Evaporation-induced flow around a droplet in different gases

Abstract: The evaporation of a sessile droplet with a pinned contact line is investigated experimentally, by analytic theory and by computation using the finite element method (FEM). Because of the low value of R2/Dtf = cv(1 − H)/ρ = 1.4 × 10-5, where R is the contact-line radius, D is the water vapor diffusivity, cv is the saturated water vapor concentration, H is the relative humidity, and ρ is the liquid water density, the evaporation can be considered as a quasi-steady-state process. Hence, the vapor concentration distribution above the droplet satisfies the Laplace equation but with a time-varying droplet surface. It is found both theoretically and experimentally that the net evaporation rate from the droplet remains almost constant with time for a small initial contact angle (θ < 40°), even though the evaporation flux becomes more strongly singular at the edge of the droplet as the contact angle decreases during evaporation. We also measured the critical contact angle at which the contact line starts to reced...

Abstract: In the evaporation of drops on surfaces two modes of evaporation are distinguished: that at constant contact angle and that at constant contact area. A theoretical analysis of each mode is developed from which predictions can be made of evaporation rate and residual mass at any time in the life of the drop for contact angles ranging from near zero up to 180°. These predictions have been compared with known theoretical values and with experimental measurements, and it is considered that the theory is reasonably accurate for drops of mass between 1 pg and an upper limit somewhat greater than 40 mg.

Abstract: A model accounting for the finite spatial dimensions of the deposit patterns in evaporating sessile drops of a colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding evaporative deposition and may be useful for creating controlled deposition patterns.

Abstract: We report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet. We show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate. Furthermore, we show that including two ad hoc improvements to the model, namely a Newton's law of cooling on the unwetted surface of the substrate and the buoyancy of water vapour in the atmosphere, give excellent quantitative agreement for all of the combinations of liquid and substrate considered.