Eur. Phys. J. Special Topics 226, 1325–1335 © EDP Sciences, Springer-Verlag 2017 DOI: 10.1140/epjst/e2016-60203-y T HE EUROPEAN P HYSICAL JOURNAL SPECIAL TOPICS Regular Article Numerical simulations of sessile droplet evaporating on heated substrate Xue Chen 1,2 , Paul G. Chen 2, a , Jalil Ouazzani 3 , and Qiusheng Liu 1 1 Institute of Mechanics, Chinese Academy of Sciences, 100190, Beijing, P.R. China 2 Aix Marseille Univ., CNRS, Centrale Marseille, M2P2, Marseille, France 3 Arcofluid Consulting LLC, 309 N Orange Ave, Orlando, FL 32801, USA Received 30 June 2016 / Received in final form 31 July 2016 Published online 2 May 2017 Abstract. Motivated by the space project EFILE, a 2D axisymmet- ric numerical model in the framework of ALE method is developed to investigate the coupled physical mechanism during the evaporation of a pinned drop that partially wets on a heated substrate. The model accounts for mass transport in surrounding air, Marangoni convection inside the drop and heat conduction in the substrate as well as moving interface. Numerical results predict simple scaling laws for the evapora- tion rate which scales linearly with drop radius but follows a power-law with substrate temperature. It is highlighted that thermal effect of the substrate has a great impact on the temperature profile at the drop surface, which leads to a multicellular thermocapillary flow pattern. In particular, the structure of the multicellular flow behavior induced within a heated drop is mainly controlled by a geometric parameter (aspect ratio). A relationship between the number of thermal cells and the aspect ratio is proposed. 1 Introduction Evaporation of a sessile liquid drop is a common phenomenon in nature. It has many important practical applications in areas including industry, biomedicine and space thermal devices which involve MEMS cooling, DNA mapping, thin film coating and micro heat pipes [1]. Therefore, there has been a rapid growth of scientific and tech- nological interest in the problem of droplet evaporation [2, 3]. The physical process which controls the complex problem of diffusion, Marangoni convection and heat conduction has been the subject of several recent reviews. Hu and Larson [4] used a finite-element method to solve the diffusion-driven problem and provided a simple empirical expression for evaporation rate, they also developed a mathematical model to study the internal flow and coupled Marangoni effect in the droplet. Semenov et al. [5] simulated the evaporation process as a quasi-steady state so that the moving boundary problem was converted to a series of fixed bound- ary problems by calculating the new spherical-cap profile according to the volume reduction. While considering a free-moving surface which is difficult to track in the a e-mail: gang.chen@univ-amu.fr