**5. Condensation on superhydrophobic surfaces**

Surface modification plays a crucial role in manipulating droplet wetting and dynamics. When micro/nanostructures are covered with hydrophobic coatings, the resulted superhydrophobic surfaces can promote the formation of highly mobile droplets in the Cassie states. More interestingly, it has been demonstrated that on such micro/nanostructured superhydrophobic surfaces small microdroplets can undergo coalescence-induced droplet jumping due to the release of excess surface energy (**Figure 8a**), which is independent of gravity [75, 76, 83, 84]. Jumping

#### **Figure 8.**

number of larger droplets decreases while the number of smaller droplets increases, and droplet size range becomes wider. Finally, the right peak vanishes and the distribution becomes unimodal. Due to the self-similarity feature of droplet size distribution, a representative large enough surface area contains various growth

*Evolution of droplet size distribution on a plain hydrophobic surface. (a) Experimental results of the transient droplet size distribution in condensation [14]. (b–d) Evolution of cluster size distribution by MD simulation: (b) cluster size distribution as a function of time, (c) cluster size distribution as a function of time by MD*

To further understand the evolution of droplet size distribution, a transient cluster size distribution model was introduced to investigate the kinetics of the initial condensation stage by MD simulation method [17]. It is well known that the growth/decay of clusters is significantly affected by the cluster size and contact angles of the condensing surface. With the increase of cluster sizes, more surface area of the cluster is exposed to the vapor, as well as the increased attachment/ detachment frequencies. When the contact angle decreased to a certain value, the attachment frequency becomes larger than detachment frequency, resulting in the continuous growth of the clusters and subsequent nucleation. The results of the evolution of cluster/droplet size distribution indicate that the transient cluster size distribution translates from a monotonic decreasing distribution to a unimodal distribution with time (**Figure 7b,c**). The cluster radius at the peak of cluster/ droplet size distribution curve shifts to the larger cluster sizes with time. However,

stages, resulting in a steady-state droplet size distribution [14, 82].

*simulation and (d) evolution of cluster radius distribution [17].*

*21st Century Surface Science - a Handbook*

**Figure 7.**

**238**

*Wetting and dynamics of the droplet on the superhydrophobic surfaces. (a) Droplet jumping due to the merge of two small droplets [83]. (b) Various wetting modes of condensed droplets on a nanostructured surface [85]. (c–i) Wetting transition of condensed droplets with the increase of surface subcooling: (c) schematic illustrating suspended droplets under a small subcooling, (d) time-lapse images of jumping droplets, (e) schematic illustrating immersed droplets under a large subcooling, (f) time-lapse images of flooding phenomenon, (g) schematic illustrating droplet nucleation in the nanostructure as a function of subcooling. ESEM images of a suspended (h) and immersed (i) droplet in nanostructures at a small and a large surface subcooling, respectively [24].*

droplets have been shown to enhance dropwise condensation through accelerating surface refreshing and reducing time-averaged droplet thermal resistance on the surface [22, 66, 86, 87]. Different from the wetting states of the injected droplets on a superhydrophobic surface, such as the millimeter-scale raindrops that are much larger than the micro/nanoscale structure features of lotus leaves, vapor condensation starts with the formation of nanoscale droplets, which can result in loss of nonwettability and flooding phenomenon on micro/nanostructured surfaces. Various droplet wetting modes (**Figure 8b**), for example, Wenzel state, Cassie state, and partially wetting state, have been observed on the superhydrophobic surface [85, 88]. Moreover, the wetting transition of condensed droplets can cause a large degradation of heat transfer performance [22, 89]. A considerable amount of work has focused on understanding the effect of surface structure and wettability on wetting transition with a variety of explanations including surface free energy models [88, 90, 91], Laplace pressure instabilities [92–94], and thermodynamic models [95, 96].

**Figure 8c**–**i** shows that the condensation mode transitions from jumping droplet condensation to flooding condensation on a nanostructured superhydrophobic surface as the surface subcooling increases from 0.3 to 3 K [24]. To illustrate the mechanism of wetting transition, a spatial confinement effect on the droplet nucleation was proposed to explain the wetting states of condensed droplets under different surface subcooling. Condensation begins with nucleation with the formation of nanoscale condensed droplets, with the diameter of several nanometers at large subcooling to hundreds of nanometers at small subcooling. Besides, the nucleation site density is inversely proportional to the critical droplet nucleation radius, *N*<sup>s</sup> 0.037/*r*min [97]. Under a small subcooling, sparse large nucleated droplets on the nanostructures tend to form as the suspended Cassie state (**Figure 8c**), promoting the subsequent self-droplet jumping and effective surface refreshing (**Figure 8d**). As the surface subcooling increases, the critical droplet radius rapidly decreases, leading to the preferred droplet nucleation at the bottom of nanostructures (**Figure 8e**). With the further increase of surface subcooling, large pinned droplets can form on the nanostructures (**Figure 8f**). This is due to the coalescence between a large number of small droplets nucleated within the structures, filling the nanostructures with liquid condensate. To validate the proposed effect of spatial confinement on droplet formation on superhydrophobic surfaces, **Figure 8g,h** shows the experimental observation of the wetting states of nucleated droplets in the nanoscale gaps at different surface subcooling. Small surface subcooling promotes the formation of suspended droplets (**Figure 8h**) due to a larger critical nucleation size (about 166 nm), while large surface subcooling results in the immersed droplet (**Figure 8i**) due to a smaller critical nucleation size. Thus, the wetting states of condensed droplets on the micro/nanostructured surfaces can be controlled by manipulating initial nucleation through adjusting the structure feature and length scale of surface structures.

efficiently removed by efficient jumping (**Figure 9c**) at a small surface subcooling of 2 K. The enhanced condensation heat flux and heat transfer coefficient on the straight nanowired surfaces as a function of surface subcooling have been experimentally demonstrated compared with conventional dropwise condensation on the plain hydrophobic surface (**Figure 9f,g**). However, condensation heat flux reaches its maximum as surface subcooling increases to 6 K and then slightly reduces as surface subcooling is increased to 15 K. Further increase of surface subcooling can increase heat flux monotonically with a similar trend as dropwise condensation on the plain hydrophobic surface. Subsequently, a hierarchical superhydrophobic surface with micro-patterned copper nanowire arrays was developed to improve droplet dynamics [21]. Micro-valleys, consisting of short nanowire arrays between long nanowire arrays, were fabricated to enable spontaneous droplet movement during droplet growing process. For the droplets formed in the micro-valleys, they can rapidly grow on the short nanowire arrays to a critical size where the droplet dimension is comparable to micro-valleys. Further growth of these droplets can push droplet out from the micro-valleys with a Laplace pressure difference between the bottom and top of the droplet, which accelerates droplet re-nucleation and

*Superhydrophobic copper nanowires for enhancing condensation heat transfer. (a) Schematic illustrating the spatial control of nucleation for mobile droplets on the top of closely spaced nanowires [65]. (b–e) Droplet behaviors on the plain hydrophobic, straight nanowired, and hierarchical nanowired surfaces, and 3D nanowire networks [71]. (f–g) Heat flux and heat transfer coefficient as a function of surface subcooling. Stable jumping droplet condensation enables the highest heat flux and heat transfer coefficient on the surface with 3D*

Although the range of surface subcooling for jumping droplet condensation has

been extended by the spatial control of nucleation using the closely arranged

growth.

**241**

**Figure 9.**

*nanowire networks [71].*

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

To delay the occurrence of flooding for achieving stable jumping droplets, various superhydrophobic surfaces with closely spaced nanostructures (**Figure 9a**) have been recently proposed to spatially control nucleation [65, 98, 99]. Minimizing the spacings using high-aspect ratio nanowires can promote to obtain a vapor density difference between the inside and outside of the nanoscale spacing. By this strategy of controlling vapor density, the closely spaced nanowires have been demonstrated to mitigate droplet nucleation in the spacing with a larger energy barrier compared with the top surface of nanowires. The formation of mobile droplets in suspended or partially wetting states is favored for jumping droplet condensation. Compared to the droplet sliding on a plain hydrophobic surface driven by gravity (**Figure 9b**), droplets on the superhydrophobic nanowired surface can be

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

#### **Figure 9.**

droplets have been shown to enhance dropwise condensation through accelerating surface refreshing and reducing time-averaged droplet thermal resistance on the surface [22, 66, 86, 87]. Different from the wetting states of the injected droplets on a superhydrophobic surface, such as the millimeter-scale raindrops that are much larger than the micro/nanoscale structure features of lotus leaves, vapor condensation starts with the formation of nanoscale droplets, which can result in loss of nonwettability and flooding phenomenon on micro/nanostructured surfaces. Various droplet wetting modes (**Figure 8b**), for example, Wenzel state, Cassie state, and partially wetting state, have been observed on the superhydrophobic surface [85, 88]. Moreover, the wetting transition of condensed droplets can cause a large degradation of heat transfer performance [22, 89]. A considerable amount of work has focused on understanding the effect of surface structure and wettability on wetting transition with a variety of explanations including surface free energy models [88, 90, 91], Laplace pressure instabilities [92–94], and thermodynamic

**Figure 8c**–**i** shows that the condensation mode transitions from jumping droplet condensation to flooding condensation on a nanostructured superhydrophobic surface as the surface subcooling increases from 0.3 to 3 K [24]. To illustrate the mechanism of wetting transition, a spatial confinement effect on the droplet nucleation was proposed to explain the wetting states of condensed droplets under different surface subcooling. Condensation begins with nucleation with the formation of nanoscale condensed droplets, with the diameter of several nanometers at large subcooling to hundreds of nanometers at small subcooling. Besides, the nucleation site density is inversely proportional to the critical droplet nucleation radius, *N*<sup>s</sup> 0.037/*r*min [97]. Under a small subcooling, sparse large nucleated droplets on the nanostructures tend to form as the suspended Cassie state (**Figure 8c**), promoting the subsequent self-droplet jumping and effective surface refreshing (**Figure 8d**). As the surface subcooling increases, the critical droplet radius rapidly

decreases, leading to the preferred droplet nucleation at the bottom of

feature and length scale of surface structures.

**240**

nanostructures (**Figure 8e**). With the further increase of surface subcooling, large pinned droplets can form on the nanostructures (**Figure 8f**). This is due to the coalescence between a large number of small droplets nucleated within the structures, filling the nanostructures with liquid condensate. To validate the proposed effect of spatial confinement on droplet formation on superhydrophobic surfaces, **Figure 8g,h** shows the experimental observation of the wetting states of nucleated droplets in the nanoscale gaps at different surface subcooling. Small surface subcooling promotes the formation of suspended droplets (**Figure 8h**) due to a larger critical nucleation size (about 166 nm), while large surface subcooling results in the immersed droplet (**Figure 8i**) due to a smaller critical nucleation size. Thus, the wetting states of condensed droplets on the micro/nanostructured surfaces can be controlled by manipulating initial nucleation through adjusting the structure

To delay the occurrence of flooding for achieving stable jumping droplets, various superhydrophobic surfaces with closely spaced nanostructures (**Figure 9a**) have been recently proposed to spatially control nucleation [65, 98, 99]. Minimizing the spacings using high-aspect ratio nanowires can promote to obtain a vapor density difference between the inside and outside of the nanoscale spacing. By this strategy of controlling vapor density, the closely spaced nanowires have been demonstrated to mitigate droplet nucleation in the spacing with a larger energy barrier compared with the top surface of nanowires. The formation of mobile droplets in suspended or partially wetting states is favored for jumping droplet condensation. Compared to the droplet sliding on a plain hydrophobic surface driven by gravity

(**Figure 9b**), droplets on the superhydrophobic nanowired surface can be

models [95, 96].

*21st Century Surface Science - a Handbook*

*Superhydrophobic copper nanowires for enhancing condensation heat transfer. (a) Schematic illustrating the spatial control of nucleation for mobile droplets on the top of closely spaced nanowires [65]. (b–e) Droplet behaviors on the plain hydrophobic, straight nanowired, and hierarchical nanowired surfaces, and 3D nanowire networks [71]. (f–g) Heat flux and heat transfer coefficient as a function of surface subcooling. Stable jumping droplet condensation enables the highest heat flux and heat transfer coefficient on the surface with 3D nanowire networks [71].*

efficiently removed by efficient jumping (**Figure 9c**) at a small surface subcooling of 2 K. The enhanced condensation heat flux and heat transfer coefficient on the straight nanowired surfaces as a function of surface subcooling have been experimentally demonstrated compared with conventional dropwise condensation on the plain hydrophobic surface (**Figure 9f,g**). However, condensation heat flux reaches its maximum as surface subcooling increases to 6 K and then slightly reduces as surface subcooling is increased to 15 K. Further increase of surface subcooling can increase heat flux monotonically with a similar trend as dropwise condensation on the plain hydrophobic surface. Subsequently, a hierarchical superhydrophobic surface with micro-patterned copper nanowire arrays was developed to improve droplet dynamics [21]. Micro-valleys, consisting of short nanowire arrays between long nanowire arrays, were fabricated to enable spontaneous droplet movement during droplet growing process. For the droplets formed in the micro-valleys, they can rapidly grow on the short nanowire arrays to a critical size where the droplet dimension is comparable to micro-valleys. Further growth of these droplets can push droplet out from the micro-valleys with a Laplace pressure difference between the bottom and top of the droplet, which accelerates droplet re-nucleation and growth.

Although the range of surface subcooling for jumping droplet condensation has been extended by the spatial control of nucleation using the closely arranged

nanowires, droplet wetting transition still occurs on both the uniform and hierarchical nanowired surfaces (**Figure 9c,d**) with the increase of the surface subcooling, resulting in the heat transfer degradation [21, 65]. This is because the active nucleation size decreases with the increase of surface subcooling while the straight nanowires tend to agglomerate and form a large number of micro-defects on the surface in fabrication processes [65, 73]. For condensation on such structured surfaces, vapor prefers to nucleate first in the micro-defects with a smaller energy barrier, resulting in the formation of large pinned droplets and flooding phenomenon [67, 68]. To avoid the agglomeration of straight nanowires, a 3D copper nanowire network fabricated has recently been demonstrated to eliminate the micro-defects between nanowires [71]. Benefiting from the interconnections between the nanowires, the surface morphology of the 3D nanowire network appears to be homogeneous without micro-defects. Compared to the droplet wetting transition on the uniform and hierarchical nanowired surfaces (**Figure 9c,d**), sustainable droplet jumping phenomena is obtained on the superhydrophobic surface with 3D nanowire networks even at a large surface subcooling of 28 K (**Figure 9e**). Benefiting from the formation of suspended and partially wetting droplets, a significant enhancement in heat transfer is realized on the 3D nanowire networks throughout the wide range of surface subcooling experimented (**Figure 9f,g**).

On such a hybrid surface (**Figure 10a**), the growing droplets in the hydrophobic regions are removed when they grow large enough to contact with the liquid film in the hydrophilic regions, resulting in a smaller removal size than that of gravitydriven departure. Another attempt in coupling droplets with a liquid film for enhanced condensation was recently reported on a hierarchical mesh-covered surface [72]. The typical structural feature of the hierarchical mesh-covered surface is composed of an interweaving microchannel network between a superhydrophobic woven mesh layer and a flat substrate, and a large number of micropores among mesh wires (**Figure 10b**). Vapor permeates freely through the mesh layer and condenses on the substrate to form a thin liquid condensate film that is confined in the interconnected channel network. When the condensate film grows out of the micropores due to the increased condensation heat flux, the surrounding liquid condensate can be drained out by the liquid film flow and eventually leaves the superhydrophobic hierarchical mesh-covered surface in the form of gravity-driven falling droplets. The thin liquid film in the interweaving microchannel network not only provides efficient low-thermal resistance condensation interfaces but also continuously transports liquid condensate to be drained out from the substrate. When the NCG presences in water vapor, condensation performance is highly dependent on the initial nucleation and mass transfer of vapor molecules in the diffusion layer near the condensing surface [103, 124, 125]. A hydrophilic copper surface with interval fluorocarbon-coated hydrophobic bumps to enable falling droplet-enhanced filmwise condensation (**Figure 10c**). Due to the decreased nucleation energy barrier on the hydrophilic regions, water vapor can rapidly nucleate, grow, and form a thin liquid film on the vertical surface. To prevent continuous thickness growth of condensate liquid film along the vertical tube, interval hydrophobic bumps are designed to remove liquid film periodically, which is enabled by the reduction of surface adhesion for condensate liquid on the hydrophobic bumps. More importantly, the condensate liquid departing from the hydrophobic bumps in the form of falling droplets can strongly disturb the NCG diffusion boundary layer.

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

High-performance condensation heat transfer in the presence of NCG was

*Emerging strategies and surface design for enhancing condensation heat transfer. (a) Hybrid surface with hydrophobic and hydrophilic stripes to enable dropwise-filmwise condensation [100]. (b) Sucking flow condensation on a hierarchical mesh structured surface [72]. (c) A hydrophilic copper tube surface with interval fluorocarbon-coated hydrophobic bumps [103]. (d) A superhydrophobic surface covered with*

**Figure 10.**

**243**

*macrogroove arrays [104].*
