Thermal effects of the substrate on water droplet evaporation

B. Sobac and D. Brutin

Phys. Rev. E 86, 021602 – Published 20 August 2012

Abstract

We experimentally investigate the behavior of a pinned water droplet evaporating into air. The influence of the substrate temperature and substrate thermal properties on the evaporation process are studied in both hydrophilic and hydrophobic conditions. Our objective is to understand the effect of thermal mechanisms on the droplet evaporation process. The experimental results are compared with the quasisteady, diffusion-driven evaporation model, which is implemented under the influence of the temperature; the model assumes the isothermia of the droplet at the substrate temperature. The results highlight a favorable correlation between the model and the experimental data at ambient temperatures for most situations considered here. The model works to qualitatively describe the influence of the substrate temperature on the evaporation process. However, with an increase in the substrate temperature, the role of the thermal-linked mechanisms becomes increasingly important; this experiment highlights the need for more accurate models to account for the buoyant convection in vapor transport and the evaporative cooling and heat conduction between the droplet and the substrate. Finally, the experimental data reveal the modification of contact angle evolution as the temperature increases and the crucial role played by the nature of the substrate in the evaporation of a sessile droplet. The influence of the substrate thermal properties on the global evaporation rate is explained by the parallel thermal effusivity of the liquid and solid phases.

Received 19 April 2012

DOI:https://doi.org/10.1103/PhysRevE.86.021602

Authors & Affiliations

B. Sobac^* and D. Brutin

Laboratoire IUSTI, UMR 7343 CNRS, Aix-Marseille Université, 5 rue Enrico Fermi, 13453 Marseille cedex 13, France

^*benjamin.sobac@polytech.univ-mrs.fr

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Vol. 86, Iss. 2 — August 2012

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Images

Figure 1
Schematic diagram illustrating the experimental setup, including a computer with drop shape analysis (DSA) software (1), a cold light source (2), a computer controlled syringe (3), a charge-coupled device (CCD) camera fitted with a macrolens (4), and an experimental cell (5). As observed in the inset, the experimental cell includes a heated aluminum block regulated in temperature (6), the substrate (7), coated with a nanoscale layer (8), and the water droplet (9).Reuse & Permissions
Figure 2
(a) Side view of a 4.2- $μ$ L water droplet on the sample surfaces at the initial moment. (b) Atomic force microscopy image of the surface coated with PFC (root mean squared roughness of 1.75 $μ$ m).Reuse & Permissions
Figure 3
Evaporation of a pinned water droplet on an aluminum substrate coated with SiO $_{x}$ as a function of the substrate temperature $T_{s}$ . (a) Contact angle $θ$ variation versus time $t$ . Inset: Zoom. (b) Volume $V$ variation versus time $t$ . Inset: Zoom. (c) Variation of the evaporation time $t_{F}$ versus the substrate temperature $T_{s}$ . Inset: Relative deviation of the evaporation time $ε_{t_{F}}$ versus the substrate temperature $T_{s}$ . (d) Variation of the global evaporation rate ${| d m / d t |}_{g}$ versus the substrate temperature $T_{s}$ . Inset: Relative deviation of the global evaporation rate $ε_{{\dot{m}}_{g}}$ versus the substrate temperature $T_{s}$ . Atmospheric conditions: $T_{a} = 25.4^{\circ}$ C, $P = 101.5$ kPa, $H = 47.5 \pm 1 %$ . Drop dimensions: $V = 3.64 μ L \pm 2 %$ , $θ_{i} = 68 \pm 1^{\circ}$ and $R = 1.44 \pm 0.03$ mm. Complementary information about the equations of fits: in panel (c), (–) $t_{F} = 1.4089 \times 10^{6} {T_{s}}^{- 2.8077}$ , (- -) $t_{F} = 7.0624 \times 10^{6} {T_{s}}^{- 2.5711}$ ; in panel (d), (–) $| {\dot{m}}_{g} | = 1.3315 \times 10^{- 13} {T_{s}}^{2.9893}$ , (- -) $| {\dot{m}}_{g} | = 1.9157 \times 10^{- 13} {T_{s}}^{2.8254}$ .Reuse & Permissions
Figure 4
Evaporation of a pinned drop of water on an aluminum substrate coated with PFC as a function of the substrate temperature $T_{s}$ . (a) Contact angle $θ$ variation versus time $t$ . Inset: Zoom. (b) Volume $V$ variation versus time $t$ . Inset: Zoom. (c) Variation of the evaporation time $t_{F}$ versus the substrate temperature $T_{s}$ . Inset: Relative deviation of the evaporation time $ε_{t_{F}}$ versus the substrate temperature $T_{s}$ . (d) Variation of the global evaporation rate ${| d m / d t |}_{g}$ versus the substrate temperature $T_{s}$ . Inset: Relative deviation of the global evaporation rate $ε_{{\dot{m}}_{g}}$ versus the substrate temperature $T_{s}$ . Atmospheric conditions: $T_{a} = 23.3 \pm 0.6^{\circ}$ C, $P = 101.8 \pm 0.1$ kPa, $H = 36.4 \pm 2 %$ . Drop dimensions: $V = 3.79 μ L \pm 3 %$ , $θ_{i} = 133 \pm 2^{\circ}$ , and $R = 0.72 \pm 0.04$ mm. Complementary information about the equations of fits: the dashed lines are sixth-degree polynomial fits in panel (a) and quadratic polynomial fits in the panel (b); in panel (c), (–) $t_{F} = 2.6228 \times 10^{6} {T_{s}}^{- 2.2481}$ , (- -) $t_{F} = 3.1285 \times 10^{6} {T_{s}}^{- 2.3124}$ and in panel (d), (–) $| {\dot{m}}_{g} | = 2.2709 \times 10^{- 13} {T_{s}}^{2.7438}$ , (- -) $| {\dot{m}}_{g} | = 7.428 \times 10^{- 13} {T_{s}}^{2.4086}$ .Reuse & Permissions
Figure 5
Normalized contact angle $θ / θ_{0}$ versus the normalized time $t / t_{F}$ as a function of the temperature of the substrate for the hydrophilic case (a) and the hydrophobic case (b). Insets: zooms. For complementary information see captions in Fig. 3 for the hydrophilic case and in Fig. 4 for the hydrophobic case.Reuse & Permissions
Figure 6
Global evaporation rate $| \frac{d m}{d t} |_{g}$ of a pinned water droplet versus the temperature of the substrate $T_{s}$ for various substrate materials. Atmospheric conditions: $T_{a} = 25 \pm 1^{\circ}$ C, $P = 1 atm \pm 1$ $%$ , $H = 47.5 \pm 5 %$ . Drop dimensions: $V = 3.75 \pm 0.55 μ$ L, $θ_{0} = 67.5 \pm 5^{\circ}$ and $R = 1.44 mm \pm 10 %$ . Complementary information about the equations of fits: (brown - -) power law fit of copper points $| {\dot{m}}_{g} | = 1.0974 \times 10^{- 13} {T_{s}}^{3.0355}$ , (purple - -) power law fit of bronze points $| {\dot{m}}_{g} | = 1.4312 \times 10^{- 13} {T_{s}}^{2.965}$ , (blue - -) power law fit of POM points $| {\dot{m}}_{g} | = 4.4651 \times 10^{- 13} {T_{s}}^{2.6267}$ , (black –) power law fit of the diffusion model $| {\dot{m}}_{g} | = 1.9493 \times 10^{- 13} {T_{s}}^{2.8151}$ .Reuse & Permissions

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