An expression for droplet evaporation incorporating thermal effects

Abstract

We propose a general theoretical expression for sessile droplets' evaporation, incorporating thermal effects related to the thermal resistance of the substrate and liquid properties. We develop an expression which accounts for thermal effects associated with evaporative cooling; the latter leads to a reduction in the rate of evaporation, which is not accounted for in the current theories, i.e. ‘isothermal diffusion theories’. The threshold for transition to a regime in which thermal effects start to be significant is identified through a dimensionless number which includes substrate and liquid properties as well as the kinetics of evaporation. The proposed theory is validated against experimental data in a very wide range of conditions and for a variety of systems. The developed expression extends the domain of use of diffusion-based models for droplet evaporation and accurately describes some aspects of the phenomenon which, to the best of our knowledge, are highlighted for the first time.

Vortices, dissipation and flow transition in volatile binary drops

“…The evaporation of drops and their profile evolution and dependence on ambient conditions has been subject to numerous studies. Various aspects of this phenomenon have been experimentally and theoretically explored, including diffusion of vapour in the ambient medium, Sefiane et al (2009) and substrate properties, Sefiane & Bennacer (2011). The dynamics of drop profile and three phase contact line and their dependence on substrate roughness and properties has also been extensively researched.…”

The effects of molecular weight, evaporation rate and polymer concentration on pillar formation in drying poly(ethylene oxide) droplets

“…In the subsequent years understanding the competing dynamic processes within evaporating sessile droplets has become an increasingly complex and interesting subject, encompassing many experimental factors such as: the solvent evaporation rate [2,3]; interactions between solvent, solute, vapour and substrate [4,5]; phase transitions within the droplet [6,7]; internal convection currents [8,9,10]; solute diffusion [11,12,13]; and the shape of suspended particles [14]. As well as to understand the fundamental science, motivation comes from a variety of industrial applications such as ink-jet printing [15], drying paints and varnishes, evaporative cooling [16], and effective chemical delivery in crop spraying.…”

Smart and green interfaces: From single bubbles/drops to industrial environmental and biomedical applications

“…The energy-production and biomedical applications represent paradigmatic examples in that sense, where expertise in science and technology must match properly with economical, societal and ethical issues. Transition from isothermal to non-isothermal regimes as described by SB dimensionless number, modified and adapted [59]. : Poly(N-isopropylacrylamide-co-acrylic acid)/Chitosan polyelectrolyte complexes for fabrication of pH/thermo-responsible microgels intended for surface functionalization of textiles.…”

“…The drop evaporation causes movements of liquid inside it, in particular, Marangoni instability can develop inside the droplet driven by gradients of surface tension due to inhomogeneity of the surface temperature [49]. The comprehensive review on thermocapillary flows in evaporating droplets is given in [55]. High-speed microparticle image velocimetry [56] was used to study velocity profiles in the droplet and infrared thermography was used to study temperature profiles at its surface [57].…”

“…In this regime, the drops can experience various degrees of cooling, which can be significant. The transition between isothermal and non-isothermal regimes is well described by using the dimensionless Sefiane-Bennacer number, SB, as detailed in [59].The dimensionless number, SB regroups all thermophysical properties of the three phases involved in the process, i.e. liquid, solid and gas.…”