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Research Papers: Evaporation, Boiling, and Condensation

# Dropwise Condensation Underneath Chemically Textured Surfaces: Simulation and Experiments

[+] Author and Article Information
Basant Singh Sikarwar, Nirmal Kumar Battoo, K. Muralidhar

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

Sameer Khandekar1

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, Indiasamkhan@iitk.ac.in

Another postulation suggests that condensation initially occurs in a filmwise manner, forming an extremely thin film on the solid surface. As condensation continues in time, this film ruptures forming distinct droplets which subsequently grow. This mechanism is not followed in the present work.

Eq. 5 can be interpreted as modified Bond number criterion, applicable for a pendant droplet which takes into account the effect of contact angle in the force balance. In case of a horizontal substrate, there is no contact angle hysteresis. The usual definition of Bond number is given by, $Bo=(2⋅r)((g(ρl−ρv))/σ)$

Typically droplet mergers happen in a time scale of 5–300 ms, depending on their respective sizes and thermophysical properties (30-32). In contrast, the entire experiment of dropwise condensation, from a virgin surface to the first fall-off or a slide-off is typically of the order of one hour. This justifies our assumption of ‘instantaneous coalescence.

There is some conflict in the calculation of volume and its experimental validation for sessile drops on inclined surfaces, as reported in (40-43). Some reports (40-42) suggest that approximating the drop shape as a spherical cap can lead to 10%–25% error in volume. Based on experimental evidence, others (43) believe that such an approximation is quite valid. To the best of the knowledge of the authors, there is no corresponding literature on the calculation of pendant drop volumes. Therefore, the spherical cap approximation has been used in the present work.

1

Corresponding author.

J. Heat Transfer 133(2), 021501 (Nov 03, 2010) (15 pages) doi:10.1115/1.4002396 History: Received April 29, 2010; Revised July 23, 2010; Published November 03, 2010; Online November 03, 2010

## Abstract

Experimental observations of dropwise condensation of water vapor on a chemically textured surface of glass and its detailed computer simulation are presented. Experiments are focused on the pendant mode of dropwise condensation on the underside of horizontal and inclined glass substrates. Chemical texturing of glass is achieved by silanation using octyl-decyl-tri-chloro-silane $(C18H37C13Si)$ in a chemical vapor deposition process. The mathematical model is built in such a way that it captures all the major physical processes taking place during condensation. These include growth due to direct condensation, droplet coalescence, sliding, fall-off, and renucleation of droplets. The effects arising from lyophobicity, namely, the contact angle variation and its hysteresis, inclination of the substrate, and saturation temperature at which the condensation is carried out, have been incorporated. The importance of higher order effects neglected in the simulation is discussed. The results of model simulation are compared with the experimental data. After validation, a parametric study is carried out for cases not covered by the experimental regime, i.e., various fluids, substrate inclination angle, saturation temperature, and contact angle hysteresis. Major conclusions arrived at in the study are the following: The area of droplet coverage decreases with an increase in both static contact angle of the droplet and substrate inclination. As the substrate inclination increases, the time instant of commencement of sliding of the droplet is advanced. The critical angle of inclination required for the inception of droplet sliding varies inversely with the droplet volume. For a given static contact angle, the fall-off time of the droplet from the substrate is a linear function of the saturation temperature. For a given fluid, the drop size distribution is well represented by a power law. Average heat transfer coefficient is satisfactorily predicted by the developed model.

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## Figures

Figure 4

(a) The cycle of major physical processes observed in the pendant mode of dropwise condensation on a horizontal substrate. (b) Qualitative comparison of experimental images of dropwise condensation on silanated glass substrate of area 25×25 mm2 (coated with octyl-decyl-tri-chloro-silane, C18H37C13Si) with corresponding images generated by simulation. The hazy patch seen in the top-left section of the last experimental image is due to the fact that the droplet has fallen on the viewing glass (view A) through which images are being recorded.

Figure 8

Comparison of experiments and corresponding simulation for the complete sequence of dropwise condensation process, from the appearance of drops of minimum radius to the drops of critical radius underneath a horizontal silanated glass substrate of 25×10 mm2 area

Figure 9

Size distribution of drops condensing underneath an inclined (15 deg) silanated glass substrate of size 25×25 mm2 as recorded in experiments and in the simulation: (a) at time=2 min from the commencement of dropwise condensation, (b) at critical state of slide-off, and (c) just after a complete sweeping action is completed by a sliding drop

Figure 10

Various temporal stages of droplet condensation on the inclined substrate (15 deg) recorded during experiments and simulation. The commencement of sliding and sweeping actions of the drop as it gathers mass during transit and renucleation of the virgin exposed surface, when the sweeping action is complete, are clearly seen.

Figure 1

Details of the experimental setup to study dropwise condensation under controlled conditions underneath a substrate. (a) Photograph shows the details of the main condensing chamber; (b) exploded view of the condensing chamber showing all the components. (c) Typical images of the condensing droplets at two different times, as captured from view A. (d) Cross-sectional view of condensing chamber. (e) Schematic diagram explaining the chemical vapor deposition process.

Figure 2

(a) Schematic drawing of a pendant drop underneath a horizontal substrate with contact angle θ. (b) Drawing of a deformed drop with unequal advancing and receding angles, and its equivalent spherically approximated profile.

Figure 3

(a) A deformed pendant drop underneath an inclined substrate. (b) Free body diagram of a static drop underneath an inclined surface. (c) Base of droplet on the substrate taken as a circle.

Figure 5

Sequence of two images observed during experiment and corresponding simulation, showing coalescence of three droplets a, b, and c, resulting in the formation of a composite drop d

Figure 6

Visual and statistical comparison of experimental and simulated spatial drop distribution patterns and the corresponding histograms of droplet frequency at the dynamic steady state

Figure 7

(a) Drop size distribution from experiments and simulation at a time of 10 min after the commencement of dropwise condensation. (b) Time-wise variation in the area coverage of droplets over the substrate.

Figure 11

Sequence of images from experiments as well as simulation showing drop slide-off and the subsequent sweeping action on a 15 deg inclined 25×25 mm2 substrate. A dynamic steady state in the process has been achieved. Once slide-off commences, the drop quickly gathers mass during the sweeping action and subsequently falls off.

Figure 12

Effect of wettability: (a) Simulated spatial droplet distribution just before fall-off of a drop underneath a horizontal substrate of 20×20 mm2 area for contact angles of 90 deg, 105 deg, and 120 deg. (b) Temporal variation in coverage area of drops. (c) Fall-off time of the drop as a function of the contact angle (for all cases working fluid: water; Tsat=30°C, ΔTsat=5°C).

Figure 13

((a) and (b)) Temporal variation in drop size distribution for condensing water vapor underneath a horizontal silanated glass substrate (contact angle of 90 deg). For clarity, data for 1–10 min are separately plotted from the data of 30–50 min. The fall-off time for the first drop was equal to 48 min in this simulation. Immediately after fall-off (at 50 min), very small drops reappear because of the virgin area created after fall-off.

Figure 14

Effect of substrate inclination: (a) Temporal variation in area coverage of drops during condensation of water in the pendant mode. (b) Drop size distribution just before fall-off (for horizontal substrate) or slide-off (inclined substrate). For this simulation, the wettability of the substrate is such that θadv=106 deg and θrcd=74 deg for angle of inclination of 5 deg and θadv=110 deg and θrcd=61 deg for angle of inclination of 10 deg; the droplet is assumed to be hemispherical on a horizontal surface; Tsat=30°C, ΔTsat=5°C.

Figure 15

Variation in drop departure time (time required for first fall-off) on a horizontal substrate with respect to the saturation temperature. Fluid employed is water, subcooling ΔTsat=5°C, contact angle=90 deg, and nucleation site density=109 m−2. For a given nucleation site density, the fall time has an uncertainty of ±3 min, depending on the random assignment of initial droplet centers on the substrate.

Figure 16

(a) Spatial drop distribution for condensation underneath horizontal stainless steel substrate just before fall-off for (i) liquid sodium (Tsat=342°C, ΔTsat=5°C, θ=108 deg) and (ii) water (Tsat=30°C, ΔTsat=5°C, θ=73 deg), with the corresponding pictorial depiction in the inset. For liquid sodium, the fall-off time is 66 min, and for water it is 48. (b) The temporal variation in the number density of drops of water and sodium from the commencement of condensation until 60 min.

Figure 17

Variation in heat transfer coefficient for dropwise condensation of water on a horizontal substrate at Tsat=30°C and Tsat=50°C with the degree of subcooling. The results from the present simulator are compared with the prediction model of Le Fevre and Rose for dropwise condensation of water on a promoter layer, as reported by Rose (1).

Figure 18

(a) Critical angle of inclination of the substrate as a function of the drop size with respect to fall-off (horizontal substrate)/slide-off (inclined substrate). (b) Effect of contact angle hysteresis on the critical radius of the drop.

## Errata

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