Skip to main content
SpringerLink
Log in

Heat Flux Density Evaluation in the Region of Contact Line of Drop on a Sapphire Surface Using Infrared Thermography Measurements

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

The paper presents a new tool “the method of IR transparent thick plate” that can be used to study the heat and mass transfer processes in the air-liquid-solid contact line area. Its distinctive feature as compared to the previously known methods is the solution of the initial-boundary problem for the heat conductivity equation, which in terms of mathematics is a correct problem. Currently, the heat and mass transfer processes in the area of the contact line are not completely understood because of its small size and a limited set of applied research methods. The challenges in modeling of contact line phenomena have to do with the fact that several physical effects such as evaporation, viscous flow, surface tension, thermocapillary stresses, London-van der Waals forces, disjoining pressure, nonequilibrium effects are coupled together and all significant in this highly localized region. This leads to difficulties in both mathematical modeling and design of experiments. The experimental part of the study includes the evaporation of a liquid drop on a sapphire substrate. The upper part of the sapphire glass is coated with a high heat-resistant black graphite paint (Graphit 33), which is a non-transparent for visual and IR-rays. Measurements of various physical, chemical and geometrical properties of this coating have been done by electron microscopy and other techniques. Trial experiments on the drop evaporation were carried out. The sapphire surface temperature fields after single drop deposition were obtained using the IR-scanner. The experimental local heat flux distribution at drop evaporation on the sapphire surface with two small local highs close to the contact line regions has been measured.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Ajaev, V.S., Kabov, O.A.: Heat and mass transfer near contact lines on heated surfaces. Int. J. Heat Mass. Tran. 108, 918–932 (2017)

    Article  Google Scholar 

  • Astarita, T., Cardone, G., Carlomagno, G.M., Meola, C.: A survey on infrared thermography for convective heat transfer measurements. Opt. Laser Technol. 32, 593–610 (2000)

    Article  Google Scholar 

  • Bateman, H., Erdelyi, A.: Tables of Integral Transforms, vol. 1. McGraw-Hill Book Co., New York (1954)

    Google Scholar 

  • Bouchenna, C.H., Saada, M.A., Chikh, S., Tadrist, L.: Investigation of Thermo-Capillary Flow Inside an Evaporating Pinned Water Droplet. Interfacial Phenom. Heat Transf. 3, 185–201 (2015)

    Article  Google Scholar 

  • Bouchenna, C.H., Saada, M.A., Chikh, S., Tadrist, L.: Generalized formulation for evaporation rate and flow pattern prediction inside an evaporating pinned sessile drop. Int. J. Heat Mass. Tran. 109, 482–500 (2017)

    Article  Google Scholar 

  • Brutin, D., Zhu, Z., Rahli, O., Xie, J., Liu, Q., Tadrist, L.: Sessile Drop in Microgravity: Creation, Contact Angle and Interface. Microgravity Sci. Technol. 21, 67–76 (2009)

    Article  Google Scholar 

  • Brutin, D., Sobac, B., Rigollet, F., Le Niliot, C.: Infrared visualization of thermal motion inside a sessile drop deposited onto a heated surface. Exp. Thermal Fluid Sci. 35, 521-530 (2011a)

  • Brutin, D., Sobac, B., Loquet, B., Sampol, J.: Pattern Formation in Drying Drops of Blood. J. Fluid Mech. 667, 85-95 (2011b)

  • Carle, F., Sobac, B., Brutin, D.: Experimental Evidence of the Atmospheric Convective Transport Contribution to Sessile Droplet Evaporation. Appl. Phys. Lett. 102, 061603 (2013)

  • Carlomagno, G.M., Cardone, G.: Infrared thermography for convective heat transfer measurements. Exp. Fluids 49, 1187–1218 (2010)

    Article  Google Scholar 

  • Carlomagno, G.M., De Luca, L.: Infrared thermography in heat transfer. Handbook of Flow Visualization, Ed. Hemisphere, London, Chapter 32, 531–553 (1989)

    Google Scholar 

  • Cazabat, A.M., Guéna, G.: Evaporation of macroscopic sessile droplets. Soft Matter 6, 2591–2612 (2010)

    Article  Google Scholar 

  • Chaze, W., Caballina, O., Castanet, G., Pierson, J.F., Lemoine, F., Maillet, D.: Heat flux reconstruction by inversion of experimental infrared temperature measurements - Application to the impact of a droplet in the film boiling regime, Int. J. Heat Mass. Tran. 128, 469–478 (2019)

  • Cheverda, V.V., Marchuk, I.V., Karchevsky, A.L., Orlik, E.V., Kabov, O.A.: Experimental investigation of heat transfer in a rivulet on the inclined foil. Thermophys. Aeromechanics 23, 415–420 (2016)

    Article  Google Scholar 

  • Cheverda, V., Karchevsky, A.: The heat flux near the contact line of the droplets on the heated foil, MATEC Web of Conf. 84, 00007 (2016)

  • Cheverda, V.V., Karchevsky, A.L., Marchuk, I.V., Kabov, O.A.: Heat flux density in the region of droplet contact line on a horizontal surface of a thin heated foil. Thermophys. Aeromechanics 24, 803–806 (2017)

    Article  Google Scholar 

  • Cheverda V.V., Ponomarenko T.G., Karchevsky A.L., Kabov O.A.: Heat flux density measurements in the contact line of the heated sessile droplet/falling down liquid rivulet, Int. Heat Transfer Conf. 6633–6640 (2018)

  • Dedok, V.A., Karchevsky, A.L., Romanov, V.G.: A Numerical Method of Determining Permittivity from the Modulus of the Electric Intensity Vector of an Electromagnetic Field. J. Ind. Appl. Math. 13, 436–446 (2019)

    Article  MathSciNet  Google Scholar 

  • Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, R.S.: Contact line deposits in an evaporating drop. Phys. Rev. E 62, 756–765 (2000)

    Article  Google Scholar 

  • Dhavaleswarapu, H.K., Migliaccio, Ch.P., Garimalla, S.V., Murthy, J.Y.: Experimental investigation of evaporation from low contact angle sessile drops. Langmuir 26, 880–888 (2010)

    Article  Google Scholar 

  • Dmitriev, A.S.: Introduction to nano-thermal physics. Moskow, BINOM, Laboratory of Knowledge (2015)

  • Dunn, G., Wilson, S., Duffy, B., David, S., Sefiane, K.: The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623, 329–351 (2009)

    Article  MATH  Google Scholar 

  • Erbil, H.Y.: Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170, 67–86 (2012)

    Article  Google Scholar 

  • Gatapova, E.Y., Graur, I.A., Kabov, O.A., Aniskin, V.M., Filipenko, M.A., Sharipov, F., Tadrist, L.: The temperature jump at water - air interface during evaporation. Int. J. Heat Mass. Tran. 104, 800–812 (2017)

    Article  Google Scholar 

  • Gatapova, E.Y., Shonina, A.M., Safonov, A.I., Sulyaeva, V.S., Kabov, O.A.: Evaporation dynamics of a sessile droplet on glass surfaces with fluoropolymer coatings: focusing on the final stage of thin droplet evaporation. Soft Matter 14, 1811–1821 (2018). https://doi.org/10.1039/c7sm02192e

  • Ge Z.B., Cahill D.G., Braun P.V.: Thermal Conductance of Hydrophilicand HydrophobicInterfaces. Phys. Rev. Lett. 96, 186101 (2006)

  • Gibbons, M., Di Marco, P., Robinson, A.J.: Local heat transfer to an evaporating superhydrophobic droplet. Int. J. Heat Mass. Tran. 121, 641–652 (2018)

    Article  Google Scholar 

  • Hu, H., Larson, R.G.: Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110, 7090–7094 (2006)

    Article  Google Scholar 

  • Jo, J., Kim, J., Kim, S.J.: Experimental investigations of heat transfer mechanisms of a pulsating heat pipe. Energy Convers. Manag. 181, 331–341 (2019)

    Article  Google Scholar 

  • Kabov, O.A., Zaitsev, D.V., Kirichenko, D.P., Ajaev, V.S.: Interaction of Levitating Microdroplets with Moist Air Flow in the Contact Line Region. Nanoscale Microscale Thermophys. Eng. 21, 60–69 (2017)

    Article  Google Scholar 

  • Kabov, O.A., Gatapova, E.Y., Semenov, A.A., Jutley, M., Ajaev, V.V., Kirichenko, E.O., Feoktistov, D.V., Kuznetsov, G.V., Zaitsev, D.V.: Experimental and Numerical Studies of Evaporation of a Sessile Water Drop on a Heated Conductive Substrate. Interfacial Phenom. Heat Transf. 6, 421–435 (2018)

    Article  Google Scholar 

  • Kabov, O.A., Zaitsev, D.V.: The effect of wetting hysteresis on drop spreading under gravity. Dokl. Phys. 58, 292–295 (2013)

    Article  Google Scholar 

  • Karchevsky, A.L.: Numerical Solution to the One-Dimensional Inverse Problem for an Elastic System. Doklady 375, 235–238 (2000)

    Article  Google Scholar 

  • Karchevsky A.L., Simultaneous reconstruction of permittivity and conductivity, J. Inverse Ill-Posed Probl. 17, 385-402 (2009)

  • Karchevsky, A.L.: Reformulation of an inverse problem statement that reduces computational costs. Eurasian J. Math. Comput. Appl. 1, 4–20 (2013)

    Google Scholar 

  • Karchevsky, A.L., Marchuk, I.V., Kabov, O.A.: Calculation of the heat flux near the liquid-gas-solid contact line. Appl. Math. Model. 40, 1029–1037 (2016)

    Article  MATH  Google Scholar 

  • Karchevsky, A.L.: Development of the heated thin foil technique for investigating nonstationary transfer processes. Interfacial Phenom. Heat Transf. 6, 179–185 (2018)

    Article  Google Scholar 

  • Karchevsky, A.L.: On a solution of the convolution type Volterra equation of the 1st kind. Advanced Math. Models & Applications 2, 1–5 (2017)

    Google Scholar 

  • Karchevsky, A.L.: Solution of the Convolution Type Volterra Integral Equations of the First Kind by the Quadrature-Sum Method. J. Appl. Ind. Math. 14, 503–512 (2020)

    Article  MathSciNet  Google Scholar 

  • Lappa, M.: Fluids, Materials and Microgravity: Numerical Techniques and Insights into the Physics, 1st edn. Elsevier Science, Oxford, England (2004)

    Google Scholar 

  • Manzhirov, A.V., Polyanin, A.D.: Integral equations. Faktorial Press, Moskva, Methods of Solution. Handbook (2000)

    MATH  Google Scholar 

  • Marchuk I., Karchevsky A., Surtaev A., Kabov O.: Heat flux at the surface of metal foil heater under evaporating sessile droplets. Int. J. Aerosp. Eng. 2015, 391036 (2015)

  • Mollaret, R., Sefiane, K., Christy, J.R.E., Veyret, D.: Experimental and numerical investigation of the evaporation into air of a drop on a heated surface. Chem. Eng. Res. Des. 82, 471–480 (2004)

    Article  Google Scholar 

  • Morozova, M.A., Novopashin, S.A.: Influence of Interfacial Phenomena on Viscosity and Thermal Conductivity of Nanofluids. Interfacial Phenom. Heat Transf. 7, 151–165 (2019)

    Article  Google Scholar 

  • Panchamgam, S.S., Chatterjee, A., Plawsky, J.L., Wayner, P.C., Jr.: Comprehensive experimental and theoretical study of fliuid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger. Int. J. Heat Mass. Tran. 51, 53685379 (2008)

    Article  MATH  Google Scholar 

  • Pinchover, Y., Rubinstein, J.: An Introduction to Partial Differential Equations. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  • Polak, E.: Computational Methods in Optimization: A Unified Approach, Mathematics in Science and Engineering, vol. 77, Academic Press (1971)

  • Polikarpov, A.P., Graur, I.A., Gatapova, E.Y., Kabov, O.A.: Kinetic simulation of the non-equilibrium effects at the liquid-vapor interface. Int. J. Heat Mass. Tran. 136, 449–456 (2019)

    Article  Google Scholar 

  • Polyanin, A.D., Manzhirov, A.V.: Handbook for integral equations. Fizmatlit, Moskva (2003)

    MATH  Google Scholar 

  • Potash, M., Wayner, P.C., Jr.: Evaporation from a two-dimensional extended meniscus. Int. J. Heat Mass. Tran. 15, 1851–1863 (1972)

    Article  Google Scholar 

  • Romanov, V.G., Karchevsky, A.L.: Determination of permittivity and conductivity of medium in a vicinity of a well having complex profile. Eurasian Journal of Mathematical and Computer Applications 6, 64–74 (2018)

    Google Scholar 

  • Saada, M.A., Chikh, S., Tadrist, L.: Evaporation of a sessile drop with pinned or receding contact line on a substrate with different thermophysical properties. Int. J. Heat Mass. Tran. 58, 197–208 (2013)

    Article  Google Scholar 

  • Schweikert, K., Sielaff, A., Stephan, P.: Heat flux during dip-coating of a superheated substrate. Interfacial Phenom. Heat Transf. 7, 269–281 (2019)

    Article  Google Scholar 

  • Schweikert K., Sielaff A., Stephan P.: On the transition between contact line evaporation and microlayer evaporation during the dewetting of a superheated wall. Int. J. Therm. Sci. 145, 106025 (2019)

  • Schweizer, N., Stephan, P.: Experimental study of bubble behavior and local heat flux in pool boiling under variable gravity conditions. Multiph. Sci. Technol. 21, 329–350 (2009)

    Article  Google Scholar 

  • Sobac, B., Brutin, D.: Triple-Line Behavior and Wettability Controlled by Nanocoated Substrates: Influence on Sessile Drop Evaporation. Langmuir 27, 14999–15007 (2011)

    Article  Google Scholar 

  • Sobac, B., Brutin, D.: Thermal effects of the substrate on water droplet evaporation. Phys. Rev. E 86, 021602 (2012)

    Article  Google Scholar 

  • Sodtke, C., Ajaev, V., Stephan, P.: Dynamics of volatile liquid droplets on heated surfaces: theory versus experiment. J. Fluid Mech. 610, 343–362 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Stephan, P.C., Busse, C.A.: Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Int. J. Heat Mass. Tran. 35, 383–391 (1992)

    Article  Google Scholar 

  • Stephan, P., Brandt, C.: Advanced capillary structures for high performance heat pipes. Heat Transf. Eng. 25, 78–85 (2004)

    Article  Google Scholar 

  • Tikhonov, A.N., Samarskii, A.A.: Equations of mathematical physics. Nauka, Moskva (1977)

    Google Scholar 

  • Vasil’ev, F.P.: Numerical Methods for Solving Extremal Problems. Nauka, Moskva (1988)

    Google Scholar 

  • Verlan’, A.F., Sizikov, V.S.: Integral equations: methods, algorithms, codes. Handbook, Kiev, Naukova dumka (1986)

    MATH  Google Scholar 

Download references

Acknowledgements

The work is supported by the Russian Science Foundation (No. 18-19-00538). Measurement of the limiting wetting angle of the substrate is performed in the framework of the state assignment of the Kutateladze Institute of Thermophysivs SB RAS. Measurement by electron microscopy JEOL 6700F is performed in the framework of the state assignment of the Nikolaev Institute of Inorganic Chemistry SB RAS.

Author information

Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, 630090, Russia

    A. L. Karchevsky, V. V. Cheverda & I. V. Marchuk

  2. Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, 630090, Russia

    V. V. Cheverda, I. V. Marchuk, T. G. Gigola & O. A. Kabov

  3. Novosibirsk State Technical University, Novosibirsk, 630073, Russia

    T. G. Gigola & O. A. Kabov

  4. Nikolaev Institution of Inorganic Chemistry SB RAS, Novosibirsk, 630090, Russia

    V. S. Sulyaeva

Authors
  1. A. L. Karchevsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Cheverda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. V. Marchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. G. Gigola
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. V. S. Sulyaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. O. A. Kabov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. L. Karchevsky.

Ethics declarations

Conflicts of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karchevsky, A.L., Cheverda, V.V., Marchuk, I.V. et al. Heat Flux Density Evaluation in the Region of Contact Line of Drop on a Sapphire Surface Using Infrared Thermography Measurements. Microgravity Sci. Technol. 33, 53 (2021). https://doi.org/10.1007/s12217-021-09892-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12217-021-09892-6

Keywords

PACS

Mathematics Subject Classification

Search

Navigation