Long-wave-instability-induced pattern formation in an evaporating sessile or pendent liquid layer
Date of Issue2018
School of Mechanical and Aerospace Engineering
We investigate the nonlinear dynamics and stability of an evaporating liquid layer subject to vapor recoil, capillarity, thermocapillarity, ambient cooling, viscosity, and negative or positive gravity combined with buoyancy effects in the lubrication approximation. Using linear theory, we identify the mechanisms of finite-time rupture, independent of thermocapillarity and direction of gravity, and predict the effective growth rate of an interfacial perturbation which reveals competition among the mechanisms. A stability diagram is predicted for the onset of long-wave (LW) evaporative convection. In the two-dimensional simulation, we observe well-defined capillary ridges on both sides of the valley under positive gravity and main and secondary droplets under negative gravity, while a ridge can be trapped in a large-scale drained region in both cases. Neglecting the other non-Boussinesq effects, buoyancy does not have a significant influence on interfacial evolution and rupture time but makes contributions to the evaporation-driven convection and heat transfer. The average Nusselt number is found to increase with a stronger buoyancy effect. The flow field and interface profile jointly manifest the LW Marangoni-Rayleigh-Bénard convection under positive gravity and the LW Marangoni convection under negative gravity. In the three-dimensional simulation of moderate evaporation with a random perturbation, the rupture patterns are characterized by irregular ridge networks with distinct height scales for positive and negative gravity. A variety of interfacial and internal dynamics are displayed, depending on evaporation conditions, gravity, Marangoni effect, and ambient cooling. Reasonable agreement is found between the present results and the reported experiments and simulations. The concept of dissipative compacton also sheds light on the properties of interfacial fractalization.
Physical Review Fluids
© 2018 American Physical Society. This paper was published in Physical Review Fluids and is made available as an electronic reprint (preprint) with permission of American Physical Society. The published version is available at: [http://dx.doi.org/10.1103/PhysRevFluids.3.034001]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.