Year 2020, Volume 40 , Issue 2, Pages 309 - 318 2020-10-31

THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION
STEFAN AKIŞININ DAMLACIK BUHARLAŞMA MODELLERİ ÜZERİNDEKİ ETKİSİ

Yigit AKKUS [1]


Droplet evaporation has been widely studied in the literature due to its key role in various applications in science and industry. The problem of droplet evaporation involves various mechanisms in both liquid and vapor phases together with the interface separating them. Modeling of this multiphase problem is not straightforward thereof studied by many researchers but in every time a few different contributing mechanisms could be highlighted. One of the pieces of this puzzle is undoubtedly the Stefan flow, which is always present during the evaporation of a liquid to an insoluble surrounding gas, yet the number of studies exploring its individual contribution to the evaporation remain very restricted. In the current study, the effect of Stefan flow is assessed by employing a recent state-of-the-art model that accounts for all pertinent physics of droplet evaporation. Results reveal that Stefan flow can be responsible for 17% of total evaporation when the droplet is placed on a high temperature substrate. Moreover, it is shown that lower performance of diffusion based models (in gas phase) can be greatly enhanced by incorporating the effect of Stefan flow into the interfacial mass flux equation. In addition, performances of existing purely diffusion and diffusion and Stefan flow based correlations in the prediction of evaporation rates are elucidated. Last but not least, under varying humidity of the surrounding gas, contribution of individual transport mechanisms in gas phase to the total evaporation rate is found to be unaffected. Based on this result, it is hypothesized that contributions of Stefan flow and natural convection have a linear dependence on the contribution of sole diffusion. The current study clearly demonstrated that Stefan flow considerably enhances the evaporation rate of droplets, especially in the case of high substrate heating. Therefore, future studies on the topic should account for the Stefan flow during the modeling of droplet evaporation.
Bilim ve endüstrideki çeşitli uygulamalarda kilit rolü olması nedeniyle damlacık buharlaşması literatürde yaygın olarak incelenmektedir. Damlacık buharlaşması problemi, sıvı ve buhar fazları ile bu fazları ayıran ara yüzeyde meydana gelen çeşitli mekanizmaları içerir. Modellenmesi kolay olmayan bu çok-fazlı problem birçok araştırmacı tarafından çalışılmıştır, ancak içerdiği mekanizmalardan sadece birkaçı ön plana çıkarılabilmiştir. Bir sıvının o sıvı içerisinde çözünmeyen gaz ortamına buharlaşması sırasında her zaman ortaya çıkan Stefan akışı, bulmacanın parçalarından biridir. Ancak Stefan akışının buharlaşmaya olan katkısını araştıran çalışmaların sayısı oldukça sınırlıdır. Bu çalışmada, Stefan akışının etkisi, tüm ilgili fiziksel mekanizmaları içeren yenilikçi bir model kullanılarak ölçülmüştür. Damlacık yüksek sıcaklıkta bir katı yüzey üzerine yerleştirildiğinde Stefan akışının toplam buharlaşmanın %17'sinden sorumlu olabileceği bu çalışmada gösterilmiştir. Ayrıca, Stefan akışının ara yüzey kütle akısı denklemine dâhil edilmesiyle difüzyon temelli modellerin (gaz fazındaki) düşük performansının büyük ölçüde arttırılabileceği gösterilmiştir. Ayrıca bu çalışmada, sadece difüzyon ile difüzyon ve Stefan akışına dayalı mevcut ilgileşimlerin buharlaşma oranlarını bulma performansları tartışılmıştır. Son olarak, gaz ortamının değişen nem oranları altında, gaz fazındaki münferit taşıma mekanizmalarının toplam buharlaşma hızına olan katkılarında bir değişiklik olmadığı bulunmuştur. Bu sonuca dayanarak, Stefan akışı ve doğal konveksiyonun katkılarının, sadece difüzyonun katkısına doğrusal bir bağımlılığı olduğu düşünülmüştür. Bu çalışma, Stefan akışının, bilhassa ısıtılmış katı yüzeyler üzerinde duran damlacıkların buharlaşma hızlarını kayda değer şekilde arttırdığını göstermiştir. Bu yüzden, bundan sonra yapılacak ilgili damlacık buharlaşması modelleme çalışmaları Stefan akışını da içermelidir.
  • Akkuş Y., Cetin B. and Dursunkaya Z., 2017, Modeling of Evaporation from a Sessile Constant Shape Droplet. In ASME 2017 15th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers Digital Collection.
  • Akkus Y., Çetin B. and Dursunkaya Z., 2019, An Iterative Solution Approach to Coupled Heat and Mass Transfer in a Steadily Fed Evaporating Water Droplet, J. Heat Transf., 141, 031501.
  • Akkus Y., Çetin B. and Dursunkaya Z., 2020, A Theoretical Framework for Comprehensive Modeling of Steadily Fed Evaporating Droplets and the Validity of Common Assumptions, Int. J. Therm. Sci., 158, 106529.
  • Bolz R. and Tuve G., 1976, Handbook of Tables for Applied Engineering Science, CRC Press, Cleveland, 2nd edition.
  • Bouchenna C., Saada M. A., Chikh S. and Tadrist L., 2017, Generalized Formulation for Evaporation Rate and Flow Pattern Prediction Inside an Evaporating Pinned Sessile Drop, Int. J. Heat Mass Tran., 109, 482-500.
  • Carle F., Sobac B. and Brutin D., 2013, Experimental Evidence of the Atmospheric Convective Transport Contribution to Sessile Droplet Evaporation, Appl. Phys. Lett., 102, 061603.
  • Carle F., Semenov S., Medale M. and Brutin D., 2016, Contribution of Convective Transport to Evaporation of Sessile Droplets: Empirical Model, Int. J. Therm. Sci., 101, 35-47.
  • Chen Y. H., Hu W. N., Wang J., Hong F. J. and Cheng P., 2017, Transient Effects and Mass Convection in Sessile Droplet Evaporation: The Role of Liquid and Substrate Thermophysical Properties, Int. J. Heat Mass Tran., 108, 2072-2087.
  • COMSOL Multiphysics® v. 5.4. www.comsol.com. COMSOL AB, Stockholm, Sweden, 2018.
  • Deegan R. D., Bakajin O., Dupont T. F., Huber G., Nagel S. R. and Witten, T. A., 1997, Capillary Flow as the Cause of Ring Stains From Dried Liquid Drops, Nature, 389, 827-829.
  • Deegan R. D., Bakajin O., Dupont T. F., Huber G., Nagel S. R. and Witten T. A., 2000, Contact Line Deposits in an Evaporating Drop, Phys. Rev. E, 62, 756.
  • Duh J. C. and Yang W. J., 1989, Numerical Analysis of Natural Convection in Liquid Droplets by Phase Change, Numer. Heat Transfer, 16, 129-154.
  • Girard F., Antoni M., Faure S. and Steinchen A., 2006, Evaporation and Marangoni Driven Convection in Small Heated Water Droplets, Langmuir, 22, 11085–11091.
  • Hu H. and Larson R. G., 2002, Evaporation of a Sessile Droplet on a Substrate, J. Phys. Chem. B, 106, 1334-1344.
  • Kabov O. A., Zaitsev D. V., Kirichenko D. P. and Ajaev V. S., 2017, Interaction of Levitating Microdroplets with Moist Air Flow in the Contact Line Region, Nanosc. Microsc. Therm. Eng., 21, 60-69.
  • Kelly-Zion P. L., Pursell C. J., Vaidya S. and Batra J., 2011, Evaporation of Sessile Drops under Combined Diffusion and Natural Convection, Colloid. Surface. A, 381, 31-36.
  • Kim J., 2007, Spray Cooling Heat Transfer: The State of the Art, Int. J. Heat Fluid Flow, 28, 753-767.
  • Kokalj T., Cho H., Jenko M. and Lee L. P., 2010, Biologically Inspired Porous Cooling Membrane Using Arrayed-droplets Evaporation, Appl. Phys. Lett., 96, 163703.
  • Lim T., Jeong J., Chung J. and Chung J. T., 2009, Evaporation of Inkjet Printed Pico-liter Droplet on Heated Substrates with Different Thermal Conductivity, J. Mech. Sci. Technol., 23, 1788-1794.
  • Lozinski D. and Matalon M., 1993, Thermocapillary Motion in a Spinning Vaporizing Droplet, Phys. Fluids A Fluid, 5, 1596-1601.
  • Lu G., Duan Y. Y., Wang X. D. and Lee, D. J., 2011, Internal Flow in Evaporating Droplet on Heated Solid Surface, Int. J. Heat Mass Tran., 54, 4437-4447.
  • Misyura S. Y., 2017, Evaporation of a Sessile Water Drop and a Drop of Aqueous Salt Solution, Sci. Rep., 7, 1-11.
  • Misyura S. Y., 2018, Non-isothermal Evaporation in a Sessile Droplet of Water-salt Solution, Int. J. Therm. Sci., 124, 76-84.
  • Robinson P. J. and Davies J. A, 1972, Laboratory Determinations of Water Surface Emissivity, J. Appl. Meteor., 11, 1391-1393.
  • Ruiz O. E. and Black W. Z., 2002, Evaporation of Water Droplets Placed on a Heated Horizontal Surface, ASME J. Heat Transf., 124, 854–863.
  • Pan Z., Weibel J. A. and Garimella S. V., 2020, Transport Mechanisms during Water Droplet Evaporation on Heated Substrates of Different Wettability, Int. J. Heat Mass Tran., 152, 119524.
  • Saada M. A., Salah C. and Lounes T., 2010, Numerical Investigation of Heat and Mass Transfer of an Evaporating Sessile Drop on a Horizontal Surface, Phys. Fluids, 22, 112115.
  • Savino R., Paterna D. and Lappa M., 2003, Marangoni Flotation of Liquid Droplets, J. Fluid Mech., 479, 307–326.
  • Sazhin S., 2005, Modelling of Heating, Evaporation and Ignition of Fuel Droplets: Combined Analytical, Asymptotic and Numerical Analysis. In Journal of Physics: Conference Series, 22, 174.
  • Semenov S., Starov V. M. and Rubio R. G., 2013, Evaporation of Pinned Sessile Microdroplets of Water on a Highly Heat-conductive Substrate: Computer Simulations, Eur. Phys. J-Spec Top., 219, 143-154.
  • Shuai S., Du Z., Ma B., Shan L., Dogruoz B. and Agonafer D., 2018, Numerical Investigation of Shape Effect on Microdroplet Evaporation, ASME 2018 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems, American Society of Mechanical Engineers, V001T04A010.
  • Smalyukh I. I., Zribi O. V., Butler J. C., Lavrentovich O. D. and Wong G. C. L., 2006, Structure and Dynamics of Liquid Crystalline Pattern Formation in Drying Droplets of DNA, Phys. Rev. Lett., 96, 177801.
  • Spalding D. B., 1953, The Combustion of Liquid Fuel, Pittsburgh.
  • Ward C. and Duan F., 2004, Turbulent Transition of Thermocapillary Flow Induced by Water Evaporation, Phys. Rev. E, 69, 056308.
  • Won Y., Cho J., Agonafer D., Asheghi M., and Goodson K.E., 2015, Fundamental Cooling Limits for High Power Density Gallium Nitride Electronics, IEEE Trans. Compon. Packag. Manuf. Technol., 5, 737-744.
  • Wu H., Chen L. X., Zeng X. Q., Ren T. H. and Briscoe, W. H., 2014, Self-assembly in an Evaporating Nanofluid Droplet: Rapid Transformation of Nanorods into 3D Fibre Network Structures, Soft Matter, 10, 5243-5248.
  • Xu X. and Luo J., 2007, Marangoni Flow in an Evaporating Water Droplet, Appl. Phys. Lett., 91, 124102.
  • Xu X., Luo J. and Guo D., 2009, Criterion for Reversal of Thermal Marangoni Flow in Drying Drops, Langmuir, 26, 1918-1922.
  • Zaitsev D. V., Kirichenko D. P., Ajaev V. S. and Kabov O. A., 2017, Levitation and Self-organization of Liquid Microdroplets over Dry Heated Substrates, Phys. Rev. Lett., 119, 094503.
Primary Language en
Subjects Engineering, Mechanical
Journal Section Research Article
Authors

Orcid: 0000-0001-8978-3934
Author: Yigit AKKUS
Institution: Aselsan AŞ
Country: Turkey


Dates

Publication Date : October 31, 2020

Bibtex @research article { isibted817053, journal = {Isı Bilimi ve Tekniği Dergisi}, issn = {1300-3615}, address = {}, publisher = {Türk Isı Bilimi ve Tekniği Derneği}, year = {2020}, volume = {40}, pages = {309 - 318}, doi = {10.47480/isibted.817053}, title = {THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION}, key = {cite}, author = {Akkus, Yigit} }
APA Akkus, Y . (2020). THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION . Isı Bilimi ve Tekniği Dergisi , 40 (2) , 309-318 . DOI: 10.47480/isibted.817053
MLA Akkus, Y . "THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION" . Isı Bilimi ve Tekniği Dergisi 40 (2020 ): 309-318 <https://dergipark.org.tr/en/pub/isibted/issue/57550/817053>
Chicago Akkus, Y . "THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION". Isı Bilimi ve Tekniği Dergisi 40 (2020 ): 309-318
RIS TY - JOUR T1 - THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION AU - Yigit Akkus Y1 - 2020 PY - 2020 N1 - doi: 10.47480/isibted.817053 DO - 10.47480/isibted.817053 T2 - Isı Bilimi ve Tekniği Dergisi JF - Journal JO - JOR SP - 309 EP - 318 VL - 40 IS - 2 SN - 1300-3615- M3 - doi: 10.47480/isibted.817053 UR - https://doi.org/10.47480/isibted.817053 Y2 - 2020 ER -
EndNote %0 Isı Bilimi ve Tekniği Dergisi THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION %A Yigit Akkus %T THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION %D 2020 %J Isı Bilimi ve Tekniği Dergisi %P 1300-3615- %V 40 %N 2 %R doi: 10.47480/isibted.817053 %U 10.47480/isibted.817053
ISNAD Akkus, Yigit . "THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION". Isı Bilimi ve Tekniği Dergisi 40 / 2 (October 2020): 309-318 . https://doi.org/10.47480/isibted.817053
AMA Akkus Y . THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION. Isı Bilimi ve Tekniği Dergisi. 2020; 40(2): 309-318.
Vancouver Akkus Y . THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION. Isı Bilimi ve Tekniği Dergisi. 2020; 40(2): 309-318.
IEEE Y. Akkus , "THE EFFECT OF STEFAN FLOW ON THE MODELS OF DROPLET EVAPORATION", Isı Bilimi ve Tekniği Dergisi, vol. 40, no. 2, pp. 309-318, Oct. 2020, doi:10.47480/isibted.817053