Microgravity Science and Technology

, Volume 31, Issue 2, pp 231–240 | Cite as

Three-Dimensional Numerical Simulation on Marangoni Convection in a Sessile Water Droplet Evaporating in its Vapor at Low Pressure

  • Yu Zhang
  • You-Rong LiEmail author
  • Jia-Jia Yu
  • Qiu-Sheng Liu
Original Article


In order to understand the effect of Marangoni convection on the evaporation rate and the flow pattern, we performed a series of three-dimensional numerical simulations on evaporation process of sessile water droplet by introducing a kinetic model. Substrate temperature and the ratio of vapor pressure varied from 299 K to 308 K and from 0.92 to 0.99, respectively. The variation range of contact angle θ was between 9.15° and 120°. Results show that the axisymmetric ring-shape temperature distribution on droplet free surface transforms into a serrated temperature distribution because of the enhancing Marangoni convection with the increase of substrate temperature. In addition, with the decrease of vapor pressure, the total evaporation rate on free surface will be increased and the Marangoni effect will be enhanced. The flow pattern is axisymmetric at 90o ≤ θ ≤ 120o when the substrate temperature is fixed. However, it shifts to a multi-cellular pattern with the decrease of contact angle as a result of the competition between Marangoni flow and the evaporation. Additionally, the total evaporation rate increases with the increase of contact angle when contact angle is above 60o, but when the contact angle is below 60o, the trend is reverted. The temperature distribution becomes distinct at a small contact angle.


Sessile droplet Evaporation Marangoni convection Kinetic model Numerical simulation 



thermal diffusivity, m2/s


gravity acceleration, m/s2


height of the droplet, m


latent heat of vaporization, J/kg


evaporation rate, kg/(m2·s)


thermal conductivity, W/(m·K)


capillary length, m


molar mass of the evaporating liquid, g/mol


pressure, Pa


evaporation flux, kg/s


contact radius, m


universal gas constant, J/(mol·K)


time, s


temperature, K

U, V, W

velocity components along three directions, m/s


velocity vector

Greek Symbols


accommodation coefficient


pressure ratio


kinematic viscosity, m2/s


contact angle, o


surface tension, N/m


density of working liquid, kg/m3





liquid-vapor interface







This work is supported by National Natural Science Foundation of China (Grant No. 11532015), Chongqing University Post-graduates Innovation Project (Grant No: CYS18041) and the Fundamental Research Funds for the Central Universities (No. 2018CDXYDL0001).


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Yu Zhang
    • 1
  • You-Rong Li
    • 1
    Email author
  • Jia-Jia Yu
    • 1
  • Qiu-Sheng Liu
    • 2
  1. 1.Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, School of Energy and Power EngineeringChongqing UniversityChongqingChina
  2. 2.Key Laboratory of Microgravity (National Microgravity Laboratory), Institute of MechanicsChinese Academy of SciencesBeijingChina

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