Dropwise condensation on solid hydrophilic surfaces

Abstract

Droplet nucleation and condensation are ubiquitous phenomena in nature and industry. Over the past century, research has shown dropwise condensation heat transfer on nonwetting surfaces to be an order of magnitude higher than filmwise condensation heat transfer on wetting substrates. However, the necessity for nonwetting to achieve dropwise condensation is unclear. This article reports stable dropwise condensation on a smooth, solid, hydrophilic surface (θ_a = 38°) having low contact angle hysteresis (<3°). We show that the distribution of nano- to micro- to macroscale droplet sizes (about 100 nm to 1 mm) for coalescing droplets agrees well with the classical distribution on hydrophobic surfaces and elucidate that the wettability-governed dropwise-to-filmwise transition is mediated by the departing droplet Bond number. Our findings demonstrate that achieving stable dropwise condensation is not governed by surface intrinsic wettability, as assumed for the past eight decades, but rather, it is dictated by contact angle hysteresis.

Fig. 1. Parameters affecting condensation heat transfer coefficient (h).

(A) Model results of h as a function of nucleation density (N_s) for varying advancing contact angle (θ_a) with departure radius r_max = 1 mm. (B) Condensation nucleation rate (J) as a function of condensing surface energy (γ). (C) h as a function of θ_a with N_s = 5 × 10¹⁰ m⁻² and r_max = 1 mm. (D) Theoretical r_max as a function of contact angle hysteresis (∆θ). (E) h as a function of r_max for varying θ_a with N_s = 5 × 10¹⁰ m⁻². The results assume a vapor pressure of 3500 Pa and a surface temperature of 20°C. Results show that hydrophilic dropwise condensation is advantageous to hydrophobic.

Fig. 2. Surface characteristics and wettability.

(A) Images showing a water droplet sliding across our PEGylated surfaces tilted by 8° relative to the horizontal. (B) High-resolution C 1s XPS spectra of the unmodified and our PEGylated surfaces. The ─C─C peak on an unmodified silicon wafer is due to adventitious carbon. The ─C─O peak on our PEGylated surface is indicative of PEGylation. a.u., arbitrary units. (C) AFM image depicting the topography of our PEGylated surface with root mean square roughness, R_rms < 1 nm, and thickness < 1 nm.

Fig. 3. Hydrophilic versus hydrophobic.

Two exemplary transient droplet size distributions during condensation captured with a macro and 20× microscope lens on the (A and B) hydrophobic substrate (θ_a/θ_r = 110° ± 4°/102° ± 5°) and (C and D) PEGylated substrate (θ_a/θ_r = 38° ± 1°/35° ± 1°), respectively. Droplet distributions were self-similar in nature. Two exemplary transient droplet size distributions captured with a macro and 5× microscope lens on a (E and F) quasi-dropwise condensing polished silicon substrate (θ_a/θ_r = 46° ± 1°/23° ± 1°) and (G and H) filmwise condensing polished copper substrate (θ_a/θ_r = 97° ± 2°/27° ± 1°), respectively. Experiments were conducted at a condensation heat transfer rate of 930 ± 100 W/m².

Fig. 4. Steady-state droplet size distribution on our hydrophilic PEGylated surface.

The dashed line shows the Rose distribution for hydrophobic surfaces with $\hat{r}=r_{\text{max}}/1.3=0.36 \text{mm}$ (valid for condensation on the C₄F₈ hydrophobic polymer), and the solid line shows the fit from the inset equation. The vertical dashed line shows the experimental maximum droplet radius (r_{max, exp} = 1.32 mm). The droplet number density at the onset of nucleation for our PEGylated (red square symbol) and hydrophobic (green triangle symbol) surfaces are shown as well. We estimate the error associated with the automated droplet detection to be less than 10%. Experiments conducted in the presence of noncondensable gases for a condensation heat transfer rate of 930 ± 100 W/m². Inset: Model results showing overall surface condensation heat flux (Q″) as a function of vapor-to-surface temperature difference (∆T) during dropwise condensation of pure steam on the hydrophobic (red circles) and PEGylated hydrophilic (blue squares) surfaces.

Fig. 5. Condensation regime map as a function of advancing contact angle, θ_a, and contact angle hysteresis, θ_a−θ_r.

The light blue and light red shaded regions represent dropwise and filmwise condensation, respectively. The dashed blue line represents Bo = 1.4. Data points in the regime map were obtained from previous works as well as this study (table S1).