When a liquid meniscus pinned in a vertical flat micro-channel is heated through the channel wall, the measured global evaporation rate rises with applied power, reaches a maximum, and then falls; the onset of an oscillatory interfacial instability coincides with that maximum, and further heating produces nucleate boiling. This phenomenology, reported by Harmand, Sefiane, Lancial and Benselama (2011) for ethanol, acetone, FC-72 and water, could not be reproduced by the one-sided, steady, wall-temperature-forced microregion models of the contact line, and its physical origin was left unresolved. The open problem is to give a mechanism-resolved, quantitative account of this configuration: identify whether the instability is driven by self-generated lateral wall-temperature gradients acting through thermocapillary stress or by coupled vapour-side dynamics, local nucleation and bulk convection, and predict the onset threshold; extend theory to unsteady, vapour-coupled, convection-coupled models that reproduce the non-monotonic evaporation curve including instability onset and transition to boiling; quantify the bulk-convection contribution to the global flux for high-volatility liquids; and map the onset thresholds across fluid properties, channel geometry, boundary conditions and ambient humidity. Prior work has addressed individual components (one-sided linear stability analyses and channel threshold experiments by Polansky and Kaya; microregion extensions by Gatapova, Kabov and Ajaev; two-phase diffuse-interface simulations by Chang, Cai and Tan), but the coupled core remains unresolved.

Background

Evaporation of a liquid meniscus confined in a microchannel is the working process of capillary-driven two-phase cooling devices such as heat pipes and capillary pumped loops used in the thermal management of high-power-density electronics; as the heat input rises, the performance of such devices is limited by what happens at the liquid-vapour interface and its contact line on the channel wall. Near the three-phase contact line the liquid-vapour interface is conventionally divided into three regions: an adsorbed nanometric film on the wall, where evaporation is suppressed by the disjoining pressure (the effective pressure correction in an ultrathin film arising from intermolecular wall-liquid forces, which can hold the film flat and non-evaporating), a so-called microregion or thin-film region where capillary pressure, disjoining pressure and viscous flow interplay to produce very high local evaporative heat flux, and the macroscopic (intrinsic) meniscus further away. Building on the classical lubrication-type description of evaporating wetting menisci by Moosman and Homsy (1980), most predictive models resolve only the liquid side of this structure: they are one-sided (the vapour phase is treated as a passive reservoir at fixed pressure and temperature), steady, and take the wall temperature as a prescribed input rather than solving the coupled problem.

The stability of such heated menisci had been studied mainly under externally imposed conditions. Pratt, Brown and Hallinan (1998) analysed and observed thermocapillary destabilisation of a heated curved meniscus when a lateral temperature gradient was imposed along the wall; Zheng, Plawsky, Wayner and DasGupta (2004) documented oscillations of an evaporating corner meniscus in a quartz constrained-vapour-bubble apparatus at higher heat inputs. Thermocapillary (Marangoni) stress denotes the tangential shear generated at a liquid-vapour interface by gradients of surface tension due to temperature variation along the interface; it is the standard candidate mechanism whenever temperature varies along an evaporating interface.

Harmand, Sefiane, Lancial and Benselama (2011) studied a vertically oriented, high-aspect-ratio flat micro-channel with an external transparent resistive heater, using infrared (IR) thermography of the channel wall, high-speed imaging of the interface, and particle image velocimetry (PIV, an optical technique that measures liquid velocity fields by tracing the motion of suspended tracer particles) for ethanol, acetone, FC-72 and water. They measured the global evaporation rate (the feed rate needed to hold the meniscus position) as a function of applied power and found a non-monotonic curve: evaporation rises to a clear maximum and then decreases. The maximum coincides with the onset of a large-scale oscillatory instability of the liquid-vapour interface; beyond it, nucleate boiling (formation of vapour bubbles at nucleation sites on the heated wall) appears and the global evaporation rate drops further. IR thermography showed that a lateral wall-temperature gradient, with the vapour side of the contact line hotter, develops precisely in this high-power range, suggesting but not proving a thermocapillary origin of the instability. A one-sided, steady microregion model driven by measured wall temperatures underpredicted the global evaporation for the most volatile liquids and, past the peak, predicted more evaporation than measured because it contains no representation of the instability or of boiling. A diffusion-based estimate showed that evaporation driven purely by mass diffusion of vapour into the ambient is negligible, and preliminary PIV revealed convective flow patterns in the bulk liquid that could augment evaporation beyond the microregion, but their magnitude was not quantified. The authors explicitly left open the mechanistic origin and quantitative threshold of the instability (thermocapillary stress versus coupled vapour-side dynamics, local nucleation and bulk convective circulation), the extension of microregion theory to unsteady interfacial dynamics coupled to the vapour phase and to bulk thermocapillary and buoyant convection, the spatial extent of significant evaporation for high-volatility liquids and the quantitative contribution of bulk convection, the influence of tracer particles on contact-line dynamics during PIV measurements, and the systematic mapping of material- and geometry-dependent thresholds (fluid properties, contact-line length, aspect ratio, boundary conditions, ambient humidity) for the onset of oscillations, the peak evaporation rate and the transition to boiling.

Problem Statement

A liquid meniscus is pinned in a vertically oriented, high-aspect-ratio flat micro-channel heated through a transparent wall, and the applied electrical power PP is steadily increased while the global evaporation rate, the interface motion and the wall temperature are monitored. The problem posed by Harmand et al. (2011) is to give a mechanism-resolved, quantitative account of this configuration: a predictive, experimentally validated description of the stability limits and evaporative performance of a confined meniscus under increasing heating. A complete solution must address items (1)-(4) below; items (1) and (2) are the core of the problem, and items (3) and (4) are the further open issues that a full account must also cover.

(1) Mechanism and threshold of the evaporation-peak instability: determine whether the oscillatory instability whose onset coincides with the maximum of the global evaporation rate versus applied power is driven by self-generated lateral wall-temperature gradients acting through thermocapillary stress, or by coupled effects of vapour-side dynamics, local boiling nucleation, and bulk convective circulation, or by a combination of these; and derive a quantitative criterion predicting the onset threshold and the nonlinear outcome, including the sustained post-peak reduction of the global evaporation rate and the transition to nucleate boiling.

(2) Predictive coupled modelling: extend the microregion description beyond one-sided, steady, wall-temperature-forced formulations by coupling unsteady interfacial dynamics, the vapour phase, and bulk thermocapillary and buoyant convection, to the point that the model reproduces the measured non-monotonic global evaporation curve, the instability onset, and the post-peak reduction across the tested fluids (ethanol, acetone, FC-72 and water).

(3) Bulk-convection contribution: quantify the magnitude of bulk convective transport and its scaling with applied power for high-volatility liquids, and determine the spatial extent of significant evaporation (microregion versus extended meniscus), for which existing PIV evidence is only qualitative.

(4) Threshold mapping with controlled measurement artefacts: determine systematically how the thresholds governing the onset of oscillations, the peak evaporation rate and the transition to boiling depend on each of the following axes: fluid properties, contact-line length, channel aspect ratio, thermal boundary conditions and ambient humidity; the influence of tracer particles on contact-line dynamics must also be controlled or quantified so that flow-field measurements do not bias the thresholds.

Solutions may combine theory, computation and experiment.

References

  1. S. Harmand, K. Sefiane, N. Lancial, A.M. Benselama, 'Experimental and theoretical investigation of the evaporation and stability of a meniscus in a flat micro-channel', International Journal of Thermal Sciences 50(10), 1845-1852 (2011). DOI: 10.1016/j.ijthermalsci.2011.02.009, https://doi.org/10.1016/j.ijthermalsci.2011.02.009
  2. S. Moosman, G.M. Homsy, 'Evaporating menisci of wetting fluids', Journal of Colloid and Interface Science 73, 212-223 (1980). DOI: 10.1016/0021-9797(80)90138-1, https://doi.org/10.1016/0021-9797(80)90138-1
  3. D.M. Pratt, J.R. Brown, K.P. Hallinan, 'Thermocapillary Effects on the Stability of a Heated, Curved Meniscus', Journal of Heat Transfer 120(1), 220-226 (1998). DOI: 10.1115/1.2830045, https://doi.org/10.1115/1.2830045
  4. L. Zheng, J.L. Plawsky, P.C. Wayner, S. DasGupta, 'Stability and Oscillations in an Evaporating Corner Meniscus', Journal of Heat Transfer 126(2), 169-178 (2004). DOI: 10.1115/1.1652046, https://doi.org/10.1115/1.1652046
  5. A.M. Benselama, S. Harmand, K. Sefiane, 'Thermocapillary effects on steadily evaporating contact line: A perturbative local analysis', Physics of Fluids 24, 072105 (2012). DOI: 10.1063/1.4732151, https://doi.org/10.1063/1.4732151
  6. Z. Pan, H. Wang, 'Bénard–Marangoni instability on evaporating menisci in capillary channels', International Journal of Heat and Mass Transfer 63, 239-248 (2013). DOI: 10.1016/j.ijheatmasstransfer.2013.03.082, https://doi.org/10.1016/j.ijheatmasstransfer.2013.03.082
  7. H. Azarkish, S. Arslan, A. Behzadmehr, T. Fanaei Sheikholeslami, S.M.H. Sarvari, L.G. Fréchette, 'Experimental and numerical investigation of a shaped microchannel evaporator for a micro Rankine cycle application', International Journal of Thermal Sciences 96, 191-200 (2015). DOI: 10.1016/j.ijthermalsci.2015.05.010, https://doi.org/10.1016/j.ijthermalsci.2015.05.010
  8. C. Buffone, K. Sefiane, C. Minetti, D. Mamalis, 'Standing wave in evaporating meniscus detected by infrared thermography', Applied Physics Letters 107, 041606 (2015). DOI: 10.1063/1.4927744, https://doi.org/10.1063/1.4927744
  9. W.G. Zhao, S.M. Thompson, H. Wang, H.B. Ma, G.L. Solbrekken, 'Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes', International Journal of Multiphase Flow 75, 250-256 (2015). DOI: 10.1016/j.ijmultiphaseflow.2015.06.003, https://doi.org/10.1016/j.ijmultiphaseflow.2015.06.003
  10. M. Kim, M. Kaviany, 'Multi-artery heat-pipe spreader: monolayer-wick receding meniscus transitions and optimal performance', International Journal of Heat and Mass Transfer 112, 343-353 (2017). DOI: 10.1016/j.ijheatmasstransfer.2017.04.131, https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.131
  11. J. Polansky, T. Kaya, 'Stability of an evaporating meniscus: Part I - Theoretical analysis', International Journal of Thermal Sciences 107, 209-219 (2016). DOI: 10.1016/j.ijthermalsci.2016.03.021, https://doi.org/10.1016/j.ijthermalsci.2016.03.021
  12. J. Polansky, T. Kaya, 'Stability of an evaporating meniscus: Part II - Experimental investigation', International Journal of Thermal Sciences 105, 75-82 (2016). DOI: 10.1016/j.ijthermalsci.2016.02.018, https://doi.org/10.1016/j.ijthermalsci.2016.02.018
  13. J. Polansky, 'An Experimental and Theoretical Investigation of Evaporating Meniscus Dynamics and Instabilities', PhD thesis, Carleton University (2016). DOI: 10.22215/etd/2016-11341, https://doi.org/10.22215/etd/2016-11341
  14. J. Polansky, T. Kaya, 'Experimental investigation of thermally driven meniscus instability in capillary tubes', International Journal of Heat and Mass Transfer 117, 458-464 (2018). DOI: 10.1016/j.ijheatmasstransfer.2017.10.014, https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.014
  15. E.Ya. Gatapova, O.A. Kabov, V.S. Ajaev, 'Evaporation and interface dynamics in microregion on heated substrate of non-uniform wettability', International Journal of Heat and Mass Transfer 142, 118355 (2019). DOI: 10.1016/j.ijheatmasstransfer.2019.07.005, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.005
  16. X. Zhang, V. Nikolayev, 'Liquid film dynamics with immobile contact line during meniscus oscillation', Journal of Fluid Mechanics 923, A4 (2021). DOI: 10.1017/jfm.2021.540, https://doi.org/10.1017/jfm.2021.540 (preprint: https://arxiv.org/abs/2108.01475)
  17. J. Chang, J. Cai, B. Tan, 'Numerical simulation of meniscus evaporation in microchannel based on diffuse interface method', Heat and Mass Transfer 58, 1949-1962 (2022). DOI: 10.1007/s00231-022-03223-0, https://doi.org/10.1007/s00231-022-03223-0
  18. P. Yadav, D. Chatterjee, S. Khandekar, 'Transport phenomena and dynamics of an evaporating water meniscus at low heat fluxes', International Journal of Heat and Mass Transfer 214, 124368 (2023). DOI: 10.1016/j.ijheatmasstransfer.2023.124368, https://doi.org/10.1016/j.ijheatmasstransfer.2023.124368
  19. A. Mostafazade Abolmaali, M. Bayat, J. Hattel, 'A multiscale analytical-numerical method for the coupled heat and mass transfer in the extended meniscus region considering thin-film evaporation in microchannels', International Journal of Heat and Mass Transfer 222, 125145 (2024). DOI: 10.1016/j.ijheatmasstransfer.2023.125145, https://doi.org/10.1016/j.ijheatmasstransfer.2023.125145
  20. Y. Wang, 'Thermal insights of the temperature gradient-induced convections in an evaporating meniscus', International Journal of Heat and Mass Transfer 252, 127500 (2025). DOI: 10.1016/j.ijheatmasstransfer.2025.127500, https://doi.org/10.1016/j.ijheatmasstransfer.2025.127500
  21. K. Hatanaka, M. Fukamachi, Y. Sato, T. Yabuki, 'Heat transfer at the contact line of an evaporating meniscus observed by fluorescence thermal microscopy', International Journal of Heat and Mass Transfer 258, 128303 (2026). DOI: 10.1016/j.ijheatmasstransfer.2025.128303, https://doi.org/10.1016/j.ijheatmasstransfer.2025.128303