The strong influence of substrate conductivity on droplet evaporation

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

Convection-enhanced water evaporation

“…This result shows that the evaporation rate linearly changes with the contact area (π R 2 ) for each event, consistently suggesting the convective evaporation for nanoliter water droplets. 9,13,14 Here the coefficient A seems to increase from 2.4 × 10 − 6 to 12 × 10 − 6 nL s − 1 µm − 2 [1 nL s − 1 µm − 2 = 10 8 µg s − 1 cm − 2 ] as R 0 decreases from 1000 to 100 µm. This trend is reasonable because the evaporation flux j 0 inversely changes with the initial contact radius as j 0 ∝ R 0 − 1 (Ref.…”

“…The upward velocity of the air/vapor mixture is given as υ = (g ρ/ρL) 1/2 where g is the gravitational acceleration (9.8 m s − 2 ), ρ/ρ is the reduced density difference (∼ 1% for water vapor), and L is the length scale of the quasi-steady buoyant convection flow in the atmosphere. 13 Taking L = 0.1 m (as a realistic condition), 14 we obtain υ = 0.1 m s − 1 . For the given L, the buoyant convection would become more significant at small scales than at large scales.…”

“…This method allows precise measurements of droplet geometry (from TI) and complete evaporation time (from RI) for nanoliter water droplets of 2 to 700 nL, which are very small compared to microliter droplets (1-3 µL) studied in common methods. 14,23 Droplet geometry (R and θ ) is monitored from TI (a spherical cap) and complete evaporation time (t f ) from RI during evaporation of a water droplet on a flat surface (e.g., Si wafer) [Figs. 1(a) and 1(b) ].…”

“…1 This phenomenon has long been studied by Maxwell, 2 Langmuir, 3 and many scientists. [4][5][6][7][8][9][10][11][12][13][14][15] Droplet evaporation plays a key role in many natural and industrial processes such as drying-mediated pattern formation 6,7 and self-assembly. 16 Most liquid droplets follow diffusion-limited evaporation, [5][6][7][8] described as dV/dt ∝ -2π R in calm air (that is, evaporation rate linearly increase with contact radius).…”

“…13,14 In addition to diffusion-limited evaporation, convectionlimited evaporation is also actually feasible for water droplets 9, 13, 14 but, its direct evidence is scarce. 13,14 Droplet evaporation is typically classified into three modes 4,15 with respect to the wetting property (the contact radius R and the contact angle θ ): the constant-R-mode (θ changes with time), the constant-θ -mode (R changes with time), and the mixed mode (both R and θ change with time). The constant-R-mode is mostly prevailing for microliter-scale water droplets on smooth hydrophilic surfaces.…”