A combined computational and experimental investigation on evaporation of a sessile water droplet on a heated hydrophilic substrate

Abstract

We numerically and experimentally investigate evaporation of a sessile droplet on a heated substrate. We develop a finite element (FE) model in two-dimensional axisymmetric coordinates to solve coupled transport of heat in the droplet and substrate, and of the mass of liquid vapor in surrounding ambient while assuming diffusion-limited and quasi-steady evaporation of the droplet. A two-way coupling is implemented using an iterative scheme and under-relaxation is used to ensure numerical stability. The FE model is validated against the published spatial profile of the evaporation mass flux and temperature of the liquid-gas interface. We discuss cases in which the two-way coupling is significantly accurate than the one-way coupling. In experiments, we visualized side view of an evaporating microliter water droplet using a high-speed camera at different substrate temperatures and recorded temperature of the liquid-gas interface from the top using an infrared camera. We examine the dependency of inversion of the temperature profile across the liquid-gas interface on the ratio of the substrate thickness to the wetted radius, the ratio of the thermal conductivity of the substrate to that of the droplet and contact angle. A regime map is plotted to demarcate the inversion of the temperature profile for a wide range of these variables. A comparison of measured evaporation mass rate with the computed values at different substrate temperature show that the evaporation mass rate increases non-linearly with respect to the substrate temperature, and FE model predicts these values close to the experimental data. Comparisons of time-averaged evaporation mass rate obtained by the previous and present models against the measurements suggest that the evaporative cooling at the interface and variation of diffusion coefficient with the temperature should be taken into account in the model in order to accurately capture the measurements. We compare the measurements of time-varying droplet dimensions and of temperature profile across the liquid-gas interface with the numerical results and found good agreements. We quantify increase in the evaporation mass flux and evaporation mas rate by the substrate heating and present the combined effect of substrate heating, the ratio of the substrate thickness to the wetted radius, substrate-droplet thermal conductivity ratio and the contact angle on the evaporation mass rate.