Journal of Colloid and Interface Science 285 (2005) 296–305 www.elsevier.com/locate/jcis Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas Benoît Haut a , Pierre Colinet b,∗ a Université Libre de Bruxelles, Service de Génie Chimique, C.P. 165/67, av. F.D. Roosevelt 50, 1050 Brussels, Belgium b Université Libre de Bruxelles, Service de Chimie-Physique E.P., C.P. 165/62, av. F.D. Roosevelt 50, 1050 Brussels, Belgium Received 10 December 2003; accepted 26 July 2004 Available online 22 December 2004 Abstract A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid–gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.  2004 Elsevier Inc. All rights reserved. Keywords: Heat transfer; Mass transfer; Evaporation; Marangoni instability 1. Introduction Evaporation being an endothermic process, it induces a cooling of the liquid–vapor phase boundary. This situation is well known to eventually generate convective instabili- ties, due to both buoyancy and thermocapillary effects [1]. Attention will here be restricted to the second of these mechanisms, generally referred to as the Marangoni effect, which is induced by the decrease of the liquid–vapor sur- face tension with an increase of temperature. Importantly, the resulting convective motions eventually modify drasti- cally heat transfer in the liquid, and hence its rate of evapo- ration. Evaporative convection driven by the Marangoni effect is known to play an important role in a number of processes, such as drying of paint films and thin-film evaporators [2]. Usually, the liquid evaporates into an inert gas, often air, and * Corresponding author. E-mail address: pcolinet@ulb.ac.be (P. Colinet). a limitation of the evaporation rate can arise from diffusion of the vapor through this inert gas. However, the role played by an additional gas component is actually much more subtle. To illustrate this, let us first consider an evaporating liquid layer in contact only with its own vapor. If it is assumed that thermodynamic equi- librium is achieved at the liquid–gas interface, temperature and pressure in the gas phase are linked at this interface (for instance by the Clausius–Clapeyron law). The dynamic vis- cosity of a gas being small, pressure fluctuations in the gas usually remain small. Therefore, fluctuations of temperature at the liquid–gas interface are strongly limited. However, the Marangoni effect is generated precisely by temperature fluc- tuations at the liquid–gas interface. Except in extreme situ- ations, it thus seems impossible that an evaporating liquid layer in contact only with its own vapor undergoes surface- tension-driven instability under a local equilibrium assump- tion at the interface. Most of the papers dealing with the interaction between evaporation and the Marangoni effect assume that the liquid is in contact only with its own vapor. They therefore concen- 0021-9797/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.07.041