNFs, producing h-HCNFs. The h-HCNFs were then incorporated into the SCNF/MTMS dispersion, and the resulting mixture was rapidly poured into a directional mold, followed by freezing at −120 °C for 5 min in a liquid nitrogen bath. The frozen monoliths were freeze-dried for 36 h in a vacuum freezer to remove ice crystals and maintain the directional porous framework, forming dried aerogels. Subsequently, the dried aerogels were calcined at 900 °C to accomplish the inorganic conversion and enhance the structural stability, producing NAVPs.

Characterization
The microstructures of NAVPs were characterized by FE-SEM (S-4800) and TEM (JEM-2100F). Compression mechanical tests were performed using a DMA (TA-Q850) instrument. The fast recovery of NAVPs rebounding from a high-speed steel ball was recorded by a FujiFilm X-T200 camera operated at 800 frames per second. The experimental set-up of spreading and evaporation dynamics of water drops mainly consisted of an induction heater, a syringe pump (LM60B-RZ1030-4), two high-speed cameras, and an infrared camera. The induction heater (PIEN-10GT-3SZ) was used to maintain the samples at a prescribed temperature, in the range of 300–1150 °C. The precision-controlled heating stage (model JF-956) used for experiments in the low-temperature range (room temperature to 250 °C). The oblique and side views of water drops were filmed with two high-speed cameras NAC MEMRECAM HX-7S (2560*1680), NAC MEMRECAM GO-5M (2560*1920) operating at 1000 frames per second.

Data availability
Source data are provided as a Source Data file. Source data are provided with this paper.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study proposes a vapor permeator (NAVP) based on ceramic hollow nanofiber aerogel. Through innovative fractal network design and preparation process, it effectively suppresses the Leidenfrost effect on the high-temperature surface and achieves efficient thermal management. The following are a few issues that need to be addressed:\n1. The study highlights that fractal network design (\"fractal structural network\" and \"integrated nanoscale/microscale tunnel architectures\") facilitates vapor evacuation. Does there exist an optimal combination of fractal parameters to maximize the Leidenfrost suppression effect?\n2. The cavitation effect of low surface energy solvents (e.g., n-hexane) is reported to mitigate drying stress and preserve hollow nanofiber integrity. Please clarify how does the solvent's surface tension quantitatively influence cavitation-induced stress relief?\n3. The NAVPs demonstrate stability under 1,000 cyclic compressions at 1,000°C. To further elucidate the mechanisms please clarify the principle of micro-nano rough surfaces resist thermal expansion and oxidative degradation.\n4.Experimental results demonstrat that the NAVP structure significantly reduces droplet lifetime compared to bare metal surfaces (Figs. 1c-d). To further strengthen this work, the role of the honeycomb-like micro-network in facilitating vapor escape could benefit from additional analysis. Specifically, a more detailed explanation of how vapor efficiently traverses the aligned pore walls of the honeycomb structure—without forming insulating vapor layers that trigger the Leidenfrost effect—would help clarify the underlying mechanism. For example, highlighting the interplay between capillary-driven vapor evacuation would deepen readers' understanding.\n5. NAVP shows potential for aerospace thermal protection systems (p. 18), where vacuum and microgravity conditions are critical. While the hierarchical pore structure effectively evacuates vapor under terrestrial conditions could the absence of gravity-driven fluid dynamics (e.g., buoyancy) alter vapor transport mechanisms? For instance, in microgravity, capillary forces may dominate vapor escape, but does the honeycomb structure inherently rely on gravity-assisted liquid redistribution? Clarifying how the design ensures vapor evacuation efficiency in such extreme environments—through simulations or experimental validation would strengthen the applicability claims.", "reviewer_2": "1. The evaporation tests involves an induction heater to heat the surfaces up to 1000 °C. Since induction heaters can induce electric currents within the water and directly heat the water, how was it controlled in these tests?\nThe details of the Leidenfrost test procedure require major revision. It is not clear how the test was performed, the size of the tested samples, and how the surface temperature was measured. Moreover, how was the liquid nitrogen test performed?\nWhat was the test chamber condition, e.g., saturated, vacuum etc.?\nIf the infrared camera was utilized to record surface temperature at 30 Hz, how were two high-speed cameras (1000 fps) and one infrared camera (30 Hz) synchronized?\n4. Do the reported temperatures correspond to local or average surface temperatures?\n5. The supplemental information states that the induction heater was used to maintain samples at 250 – 1150 °C. However, Fig. 1 shows the test results are 100 °C. Which heating mechanism was used at this temperature?\n6. Since liquid nitrogen properties are significantly different than water, why 16 µL droplet was used for both fluids?\n7. In Fig. 5d-e, the surface temperature was heated to 1000 °C and subjected to multi-impact mode at a flow rate of 4 mL min-1. How many impacts correspond to the presented 691 °C temperature difference? Is it possible that the number of impacts are further increased the surface temperature decreases to room temperature?\n8. The cooling efficiency decay rate was found to be less than 3% after 17 cycles. What is the reason associated with this decay?\n9. The contact angle of the nanofiber was claimed to be varying from 10° to 65° and this gradient was associated with heat transfer enhancement. How was it measured? Since nitrogen is low surface tension fluid is it the same mechanism for heat transfer enhancement with nitrogen?\n10. The NAVP is shown to be a revolutionary solution for spacecraft re-entry thermal protection system. However, technology requires a 6 mm vertical distance from the droplet release to the cooling surface. Therefore, it is not clear how technology can benefit the spacecraft re-entry vehicles. Moreover, the results are presented up to 1000 °C whereas re-entry vehicles experience ~ 3000 °C. How does the thermal performance of NAVP compare with conventional thermal protection systems at these extreme flight temperatures?\n11. If the proposed technology is utilized in aerospace and space systems, the overall weight of the system may increase due to the requirement of coolants, fluid delivery and control systems. It seems that the weight of the payload is increased as compared to the stated reduction of payload weight. Please clarify.\n12. What is the effect of reentry high Mach and transient flight conditions on droplet delivery and NAVP heat transfer performance?\n13. What is the effect of substrate materials?\n14. In Eq. (1), evaporative/convective effects are considered in effective heat transfer coefficient. Since radiation is signification at high temperatures, why is it neglected? Moreover, why does Eq. (1) consider only substrate thermal conductivity instead of effective thermal conductivity from the porous layer?\n15. Please include reference for “For instance, in the context of spacecraft thermal protection systems, each additional kilogram of thermal control material incurs an estimated $20,000-50,000 in launch costs.”\n16. Please include reference for “NASA-62 STD-5017 stipulates that the surface density of thermal protection systems should be less than 100 mg cm-3, with a target density of less than 10 mg cm-3”.\n17. The surface of NAVP exhibits an arithmetic average height (Sa) of 17.58 μm roughness. How does the LFT compares with a bare surface of similar 17.58 μm roughness with the reported bare surface of roughness ~ 0.1 μm?\n18. The suppression of the LFT on NAVPs was demonstrated with liquid nitrogen at 1100 °C resulting in a sub-second lifetime. What is the liquid nitrogen lifetime on bare metal?\n19. Please provide quantitative slip velocity and interfacial thermal resistance comparison for bare surface and NAVP.\n20. The vapor thermal conductivity is reported as 0.026 W m-1 K-1. What is the corresponding temperature?\n21. The surface tension of water was reported as 72 mN m-1. Why the properties are considered at room temperature instead of saturation conditions?\n22. The thermal mechanical coupling boundary conditions were rigorously validated through high-enthalpy wind tunnel experiments. Please provide reference or test results to demonstrate the validation studies.", "reviewer_3": "see the attachment."}, "author_response": "Point-by-Point Responses to the Comments\nResponse summary: We sincerely appreciate the reviewers’ insightful and constructive\ncomments, which have greatly helped improve the clarity and quality of our manuscript.\nIn response, we carefully revised the text and addressed similar issues throughout the\nManuscript. We hope that our explanations and revisions meet the reviewers’\nexpectations. Detailed point-by-point responses are provided below, with our replies\nin blue italics and the reviewers’ comments in black.\nComments from Reviewer #1:\nThis study proposes a vapor permeator (NAVP) based on ceramic hollow\nnanofiber aerogel. Through innovative fractal network design and preparation process,\nit effectively suppresses the Leidenfrost effect on the high-temperature surface and\nachieves efficient thermal management. The following are a few issues that need to be\naddressed:\nResponse: We sincerely thank the reviewer for the positive and encouraging summary\nof our work. We are grateful that the reviewer recognizes the novelty of the NAVP\ndesign based on ceramic hollow nanofiber aerogels, as well as its effectiveness in\nsuppressing the Leidenfrost effect and enhancing thermal management performance.\nThe recognition of our efforts in both the fractal structural design and the fabrication\nstrategy is highly motivating. In the revised manuscript, we have further clarified the\nunderlying mechanisms and improved the descriptions related to the vapor transport\nbehavior and thermal regulation application, as suggested. We hope these revisions\naddress any remaining concerns and better convey the significance of our work.\n1. The study highlights that fractal network design (“fractal structural network” and\n“integrated nanoscale/microscale tunnel architectures”) facilitates vapor evacuation.\nDoes there exist an optimal combination of fractal parameters to maximize the\nLeidenfrost suppression effect?\nResponse: We sincerely thank the reviewer for this insightful and fundamental question.\nAs suggested by the reviewer, determining the optimal fractal parameters is\ncentral to our strategy for enhancing vapor evacuation and suppressing the Leidenfrost\neffect. Accordingly, we present (I) a derivation linking fractal geometry to effective\n1\nvapor permeability, and (II) model predictions with a visualization of the design\nlandscape that delineates the optimal parameter window.\nI. Theoretical Model\nThe NAVP system features a hierarchical tunnel architecture consisting of\nnanoscale fibrillar pores (100-200 nm) embedded within a microscale cellular matrix\n(20-100 μm), forming a multi-level fractal network. To characterize the vapor\ntransport behavior in such a complex porous structure, we employed a fractal porous\nmedia model that accounts for the hierarchical and self-similar features of the system.\nThe total vapor permeability (k) was derived by integrating the Hagen–Poiseuille flow\nacross a fractal-distributed pore network, weighted by the volumetric contribution of\neach pore size. The resulting expression is given by: 1,2,3,4\nk ~ ϕ∙r4 ∙\n3-Df\n∙Λ (1)\nmax\n7-Df\nHere, ϕ is porosity, r is the maximum pore radius, D ∈ [2~3]is fractal dimension,\nmax f\nand Λ denotes the topological connectivity factor accounting for network percolation\nand continuity. This expression reveals a strong nonlinear dependence of permeability\non both structural complexity and pore size scaling.\n1.1. Derivation of Eq. 1\nAccording to the fractal pore model by Pfeifer & Avnir,1 the pore volume\ndistribution follows: 2,3\ndV ~r2-Df (2)\ndr\nIntegrating over the full range of pore radii gives the total pore volume V , which\np\nis proportional to the porosity ϕ:\nϕ ~∫\nrmaxr2-Dfdr\n=\nr\nm\n3-\na\nD\nx\nf (1-r\nm\n3-\na\nD\nx\nf)\nD\nf\n∈ [2, 3] (3)\nrmin 3-Df\nwhere r =\nrmin\n≪1.\nratio\nrmax\nThe volumetric flow rate Q through a single cylindrical pore of radius r follows\n0\nthe Hagen–Poiseuille law:\nπr4 ∆P\nQ (r) = ∙ (4)\n0 8μ L\nTherefore, the total vapor flow rate Q\nt\nthrough the network is obtained by\nintegrating the product of single-pore flow rate and pore volume distribution:\nt rmin\nBy Darcy’s law, the permeability k is:\nkA ∆P r\n7-Df\n(1-r\n7-Df)\nQ = ∙ ⇒ k ~ max max (6)\nt 8μ L 7-Df\nUsing Darcy’s law and eliminating common terms, the resulting permeability\nbecomes:\nk ~ ϕ∙r4 ∙ 1-r m 7- a D x f ∙ 3-Df (7)\nmax 1-r 3-Df 7-Df\nmax\nThis is the general form of permeability as a function of fractal geometry and\nporosity. For r ≪1, both correction terms converge to unity:\nratio\nk ~ ϕ ∙r4 ∙\n3-Df\n(8)\nmax\n7-Df\nTo account for percolation continuity, we introduce the topological factor Λ,\nwhich scales with the difference between the actual porosity ϕ and the percolation\nthreshold ϕ . According to percolation theory:\nc\n0 ϕ < ϕ\nΛ ={\nc\n(9)\n(ϕ-ϕ )t ϕ ≥ ϕ\nc c\nWhere ϕ is critical porosity for percolation, t is critical exponent, t ≈ 2 is the universal\nc\nexponent for three-dimensional percolating systems. This correction factor introduces\na strong penalty for low-porosity structures in which vapor pathways become\nfragmented or non-percolating, thereby ensuring that the effective permeability k\nasymptotically approaches zero as the porosity ϕ approaches the percolation threshold\nϕ .\nc\nII. Model Prediction and Optimal Parameter Window\nFurtherly, we mapped Eq. 1 k (D r ) over the design space D ∈ [2, 3], r ∈\nf, max f max\n[10, 100]μm, and ϕ near the high-porosity regime (≥92%). generating both 2D\ncontour plots and 3D surface visualizations (Revised Figure 1). These visualizations\nrevealed distinct sensitivity zones and an optimal parameter window for tuning vapor\ntransport performance.\nnormalized vapor permeability k with respect to fractal dimension D and pore radius\nf\nr . Yellow-green denotes higher relative permeability, indicative of more efficient\nmax\nvapor evacuation, while the contour gradients reveal the distinct and coupled\nsensitivities of vapor transport to both geometric parameters. (b) Corresponding two-\ndimensional contour map superimposed with representative experimental data points\n(black box symbols), which are good agreement with the predicted r -D trends. The\nmax f\nregion above the yellow dotted line (r ＞ 90 μm) denotes mechanical structural\nmax\ninstability and even collapse of NAVPs, highlighting the limitation of excessively lager\npores scale for practical applications.\nAs shown in Revised Figure 1, permeability exhibits a strong and monotonic\nsensitivity to the maximum pore size r , scaling approximately as r 4, consistent\nmax max\nwith Hagen–Poiseuille flow through laminar cylindrical pores. This implies that even\nmodest increases in microchannel radius can yield substantial enhancements in vapor\nflux, highlighting the critical role of pore size engineering in enabling rapid vapor\nevacuation. On the other hand, the dependence on fractal dimension D is strongly\nf\nnonlinear, as captured by the correction term\n3-Df\nin Eq. 1. When D\nf\napproaches 2—\n7-Df\ncharacteristic of open, sparse, and low-tortuosity pore networks—the correction factor\nrises sharply, yielding disproportionately large gains in permeability through more\ndirect transport pathways. However, such open geometries may inherently reduce\nstructural integrity. Conversely, as D approaches 3, the network becomes increasingly\nf\nspace-filling and tortuous, which diminishes vapor mobility despite a potential\nincrease in surface area. This interplay highlights a geometric trade-off between\ntransport efficiency and mechanical robustness in fractal porous networks.\nBased on computed permeability landscapes and mechanical constraints, we\nidentified an optimal regime for Leidenfrost suppression: D ≈ 2.65, r ≈60 μm, ϕ ≥\nf max\n95.2%, Λ＞0.95 and a bimodal pore distribution from ~200 nm to 40–60 μm. It is worth\n4\nnoting that a fractal dimension in the range of D =2.65±0.1 offers a balance between\nf\nenhanced vapor permeability and mechanical stability. A maximum pore size of 40-\n60 μm enables effective vapor escape while maintaining structural coherence. The\nporosity must exceed 95% to ensure the percolation connectivity factor Λ remains\nabove 0.95, thereby maintaining a fully connected vapor pathway. Additionally, a\nbimodal pore size distribution spanning from ~200 nm to 40-60 μm promotes both\nnanoscale capillary pumping and macroscale vapor channeling. Collectively, this\ncombination enables efficient vapor evacuation, enhanced capillary action, and robust\nmechanical performance. Experimental tests confirm that samples in this range\nmaintain structural integrity while maximizing Leidenfrost suppression.\nIn short, our results confirm the reviewer’s insight: suppression of the Leidenfrost\neffect arises from the synergistic interplay of fractal complexity, pore size distribution,\nand network connectivity, which our fractal–permeability model quantitatively\ncaptures.\nWe sincerely appreciate the reviewer’s thoughtful question once again, which\nprompted this important quantitative analysis.\n2. The cavitation effect of low surface energy solvents (e.g., n-hexane) is reported to\nmitigate drying stress and preserve hollow nanofiber integrity. Please clarify how does\nthe solvent's surface tension quantitatively influences cavitation-induced stress relief?\nResponse：We sincerely thank the reviewer for this insightful comment, which helped\nus clarify the role of solvent surface tension in cavitation-induced stress relief and\nthereby improve the overall quality of the manuscript. In the revised manuscript, we\nhave supplemented a detailed quantitative analysis, integrating classical nucleation\ntheory and mechanical energy calculations.\nI. Cavitation Thermodynamics\nSurface tension (γ) plays a crucial role in determining the energy barrier\nassociated with cavitation—that is, the formation of vapor bubbles when the local\npressure (P) in a liquid drop below its saturated vapor pressure (P ). According to\nl v\nclassical nucleation theory, the Gibbs free energy change required to form a spherical\nvapor bubble of radius r is expressed as:\n∆G(r) = 4 πγ3∆P + 4πr2γ (10)\n3\n5\nwhere ΔP is the pressure difference between P and P. The first term accounts for the\nv l\nvolume (bulk) energy change, while the second term represents the surface energy cost\nof creating the bubble.\nTo find the critical radius r , we set the first derivative of ΔG(r) to zero"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I am happy with all the modifications made by the authors and now the manuscript warrants its publication.", "reviewer_2": "The authors have sufficiently addressed the review comments and added necessary modifications to the manuscript.", "reviewer_3": "The authors have submitted a well-structured and comprehensive response to the reviewers’ comments. All issues raised in the earlier review have been addressed thoroughly, and the revisions substantially improve both the clarity and the rigor of the manuscript. The explanations and justifications provided are sound, and the additional modifications strengthen the overall contribution.\nIn my assessment, the revised manuscript meets the standards of the journal and is suitable for acceptance."}, "author_response": "Response to Reviewers' Comments\nWe sincerely appreciate the reviewers for their constructive feedback, which has\nbeen invaluable in improving the clarity, rigor, and overall quality of our manuscript.\nREVIEWERS' COMMENTS\nReviewer #1:\nI am happy with all the modifications made by the authors and now the manuscript\nwarrants its publication.\nResponse: We sincerely thank the reviewer for their positive evaluation. We are pleased\nthat the revisions have satisfactorily addressed the reviewer’s comments.\nReviewer #2:\nThe authors have sufficiently addressed the review comments and added necessary\nmodifications to the manuscript.\nResponse: We sincerely thank the reviewer for their positive evaluation. We are glad\nthat the revisions have met the reviewer’s expectations, and we appreciate the\nreviewer’s time and effort in reviewing our manuscript.\nReviewer #3:\nThe authors have submitted a well-structured and comprehensive response to the\nreviewers’ comments. All issues raised in the earlier review have been addressed\nthoroughly, and the revisions substantially improve both the clarity and the rigor of the\nmanuscript. The explanations and justifications provided are sound, and the additional\nmodifications strengthen the overall contribution.\nIn my assessment, the revised manuscript meets the standards of the journal and is\nsuitable for acceptance.\nResponse: We sincerely thank the reviewer for their thorough and positive evaluation.\nWe are delighted that the revisions have addressed the reviewer’s comments\nsatisfactorily and that the improvements enhance the clarity and rigor of the manuscript.\nWe greatly appreciate the reviewer’s time and constructive feedback."}]

Decision letter