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Surface Engineering for Phase Change Heat Transfer: A Review

Among numerous challenges to meet the rising global energy demand in a sustainable manner, improving phase change heat transfer has been at the forefront of engineering research for decades. The high heat transfer rates associated with phase change heat transfer are essential to energy and industry applications; but phase change is also inherently associated with poor thermodynamic efficiencies at low heat flux, and violent instabilities at high heat flux. Engineers have tried since the 1930's to fabricate solid surfaces that improve phase change heat transfer. The development of micro and nanotechnologies has made feasible the high-resolution control of surface texture and chemistry over length scales ranging from molecular levels to centimeters. This paper reviews the fabrication techniques available for metallic and silicon-based surfaces, considering sintered and polymeric coatings. The influence of such surfaces in multiphase processes of high practical interest, e.g., boiling, condensation, freezing, and the associated physical phenomena are reviewed. The case is made that while engineers are in principle able to manufacture surfaces with optimum nucleation or thermofluid transport characteristics, more theoretical and experimental efforts are needed to guide the design and cost-effective fabrication of surfaces that not only satisfy the existing technological needs, but also catalyze new discoveries.


Introduction
This review discusses the increasingly important contributions of advanced materials and novel fabrication techniques in enhancing phase change heat transfer and the related energy applications.
Technologies based on phase change heat transfer have been serving mankind for more than two millennia, 1 with some examples shown in Figure 1. Phase change is essential to energy applications, where it drastically enhances heat transfer because latent heat is typically much larger than sensible heat. 2 For instance, the latent heat needed to boil one gram of water (h=2260 J g -1 ) is more than 100 times larger than the heat required to increase the temperature of the same amount of water by 5K (c p T = 21 J g -1 ). In addition, phase change is frequently accompanied by fast and large changes in specific volume, which result in enhanced heat transfer due to convection.  Figures (a, b, c) reprinted with respective permissions of ASME, by courtesy of the Getty's Open Content Program, and with the permission of the Taylor and Francis Group.
Three phase-change processes with industrial relevance are considered in a synthetic manner: boiling, condensation and ice/frost formation. After a presentation of how to characterize phase change, the properties of an optimum surface for each of these three modes of phase change is described; then the fabrication/manufacturing techniques available to modify surface texture and chemistry are described; next, the ways that these techniques have been used to date to enhance phase change heat transfer are reviewed. An emphasis is placed on the fast-developing area of wettability engineering, which relies on manipulating both surface texture and chemistry using special features, such as advanced materials. Then, an assessment is given on the prospective energetic, economic and environmental benefits of advanced surface engineering for phase change heat transfer. Finally, several research needs and priorities are identified and outlined, towards the goal of engineering optimum surfaces for phase change heat transfer.
The review also aims at bridging the gap between the materials and heat transfer communities towards achieving the common goal of designing and deploying optimum material systems to enhance heat transfer performance and minimize thermodynamic inefficiencies, towards more sustainable energy transmission and production.

Characterization of phase change heat transfer
As mentioned in the introduction, the amount of heat exchanged during phase change heat transfer is very high. Therefore, phase change heat transfer is needed in many industrial applications 5 , such as during thermal generation of electricity, desalination, metallurgy, electronics cooling and food processing.
Industrial applications with phase change typically use water-based fluids or refrigerants, depending on considerations of the amount of heat to be transferred, operating conditions, and interactions of the fluid with electronic components 6 . Figure 2 describes and compares the three phase change processes considered in this review, according to their physical mechanisms, time scales and length scales. Boiling, condensation, and frost formation are each multiphase and quasi-steady processes, as shown with arrows arranged in circles. For instance, nucleate boiling involves the temporal sequence of nucleation, bubble growth and detachment, and a similar cycle is observed for condensation and freezing, as described in the caption of Figure 2. As will be demonstrated later in section 1, these quasi-steady processes exchange heat optimally when the solid surface is in contact with both the discrete and continuous phase, e.g. the respective vapor and liquid in the case of nucleate boiling. However, phase change processes can experience instability towards a steady state of lower thermodynamic efficiency. After this transition, shown with an upward arrow in Figure 2, the solid surface is in contact with only one fluid phase, e.g.
with vapor in film boiling. In fact, the art of designing optimum surfaces for phase change heat transfer relies on keeping the solid surfaces in contact with both the continuous and discrete fluid phases, for the sake of optimum thermodynamic performance.  [14][15][16][17] or frost formation 18,19 . The quasi-steady mode is represented with circular arrows; it is most efficient thermodynamically and the time and length scales are mentioned. In boiling, it involves the succession of bubble nucleation (a), growth (b), and detachment (c). In condensation, it involves the succession of drop nucleation (a), growth (b), coalescence (c), and detachment (d). In desublimation or atmospheric frost growth, it involves crystal growth (a), layer growth (b), then dendrite or bulk growth (c), and removal by external forces, like scraping (d). When phase change occurs faster than the removal of the discrete phase, instability occurs and the process transitions towards a single-phase mode which is thermodynamically less efficient. Photograph of the boiling process is reprinted from 11 , copyright 2012, with permission from Elsevier. Photograph of the condensation process is reprinted with permission from 16  A traditional description of these phase change processes is given with the phase diagram in Figure 3. The diagram also describes the terminology used in this review: Boiling (liquid to vapor phase change); condensation (vapor to liquid); sublimation (solid to vapor); desublimation (vapor to solid), also known as atmospheric deposition. The term frosting can also be used for the vapor to solid phase change. However, frosting may also describe the transition from vapor to solid via the liquid phase; melting (solid to liquid); solidification or freezing (liquid to solid); icing describes the transformation of water to ice. Thermodynamically, a first measure of phase change heat transfer performance is the maximum heat flux exchanged between a solid surface and the fluid. For a boiling fluid, the critical heat flux (CHF) is the highest heat flux that can be exchanged, before the individual vapor bubbles merge into a vapor layer that insulates the surface from the liquid. Optimizing CHF can be seen as optimizing the heat transport, in the sense implied by the first principle of thermodynamics.
A second measure of performance of phase change heat transfer is the heat transfer coefficient HTC=q''/the ratio of the heat flux q'' to the difference between the solid surface temperature and the temperature of the fluid. HTCs are a measure of thermodynamic efficiency of heat transport, in the meaning of the second law. HTCs associated with phase change are typically one to two orders of magnitude larger than HTCs in single phase, because the latent heat minimizes .
The characteristics of a solid surface that maximize HTC depend on the fluid and the . The largest HTCs are typically achieved in regimes where both the continuous and discrete phases are in contact with the solid surface, such as the nucleate boiling regime or the analogous regime of dropwise condensation 21 . In these regimes, the solid surface interacts with multiple liquid and vapor volumes, maximizing interfacial and convective transport. For that reason, wettability engineering could play a critical role to improve phase change heat transfer.
If q'' is increased beyond CHF, the HTC is drastically reduced because heat is no longer transferred convectively but radiatively. This causes a significant and often destructive surface temperature increase [22][23][24] , called dry-out and recently seen in Fukushima, Japan 25 . Similar considerations can be made for condensation, where the transition from dropwise condensation to film condensation drastically reduces HTC.
An optimum surface for phase change heat transfer is therefore a surface that optimizes heat transport according to the first and second principles of thermodynamics.
Phase change heat transfer is difficult to model or investigate experimentally, because it is a transient and multiscale phenomenon involving dynamic motion of multiple interfaces. The inherent complexity of phase change heat transfer appears in Table 1, which lists the forces and mechanisms governing the associated transport of heat and mass. Traditionally, the relative importance of pairs of forces or mechanisms is expressed with dimensionless numbers. Heat and mass transport is characterized with the Fourier, Biot, Nusselt and Jakob numbers. Fluid flow is characterized with the Reynolds, Bond, Weber, Froude, capillary, and Galilei numbers, as well as the drag coefficient. The relative importance of fluid flow transport -as compared with heat and mass transport-is expressed in terms of the Prandtl, Schmidt, Grashof and Eckert numbers. The influence of geometric/physical properties is expressed with numbers such as void fraction, wetting angle, density ratio, viscosity ratio and surface roughness. This extraordinary large quantity of twenty dimensionless numbers suggests that phase change heat transfer cannot be described with general theories, and that full similarity is impossible to obtain in experimental studies 26 .  Finally, let us consider how the development of micro-and nanotechnologies has impacted phase change heat transfer over the last 40 years. Drastic improvements have been made in implementing phase change heat transfer solutions closer to the heat source 6 , as in electronics packaging. However, has the development of micro-and nanotechnologies improved the primary performance of surfaces for phase change heat transfer, such as the CHF and HTC? Figure 4 shows that, for the widely-studied process of water boiling on a copper surface, HTCs and CHFs have respectively increased by a factor 2 and 3 over the last 40 years. These improvements are significant; however several other technologies, such as computing power or energy density in batteries, have improved their performance by orders of magnitude over the same 40 years. Also, the theoretical limits of these improvements are either largely unknown or much higher, as exemplified by the "kinetic limit" obtained using the kinetic theory for the maximum heat flux. This limit can be reached if all molecules are emitted at the speed of sound from the liquidvapor interface. As established by Schrage 27 , for water at atmospheric pressure, the kinetic limit 4 ,

Boiling
with c the speed of sound, is plotted in red in Figure 4. In that context, it seems worthy to review the fundamental mechanisms that govern phase change heat transfer, and new ways of engineering surfaces to enhance these mechanisms with the ultimate goal to raise the practically attained performance closer to theoretical limits.

Characteristics of optimum surfaces for boiling heat transfer
Boiling is a multiphase and multiscale energy transfer process from a heated surface to a liquid resulting in its vigorous vaporization. The first boiling curves, relating the heat flux to the superheat of a solid surface, were measured by Nukiyama 39 . Applications of boiling vary, but in general, surfaces can be engineered to facilitate nucleation or maximizing the critical heat flux by preventing film boiling 27,[40][41][42][43][44][45][46][47][48][49][50][51] .
Let us describe here the physical aspects of the nucleation process, nucleate boiling and CHF, with emphasis on the contributions of the solid-fluid interface.
As a starting point, we summarize the thermodynamic processes of vapor formation in boiling, based on the extensive descriptions in 5,52 . In Figure 3, the solid line corresponds to the co-existence or binodal curve, where liquid and vapor can both exist in a stable state. Metastable states can also exist in the vicinity of the binodal curve. For instance, point A is a metastable liquid state, B a metastable vapor state.
Technically, boiling refers to the phase change of a metastable liquid (A) to a stable vapor phase (C).

Nucleation
Nucleation can occur at a solid surface, or within the bulk of the metastable liquid; the former process is called "heterogeneous nucleation," while the latter is called "homogeneous nucleation." Equilibrium thermodynamics can be used to predict the conditions for the incipience of boiling, i.e. the generation of an enough stable vapor nucleus. For a closed system at thermodynamic equilibrium, constant pressure and temperature, boiling occurs under conditions of thermal, mechanical and chemical equilibrium 52 . The thermal equilibrium means that the temperature of the vapor phase and liquid phase are equal. The radius r * of a vapor nucleus in mechanical equilibrium with the surrounding liquid is given by the Young-Laplace equation: (1) In engineering systems, the requirement of chemical equilibrium corresponds to p V ≈ p sat , i.e. p C ≈ p E (in Figure 3 for a pure liquid). Thus, boiling involves the phase change of a metastable liquid at a pressure lower than the saturated pressure (point A at T L and p L in Figure 3) into a stable vapor phase (point C, usually approximated by E at T L and p sat >p L ).
The superheat temperature ΔT=T L -T sat required for the nucleus to grow spontaneously is obtained from the pressure difference in eq. (1) , using a linear approximation of the P-T saturation curve 52 as ( The incipience of boiling can be determined by considering the evolution of vapor nuclei. Nuclei occur naturally in the bulk liquid by density fluctuations, and may either collapse or grow depending on their Gibbs free energy 5 The Gibbs free energy corresponds to the thermodynamic work required for the creation of a nucleus with radius r in the bulk fluid. By the second principle of thermodynamics, the nuclei that will grow spontaneously are the ones with (3), G hom is maximum at r*, and only the nuclei with r>r* will grow spontaneously 53 . In engineering systems, the incipience of boiling corresponds to the production of stable vapor nuclei at a rate J of [10 3 -10 7 ] cm -3 s -1 , with J depending 5 exponentially on the ratio of the free energy of the equilibrium vapor nucleus, over the Boltzmann constant k B times the system temperature: with C being a function of the liquid properties. For water at atmospheric pressure, a nucleation rate J = 10 7 cm -3 s -1 corresponds to a superheat temperature equal to 204°C, a pressure difference larger than 8atm, and vapor nuclei with sizes O(30nm). These temperature and pressure values are much larger than experimental values on technical surfaces, where the onset of nucleate boiling typically occurs at a superheat of 6-10°C 54, 55 . Homogeneous nucleation appears therefore to play a weak role in technical boiling.
Indeed, it is commonly assumed that the solid-fluid interface facilitates the nucleation process. This 'heterogeneous nucleation' process is described, for atomically smooth surfaces, by a reduction of the free energy when nuclei are created on a surface 56 : Here,  is the wetting angle, as defined in section 2.5, and heterogeneous nucleation is observed for J=O(10 10 m -2 s -1 ) 52 . For superhydrophobic surfaces,  tends exponentially toward 0 so that nucleation occurs at negligible superheat; for metallic surfaces with ≈30°,  tends toward 1, negating the thermodynamic advantage of nucleating on a surface rather than in the bulk. In fact, the superheat estimated using the above two equations (ΔT≈188°C for smooth Teflon with  =120°, or 211°C for smooth metal with  =30 o ) is again much higher than the 6-10°C superheat observed with water on real surfaces.
In fact, surfaces typically facilitate nucleation because of their natural pits and cavities. Gas or vapor entrapped in these geometries enhances the process of heterogeneous nucleation. Rigorous analysis of how a complex geometry enhances nucleation is possible and presented in section 3.1, it is however a challenging task given the inherent randomness in surface texture and chemistry. As a result, experiments are typically conducted to measure the rate of nucleation or the spatial density of active nucleation sites n. n as a function of T for a wide range of wetting angles (Figure 5a). They found that nucleation occurred on a superhydrophobic surface at superheats that were two orders of magnitude lower than those on a smooth hydrophilic surface. For real surfaces, a general trend similar to the one obtained on ideal surfaces is illustrated in Figure 5a: the lower the surface wettability, the lower superheat needed for nucleation.

Nucleate boiling
At higher superheat, sufficient to sustain the quasi-steady regime of nucleate boiling (see Most models of nucleate pool boiling describe the heat flux as a power law of the superheat ΔT and the density of active nucleation sites n 52 : When the heat flux increases, transition from nucleate to film boiling occurs, and radiative heat transport becomes the dominant transport mechanism. The CHF is the maximum heat flux reached at this transition, and its mechanism has been considerably investigated because of its industrial relevance 67 where C L is a constant equal to 0.149 68 48 suggests that "CHF is controlled by the microhydrodynamics and rupture of an extended liquid microlayer, sitting and vaporizing autonomously on the heater surface," a process which is influenced by surface wettability.
From this body of experiments and theories, a dilemma appears given the above considerations on nucleation and critical heat flux. On the one hand, HTCs at low heat flux are enhanced on surfaces with low wettability. On the other hand, HTCs at high heat fluxes are enhanced on surfaces with high wettability, and so is the CHF.

Characteristics of optimum surfaces for condensation heat transfer
Like boiling, condensation is a multiscale and multiphase phenomenon. In technical applications, condensation refers to the phase change of a metastable vapor (point B in Figure 3) into a stable liquid (D).
Condensation has been studied on typical engineering geometries, along plates and channels, or inside channels as reviewed in 73 . For the sake of simplicity, this review is focused on external condensation, which may occur either as a liquid film or in the form of individual drops, see Table 1. Dropwise condensation (DwC) is facilitated for fluids with high surface tension or on low-energy surfaces 74 , and occurs via the quasi-steady process described in Figure 2. For many engineering applications, the condensate is water which tends to wet metal surfaces, and the condensing droplets eventually end up forming a film on the surface, leading to film condensation (FC). By its geometry and multiphase structure, DwC is a process analog to convective boiling. DwC typically occurs in dehumidification or ammonia-based processes, while FC is prevalent in most other technical applications.
When the affinity between the condensing liquid and the solid surface is high, droplets of condensate nucleate on myriads of nucleation sites (nanoscale surface defects) on the cooled substrate. The droplets grow by sustained condensation caused by continuous cooling; droplet growth also occurs by impact and coalescence during the sliding of drops caused by gravity or by coalescence induced by droplet growth 75 .
Heat transfer takes place from the gas phase to the substrate through the condensing droplets (except on areas that are not covered with droplets, where the heat transfer is direct). In DwC, progressive coalescence exposes new domains on the substrate for fresh nucleation and growth. DwC has received much attention from the heat transfer community due to its potential to produce heat transfer coefficients (HTC) that are an order of magnitude larger than in the film condensation mode 76 . Despite the initial promise for high performance, and extensive research over several decades -barring a hiatus in the '90sachievement of sustained DwC has remained elusive till this date. The DwC process, its performance and technical applications have been extensively reviewed in 74 , which also describes a theoretical prediction of the HTC. Several groups have made notable contributions to the theoretical and experimental characterization of DwC and the pertinent heat transfer correlations since its first report 77 .
The mechanism responsible for DwC is subject to debate 52 , be it either drops nucleating and growing on a dry surface 78 , or drops resulting from the breakup of an unstable thin film 79 The factor  in Eq. (8)) is the analog to that in Eq. (5), and Eq. (8) implies the exact opposite trend as in boiling, that is, heterogeneous nucleation in condensation is easier on a hydrophilic surface rather than on a hydrophobic one.
Theoretical models [80][81][82] to predict DwC heat transfer rates typically consider the heat transfer across a single hemispherical condensing droplet as shown in Figure 6a Resistances to DwC heat transfer are due to thermal conduction (R liq ) through the liquid drop and mass transfer at the liquid-vapor interface (R int ) 52 . The substrate thermal resistance (R sub ) may also play a role due to droplet recalescence, i.e., the rejection of the latent heat of condensation 83 . On an actual condensing substrate, droplets of different sizes co-exist: the ratio of the largest drops (~1mm) to the smallest drops (1nm) being typically 10 6 . For inclined surfaces, the largest size r max at which the droplet slides by gravity is found to increase with increasing liquid surface tension and contact angle hysteresis, and decreases with increasing equilibrium contact angle and tilt angle 84 .
The determination of the overall condensation heat transfer coefficient across the condenser surface requires integrating the heat flux at each droplet base (as obtained from the thermal resistance model described in Figure 6a over the entire spectrum of droplet sizes (r min < r <r max ) and estimating the driving Measurements show that the drop-size distribution follows a statistically time-invariant pattern. For smaller droplets with r min < r < r E , where r E = (4n) -1/2 with the nucleation site density n on the order of 10 13 to 10 15 m -2 85 , the distribution of drop sizes can be obtained from a population balance 86 . For larger droplets with r E < r <r max , the fractional surface area covered by a droplet with base radius greater than r follows the distribution in 75,86,87 . Substantial effort has been expended in numerical simulations of droplet nucleation 88 and drop growth and coalescence 87 .
Besides the thermophysical properties of the fluid and the solid substrate, the HTC in DwC also depend on other key parameters like degree of subcooling, heat flux, maximum droplet radius, presence of noncondensable gases, and gas phase pressure. The HTC increases with the degree of subcooling or the surface heat flux due to enhanced creation of active nucleation sites 89 . The droplet size also has an impact on HTC. Bonner 90 showed that for droplet radii less than a few hundred nanometers, the overall heat transfer is limited by R int , while for larger droplets, the influence of R liq dominates (see Figure 6b).
Effective DwC technologies, therefore, should typically aim at removing the droplets from the surface before they grow too large, preferably at an order of magnitude lower than the capillary length of the liquid 14 . Interestingly, the HTC is severely reduced in the presence of even minute amounts of a noncondensable gas 74,91 : HTCs are reduced by up to 30% for DwC 92 and 50% for FC 93 with a concentration of noncondensable gas of 0.5% by volume. This illustrates that noncondensable gases influence the nucleation process in condensation, as they also do in boiling. Besides, the presence of air adds a diffusion resistance (R bl ) to steam-air boundary layers 93 (see Figure 6a) and alters the relative contribution of latent and sensible heat transfer 92 . Most importantly, several industrial applications involve condensation of binary fluids, where Marangoni stresses promote similar structures to dropwise condensation 94,95 . Vapor-side pressure influences the HTC primarily through the R int . Tanasawa 96 reported that for water vapor DwC, the interface heat transfer coefficient varied from 0.383 MWm -2 K -1 at 0.01 atm to 15.7 MW m -2 K -1 at 1 atm. Forces responsible for the removal of the condensate are different in nature and weaker in condensation than in boiling, see Table 1. This removal typically occurs by shear or gravity forces; rather than shear and buoyancy in boiling. The transition from drop-to film-wise condensation, schematically shown in Figure 2, is a process similar to the boiling transition from nucleate to film boiling, and similarly, it is poorly understood. A typical value of the peak heat flux corresponding to that transition for steam is 10MW m -2 , as reported in 74 . At least two transition mechanisms have been proposed for the transition from DwC to FC 74 : (1) under high heat flux, the droplet growth rate exceeds the condensate removal rate, leading to increased coverage of condenser surface area by the condensate and merging; or (2) the density of active nucleation sites increases with increasing T, leading to a situation where condensates from neighboring active nucleation sites merge into a wetted patch.
Nusselt provided a simple model for HTC in film condensation, assuming laminar flow, pure vapor and negligible convection 97 with L,  L and k L standing, respectively, for the length of a vertical plate, viscosity of the liquid, and thermal conductivity of the liquid. Later, Rohsenow 98 included thermal advection effects with a latent heat term that depends on the Jakob number.
To summarize, the salient issues specific to condensation on solid substrates are (i) the design of substrates that promote heterogeneous nucleation, (ii) the efficient drainage of the film or the evacuation (removal) of the drops from the condensing surface. The first factor bears a direct influence of the surface wettability, while the second depends both on the condensing surface and the acting physical forces.

Characteristics of optimum surfaces for freezing and desublimation
As per the definitions related to Figure 3 and Table 1, there are at least eight terms describing phase change from or towards the solid phase. Solidification (freezing) commonly occurs in technological processes, such as free-form manufacturing, rapid prototyping, metals processing, microelectronic fabrication, etc. Despite the large number of technologically relevant fluids that can undergo solidification, for the sake of simplicity, this section concentrates only on aqueous systems.
During the densification and bulk-growth phase, the frost thickness and density increase, resulting in significantly lower thermal conductivity and reduced heat transfer, see Figure 7a. Eventually, the frost thickness reaches a maximum, as shown in Figure 2; the temperature of the frost surface is no longer cold enough to promote further frost growth, and an equilibrium heat flux is reached 99

Freezing/Icing
The formation of ice from a metastable supercooled liquid occurs via ice nuclei, i.e. tiny transient crystalline clusters existing in various sizes within the water phase. Continuous size fluctuations of these clusters occur due to the simultaneous addition of molecules and detachment of the same. Based upon the various thermodynamic parameters, the nucleus size may grow large enough to become stable, i.e. for growth to become more probable than decay. This designates the critical size for stability, and hence further nucleation of the solid phase. Stability of ice nuclei mainly depends upon their surface-to-volume ratio. As the size of the ice phase increases, this ratio decreases, thus making the number of molecules returning to the liquid from the ice surface far less significant compared to the number of interior molecules, hence establishing stability of the nucleus and facilitating growth. Nucleation of this type is known as homogeneous nucleation. There exists another type of nucleation where the nucleus forms on some pre-existing solid structure, thus making the stability of the nucleus more probable. This type of nucleation is known as heterogeneous nucleation and is far more common than homogeneous nucleation due to its smaller free energy barrier, as described in section 1.1. Hence, heterogeneous nucleation is sought for technical applications; it is also similar to the nucleation process discussed in the condensation section. As seen from Eq. (8), which also applies here, increasing the contact angle delays condensation, and thus ice formation 104-110 . In fact, since high contact angles decrease the contact area between the water and the cold surface, if the pressure is high enough to condense first and then freeze water, the decreased contact area will slow heat transfer and delay freezing time 105 . Additionally, low energy surfaces usually have low adhesion to water and ice 105 ; coupled with engineered forced convection, these surfaces efficiently prevent ice buildup.
In addition to ice formation within the liquid water phase, ice can also form on a solid surface directly from the vapor state; this phenomenon is known as desublimation, atmospheric deposition. The term frosting is ambiguous (see section 1) and will not be used here.

Desublimation/Frosting
Frost is formed when humid air comes in contact with a solid surface at a temperature below the freezing temperature of water. Frost can form either by condensing then freezing or directly through solid deposition 104 . In the former, frost formation has two distinct phases, similarly to the condensation process: nucleation and growth. Before frost forms, the heat transfer is dominated by single phase convection. At the onset of nucleation, heat transfer is dominated by multiphase convection. In frosting, nucleation depends on surface structure and the availability of nucleation sites.
Several studies have been conducted on the ice/frost repellency of superhydrophobic surfaces 20,105,110 .
However, due to the increased surface area and roughness, some superhydrophobic surfaces have shown increased frost nucleation compared to smooth hydrophobic surfaces 105,108 . Other research has also shown that a low contact angle hysteresis prevents frost nucleation 111 . Kim et al. 111 studied liquidinfused porous surfaces, which provide a defect-free molecularly flat liquid interface, while maintaining a high contact angle. The lowest rates of frosting were observed on surfaces that had both a high contact angle and low contact angle hysteresis.
After nucleation and cooling, frost goes through two distinct growth phases, see Figure 7b. First, the frost goes through the solidification and tip growth stage, with conduction and multiphase convection dominating the heat transfer. Then, during the densification and bulk-growth stage, the temperature increases at the interface between the frost and the atmosphere and the frost layer eventually reaches an equilibrium thickness and temperature with the environment. During this period, the heat transfer is dominated by conduction. The final frost thickness depends on the surface temperature and relative humidity. The thermal conductivity of the surface has been shown to affect frost growth 112 . On low thermal conductivity surfaces, a supercooled mm-sized droplet freezes slowly, with evaporation triggered by the latent heat released upon recalescent freezing. Eventually, the gas volume around the droplet reaches saturation and vapor microdroplets coalesce to form smaller droplets that deposit around the droplet, eventually crystallizing and forming a frost halo. Experiments in 112 under controlled humidity conditions establish how a balance between heat diffusion and vapor transport determines the final expansion of the frozen condensate halo, which, in turn, controls frost formation and propagation.
The surface energy may also influence the frost growth and density 109 . Once a thin layer of frost is deposited, the surface energy of the base surface should no longer affect the growth of subsequent frost 107,113 . However, the surface energy influences the initial shape of the crystal, therefore modifying the kinetics and changing the dendritic frost growth patterns 109,114,115 . Experimental evidence suggests that hydrophilic surfaces produce a higher density frost 114 , while hydrophobic surfaces form more dendrites creating a looser frost structure 114 .
In summary, surfaces with low wettability prevent, delay or slow down the formation of ice from a metastable, supercooled liquid. The role of roughness on frost formation is not clear at present. Also, the more wettable the surface, the denser the frost layer.

State of the art methods for micro-and nanofabrication of surfaces
Several approaches and numerous techniques are available to fabricate the surfaces of interest for phase change heat transfer. The phase change on a solid surface is affected by the energy and texture of the surface. The surface energy is of chemical nature but manifests itself physically as a contact angle. Aside from some practical issues, such as changes over time and temperature, the surface energy is a relatively simple parameter as it is inherent to each material. The surface texture, on the other hand, is geometric in nature and can have many variables, such as pitch (periodicity), spacing, depth, shape, and randomness.
Another important variation for phase change heat transfer is the local control of the surface energy and texture, i.e., a surface can juxtapose regions with different chemistries and textures. These infinite possibilities of multiscale spatial arrangements leave ample room for heat transfer enhancement. Here we discuss the fabrication methods used to control the energy and texture of surfaces for phase change heat transfer.

Surface machining and roughening
Compared with a smooth surface, a roughened surface enhances the phase change heat transfer by increasing the net contact area for heat transfer and the number of nucleation or precipitation sites 116 . To roughen the surface, various mechanical methods have been used, such as sandpapering and abrasive blasting 117 . The surface structures obtained are relatively simple, i.e., consisting essentially of low peaks and valleys, and randomly distributed. Conventional machining has also been used to obtain more elaborate surface structures aimed specifically to enhance nucleate boiling, e.g., Figure 8a. These surface structures show a regular pattern due to the sequential nature of the sharp-tip machining processes.
Chemical and electrochemical methods can produce more pronounced and complex structures, such as porous surfaces, e.g., Figure 8b. The surface structures are randomly distributed, but the roughness parameters (e.g., average pitch, porosity) can be controlled by the processing conditions, such as etchant chemistry, etching time, and current density. The roughening processes are suitable for large area and mass manufacturing, while the machining processes are less economical. Because of their high thermal conductivity, metallic surfaces are preferable for phase change heat transfer.

Surface coating
The surface textures can be added on the base surface by coating. Compared with the subtractive methods of the previous section, the coated textures can be more complex in geometry and more versatile in material selection. The texture can be as complex as a three-dimensional porous network, and the material can be a metal, ceramic, polymer, or a combination of them. The coating methods are numerous, including sintering, spray coating, dip coating, plasma coating, electroplating, and gluing, just to name a few. For metal oxides, Zhou et al. 119  developed a method to glue dispersed particles into highly porous structures, as depicted in Figure 9c.
Because a polymeric material glues the particles together, a wide range of materials can be used as the constituent particles. The resulting porous surface was used to enhance boiling heat transfer for cooling electronics by immersion. The surface structures made with coating techniques tend to be complex and randomly distributed in size and shape. The size of the structures and the thickness of the coating can vary from a few nanometers to hundreds of micrometers.

Lithographic fabrication
In contrast to the surface roughening and coating processes, which produce mostly a random distribution of certain surface structures and sizes, lithographic processes can produce surface textures of exact shapes and sizes. The lithographic patterns can be at the micrometer scale using standard photolithography or at the nanometer scale using electron-beam lithography. There are other related fabrication methods, such as interference lithography, but they usually have additional limitations. The patterns may be formed by a lithographic process of photoresist coated on the surface or by direct printing using the so-called soft lithography. Using the well-defined patterns as an etching mask, the substrate is carved out by various sophisticated etching processes to create surface textures with depths or heights up to hundreds of micrometer. The etching is usually not performed after soft lithography, which is most convenient when the surface texture is merely a pattern of a thin layer including a chemical coating. Requiring a clean room and expensive equipment, lithographic fabrication is not suitable for large-area applications.
However, it provides a unique capability to study the phase change on textured surfaces with sizes and

Multiscale surface textures
Surface textures featuring multiple length scales are called multiscale or hierarchical textures 130  As a summary, Table 2 reviews all the processing methods by category and mentions the distribution, size and shape of the patterns as well as the suitable material and scale of application.

Wettability engineering
Wettability describes the spreading of a liquid on a surface. Wettability engineering is important in e.g.
the automotive industry for repelling water from windshields or paints 136 , preventing fouling 137 and reducing friction in moving parts 138 ; in the marine industry to prevent fouling 139 ; in the electric power industry to prevent fouling on solar cells 140 ; in biology to prevent bacterial contamination 141,142 , and in the electronic 143 and chemical industries 144 .
The wettability of a surface can be modified by engineering its texture and (or) its chemistry. A first characterization of wettability is the static wetting of liquid droplets on flat substrates 145, 146 147 . Figure 11 shows the possible wetting regimes of sessile droplets on a substrate, where θ E is Young's contact angle, and the spreading parameter S is defined as where σ SV , σ SL , and σ LV are the surface tension at the solid/vapor, solid/liquid, and liquid/vapor interfaces, respectively 146 . When S > 0, a liquid droplet will completely (or perfectly) wet the substrate (i.e., θ E =0°) to form a liquid film with nanoscale thickness. This property is typically obtained on surfaces that have high values of σ SV (≈500-5,000 mN m -1 ), e.g., metals 146 . When S < 0, a liquid droplet will partially wet the substrate forming a non-zero contact angle (i.e., θ E > 0°). When θ E ≤ 90° a substrate is called wetting or-in the special case of water -hydrophilic. When θ E > 90° a substrate is called non-wetting or -in the special case of water -hydrophobic. This hydrophobic regime is usually observed on substrates which have lower values of σ SV (σ SV ≈10-50 mN m -1 ), e.g., plastics 146 . By balancing the horizontal projections of capillary forces at the triple contact line, Young 148 and Dupré thereafter 149 obtained From Eq. (11), θ E is a function of the liquid, solid and vapor properties, so that a surface which is nonwetting to a liquid may be wetting to another.
Thereafter, Wenzel 150 and Cassie and Baxter 151 described how surface texture influences wettability, see with r being the roughness, defined as the ratio of the true surface area to the projected surface area. For the hydrophobic case (θ E > 90°), the Cassie-Baxter case is preferred to the Wenzel state if  E is smaller than a critical angle  C , with where Φ S is the solid-liquid fractional surface area, and the value of the apparent Cassie-Baxter contact angle is 146 For the hydrophilic case (θ E ≤ 90°), the Cassie-Baxter case is preferred to the Wenzel state if , and the value of the apparent Cassie-Baxter contact angle is For hydrophobic surfaces, the more enhanced the surface texture is (i.e., high r, low Φ), the lower θ C ; therefore, the Cassie-Baxter wetting state becomes more probable. When a droplet transitions to a Cassie-Baxter state, and θ*>150°, the solid surface is said to be superhydrophobic. In general, roughness tends to  Additionally to these considerations, it is important to add that roughness influences both the static contact angle and the so-called contact angle hysteresis (difference between the advancing and receding values). In the classic experiment of Johnson and Dettre 158 , advancing and receding contact angles were measured as a function of the roughness of a wax sample with constant chemical properties. The main outcome of this experiment was that an increase in the roughness caused an increase of the advancing contact angle and a decrease of the receding angle (increase of the hysteresis angle) until a saturation value. At this point, the hysteresis drastically decreased and the receding angle became closer to the advancing contact angle. Texturing the surface appears consequently as an efficient strategy to change the wetting behavior 146 . It is interesting to note that droplets on superhydrophobic surfaces in the Cassie-Baxter state have a low contact angle hysteresis. In many cases, though not all (see rose petal effect), superhydrophobic surfaces characteristically have low contact angle hysteresis; this leads to drops having low sliding angles and ultimately self-cleaning behavior (sliding angle < 10°; lotus effect). A small hysteresis has been proposed to be a necessary condition to the superhydrophobicity of a surface 147 .
Tilting the surface will result in a rolling motion of the droplet, as shown experimentally 159,160 . The sliding or roll-off angle has significance in condensation processes as it plays a role in removing (also called shedding) droplets of condensate 154 , see section 3.2. Table 3 and the related discussion describe the methods utilized to alter the intrinsic wettability (θ e ) of a surface in a spatially uniform manner (i.e., homogeneous wettability). Surface chemistry (or surface energy) can be modified e.g. by forming oxides on the surface, if hydrophilicity is desired, or by depositing low-surface energy materials (e.g., fluoropolymers, fluorosilanes) if hydrophobicity is desired. Table 3 presents a representative series of coating techniques for modifying the chemistry of a surface. i For hydrophilic oxides (e.g., copper oxide), the chemistry and resulting wettability can be tuned by varying the degree of oxidation of the surface 161 or by UV irradiation 162,163 . For hydrophobic surfaces, the chemistry can be controlled by choosing low-surface energy solid materials. The chemical bonds in low-surface energy solid materials are in order of decreasing surface energy: -CH 2 > -CH 3 > -CF 2 > -CF 2 H > -CF 3 (i.e., CF 3 is the least wettable) 164 . As an example of an original synthesis method for forming a hydrophobic surface, Hummel spray deposited poly(tetrafluoroethylene) on a metallic surface 51 . Phan et al. 165,166 describe specific methods capable of tuning static contact angle values from 22° to 112° as well as their performance under nucleate boiling conditions. An issue with hydrophobic materials is their low thermal conductivity, typical of organic materials. Other approaches to producing hydrophobic surfaces are promoters (i.e., waxes), silanes, fluorinated acids, and self-assembled monolayers (SAMs). i Table 3 is by no means a comprehensive list of coating techniques. References were chosen based upon applicability to phase change heat transfer.   Besides surfaces with spatially homogeneous chemistry and wettability, there are surfaces with wettability contrasts, juxtaposing hydrophobic regions with hydrophilic regions 185 . Such surfaces have an affinity towards both the liquid and vapor phases, a quality that we name biphilic. In nature, the biphilic wings of the Namib desert beetle (Figure 12 optimize its water intake 186 ; while hydrophilic regions of the wing help collect water drops from fog-laden winds, the hydrophobic regions help the drops detach and roll down to the beetle's mouth 187 . In 1965, the first biphilic surfaces by Hummel 51 (see Figure 13), who sprayed hydrophobic polymer drops onto a steel surface, showed a heat transfer coefficient about 2 to 7 times higher than the bare steel surface. The various methods to fabricate surfaces with non-spatially homogeneous wettability, either biphilic or with wettability gradients, are described schematically in Figure 14 and listed in detail in Table 4.  Essentially, most methods for biphilic surfaces can be classified into one (or a combination) of the following three categories (see Figure 14): 1) hydrophobic or hydrophilic domains on a coating with initially homogeneous wettability are achieved by an additive process, such as depositing a polymer coating (additive); 2) hydrophobic or hydrophilic domains are revealed by a subtractive process on a coating with initially homogeneous wettability, e.g., a pristine PTFE coating on a metal substrate is removed at specified areas, by say mechanical or etching methods, to reveal the underlying hydrophilic metallic substrate (subtractive); 3) surface chemistry of an initially homogeneous coating is either chemically degraded (e.g., plasma) or reacts to transform its wettability (e.g., hydrophobic to hydrophilic) usually through exposure to radiation (reactive).   wettability contrast on alloy steels by applying nano-flake or needle patterns of multiscale micro/nanostructured iron-oxides on steel surface and subsequently tuning the surface energy. These surfaces were exposed to water mist, which readily covered the entire hydrophilic patterns, and created droplets with spherical shape on the surrounding superhydrophobic domains. The main advantage of this approach was that it utilized an industrially relevant, thermally conductive substrate, with scalable processing techniques. Betz et al. 58  porous, re-entrant, morphology of the electrospun surfaces led to super-repellency (i.e., high advancing contact angle and low contact angle hysteresis for water and various low-surface tension liquids, such as heptane). When these surfaces were exposed to oxygen plasma, they turned super-wettable (i.e., advancing and receding contact angles near zero for both water and heptane). These surfaces displayed preferential nucleation behavior under boiling and condensation conditions of low-surface tension liquids.

Engineered surfaces for boiling heat transfer
The concept of engineering surfaces to achieve higher performance in boiling dates as far back as 1931 208 . Fundamental studies began to appear in the 1950s 117,209,210 . In the 1960s, fabrication techniques headways allowed a more precise manufacturing of these enhanced geometries, followed by an increasing number of patents 116 . Webb reviews the historical evolution until 2004 of enhanced surfaces for boiling in great details 49,116 , and recent developments have been reviewed by Bergles and Manglik 211 . This section describes the main engineering attempts to produce surfaces with high boiling performance, i.e.
high HTC and CHF. Historically, engineers have first designed surfaces with enhanced nucleation rates and high HTC. A second direction was later taken to increase CHF. More recently, engineers have designed multifunctional surfaces which increase both HTC and CHF. The reliability and repeatability of boiling experiments, crucial for industrial applications, will also be discussed.
Controlling the surface texture to enhance thermodynamic efficiency: An early attempt with enhanced surfaces to improve the HTC is by Jakob and Fritz 208 who roughened copper plates with machined groves of 16μm depths and ½ mm pitch; they observed 3 times improvement in HTC in nucleate boiling. The improvement did not last longer than 3 days, because of a slow degassing of the cavities, a phenomenon explained analytically in 212 . Berenson 50 increased HTC by a factor 6 by roughening metallic surfaces.
Kurihara and Myers 210 showed -on roughened surfaces-that HTC ~ n 1/3 , with n the spatial density of active nucleation sites. Boiling improvements due to surface roughening were seen as of little industrial relevance because of the fast aging of the surfaces. Thus, to better understand and control the influence of surface texture on the nucleation site density in boiling, researchers have focused their efforts on the nucleation process on surfaces with engineered or well characterized cavities.
As shown in section 1.1, heterogeneous nucleation reduces the superheat needed to nucleate, by decreasing the free energy and by providing natural pits and cavities that entrap gas ii or vapor 5,213  As shown in Figure 15, cavities are geometric means to manipulate the curvature of the liquid-vapor interface during the evolution of the volume of the vapor pockets, for the purpose of helping nucleation or preventing extinction or flooding. Geometrically, a cavity is formed when a portion of the horizontal surface enters into the substrate. For a typical cavity, its inner surface enters downward with a slope at an angle between 0° and 90° from the horizontal surface. A conical cavity is a common example. If the slope increases beyond 90°, the inner surface is considered to re-enter outwards from a vertical surface, and the cavity is called a re-entrant cavity. If the slope further increases beyond 180°, the inner surface is considered to re-re-enter upwards from a horizontal surface, and the cavity is called a doubly re-entrant cavity. Note that this definition assumes an axisymmetric or 2D cavity. Physically, a re-entrant cavity is a ii The rest of this discussion neglects the role of gas in cavities, because it is mostly transient and unpredictable, in contrast to the role of vapor cavity for which the curvature of the liquid-vapor interface changes its sign once it penetrates the cavity mouth. During penetration in a doubly re-entrant cavity, the interface curvature reverses twice.
The state of cavities can be predicted from their geometry, the superheat, wettability and surface energies.
Section 1.1 shows that the phase change in boiling occurs when a metastable liquid (point A, Figure 3) becomes stable vapor (point E). According to equation (2), the superheat needed to nucleate from a cavity with mouth radius R is proportional to the maximum curvature 1/r min of the vapor pocket during its growth. Figure 15a shows that the maximum curvature is found at the mouth of the cavity 214 for typical conical cavities with >2where  is the cone angle. This explains why the curvature 1/R, with R the mouth radius, is used to estimate the superheat needed to activate nucleation in the cavity 214 .
Flooding of cavities can also be described from their geometry using the same equation (2). If the fluid-  Rohsenow 221 manufactured doubly reentrant cavities (100-600µm) by drilling and tapering. They found a seven fold enhancement in HTC compared to mirror surfaces. One key issue is to find a practical and economical method to make these cavities at the suitable length scales. Later, Kim 216 investigated analytically and experimentally the relation between geometry and state of re-entrant cavities. He showed that for fully wetting systems, such as the ones involving refrigerants, three parameters determine the cavity state: the superheat, the radius of the neck r neck and the inverted radius of the cavity r inv (see Figure   15b). For a doubly re-entrant cavity, r neck ≤r inv , and an ideal doubly re-entrant cavity has r neck = r inv .
Clusters of points in Figure 15c show the distribution of cavities on a real surface. The T corresponding to the respective activation and extinction of the cavity can be obtained using equation (2), with r* respectively equal to r neck or r inv . It appears from Figure 15c that for fully wetting systems, small cavities are more resistant to flooding than large cavities in case of subcooling, but also require larger superheat to nucleate.
To manufacture re-entrant cavities, two industrially relevant approaches have been developed. The first two types of cavities (Gewa-T, Thermoexcel-E) are fabricated by flattening or bending fin-like protrusions, while the latter (High Flux, [222][223][224] ) are fabricated by sintering metallic particles. These complex surface geometries enhance not only nucleation, but also fluid transport. For instance Chien and Webb studied the interactions of cavities interconnected via pores and channels 49 225 . Their suction evaporation model predicts optimum pore diameter that balance CHF and HTC 49 241 . Figure 16 presents a micrograph of superhydrophilic silicon nanowires which achieved a 100% increase in the CHF value for water, as compared with smooth silicon 232 . Also, Ahn and co-workers 242

Spatial patterning of wettability to improve both HTC and CHF:
The ability to spatially pattern wettability is important to the design of ideal boiling surfaces. As seen in the conclusions of section 1.1, an ideal boiling surface has complex requirements on its wettability: it requires hydrophobicity to promote nucleation and HTC at low heat flux, and hydrophilicity to maintain water transport to the hot surface for preventing early CHF 42 . Therefore, biphilic surfaces, which juxtapose regions of high and low wettability, offer an elegant solution to this dilemma. Measurements have shown that biphilic surfaces significantly enhance the heat transfer performances (HTC and CHF) in pool boiling 43,51 . The enhancement was explained by the efficient management of both the vapor and liquid transport, maximizing nucleation rates and delaying critical heat flux 43 .
The first reports (given in the form of US Patents) of biphilic surfaces come in the late 1960's by Hummel 51 and by Gaertner 189 , see Figure 12. The emphasis is on stabilizing gas and vapor cavities to prevent cavity flooding, that resulted, as an example, in an increase of a factor 5 of the HTC for the biphilic surface compared to clean surface 51 . Betz et al. have shown that biphilic and superbiphilic surfaces (see Figure 18) also act to delay the formation of the vapor film that insulates the surface from the liquid and therefore increase the CHF by 65% as compared with a uniform non-wettable surface 43  Finally, biphilic surfaces have also been manufactured for lower surface tension liquids like methanol 202 .

Engineered surfaces for condensation heat transfer
Theoretical insights of condensation phenomena have been used as an effective tool to engineer condenser surfaces. Early reviews of methods to enhance heat transfer in condensing equipment and technical ways to favor dropwise condensation have been provided by Bergles and Morton 254 and Williams et al. 255 . These involve (a) changes in geometry to either increase surface area and/or help remove the condensate, such as 75  shown that the use of iCVD copolymer thin films grafted to a metal substrate shows more robust (no ageing up to ~ 50 h) hydrophobicity than fluorosilane SAMs and nearly seven times larger heat transfer (HTC ~ 40 kWm -2 K -1 ) for steam condensation than FC. Superhydrophobic coatings typically enhance droplet mobility and induce faster droplet sliding due to the low contact angle hysteresis. This, in turn, augments convective heat transfer between the rolling droplet and the substrate 268 . However, condensate removal on all these monophilic coatings necessarily relies on an external force (e.g., gravity), and therefore has limited effectiveness for smaller droplets or on horizontal static surfaces. Also, homogeneous hydrophobic surfaces have a higher thermodynamic barrier to nucleation (see Eq (8)), compared to hydrophilic surfaces. More advanced features in terms of chemistry and texture of condensing surfaces have therefore been developed in the recent years to overcome these shortcomings.
Effect of surface texture on droplet mobility: Manufacturing surface textures for improving DwC heat transfer has been attempted with mm-size grooves 269  Wenzel state, depending upon whether the equilibrium contact angle (on the smooth surface)  E is, respectively, larger or smaller than a critical angle  C , which is a function of the surface geometry (see Eq. (13) and (14)) 151 , 275 . However, this theory only holds if the drop size is larger than the texturing length scales: water droplets ensuing from condensation on a rough superhydrophobic substrate have been found to behave differently from deposited or impinging droplets 270,274,276,277 . If the minimum droplet size (r min ) is smaller than the length scale of the surface roughness (as in the case of micropatterned surfaces), the initial phase of droplet nucleation and growth does not differ from that on a smooth surface 277 . The nucleation and the early growth of the droplet occurs with the same probability at the base and the tip of the structure. For micro-textured surfaces having  E < C < * , the coalescence of droplets through the formation of liquid bridges gives rise to a metastable Cassie-like state, which finally gives way to a more stable droplet in a Wenzel state that keeps growing in size 277 (the temporal growth of droplet diameter follows D~t 1/3 for the initial phase, until D is smaller than the microstructure length scale, and then a selfsimilar trend of D~t). This apparent loss of hydrophobicity and affinity towards Wenzel wetting has been reported in other studies too 271,274,278 . Although the Wenzel mode of wetting on textured surfaces minimizes the droplet-to-substrate contact thermal resistance, it is detrimental to droplet mobility. Efforts have been devoted to achieve a transition from Wenzel to a Cassie state during droplet growth to enhance droplet mobility. Dorrer and Rühe 156 reported such transitions during condensation on a silicon surface textured with silicon micro-posts and coated with a hydrophobic fluoropolymer ( E ~ 118 o on a smooth surface, which was greater than the  C for the textured surface). They reported that droplets nucleate and grow at the valleys and the tips of the structures and form liquid bridges in the microcavities within the posts during the initial phase. This was akin to the observation of Narhe and Beysens 277 , except that the microdroplets for the case of Dorrer and Rühe 156 grew tall enough to touch the overlying liquid bridges (originating from the coalesced droplets at the tips of the micro-posts) and were drawn up to a more stable Cassie state. It has been demonstrated that for textured condensing surfaces to retain superhydrophobic behavior, topological features of aspect ratio (the height to width ratio of the micro-structures) must be greater than one, and the depth of the separation between the structures must be less than 500 nm 273 . With the advent of nanofabrication, a few recent works have attempted condensation studies on homogeneously textured surfaces having feature size ranging from 100 nm (electrodeposited nanopillars) to 10 µm (microfabricated on Si) 272 , or carpeting with carbon nanotubes 279,280 , which offer promise of improved droplet mobility.  In the case of dropwise condensation, one of the earliest studies utilizing biphilic surfaces was performed by López et al. 190 The sample surfaces juxtaposed hydrophobic (water contact angle 120°) and hydrophilic (CA 30°) domains, and were fabricated by patterning SAMs of different alkanethiolates on gold and of alkyl siloxanes on glass. Water vapor condensation on such cold surfaces was used to visualize their spatial heterogeneity. Biomimetic micropatterning has been attempted by several groups to achieve enhanced DwC on superbiphilic surfaces. These patterns primarily used discrete superhydrophilic spots that exhibit highly enhanced nucleation rate on a superhydrophobic background 201,203 . Garrod et al. 199 investigated the effect of varying the size and pitch of the superhydrophilic spots on condensation rate.
They found that water collection rate and microcondensation efficiency peaked for superhydrophilic spot width and pitch of 500m and 1000m, respectively. The biphilic structures of Thickett et al. 192  However, like in the case of multi-scale textured surfaces, the HTC in DwC of these hybrid surfaces, and their ability to maintain sustained DwC under high heat flux conditions still needs to be quantified.

Engineered surfaces for applications with ice or frost
The technological challenges faced when attempting to avert frosting and icing are both multifaceted and numerous. Thus, engineers have long resorted to combining external means (mechanical, thermal, or chemical) to avoid ice formation/deposition even in the late 20 th century. A passive strategy to achieve this goal includes delaying ice nucleation and the onset of mass solidification. This can be achieved by modifying the chemistry of the surface or its micro-and nanoscale texture. For example, surfaces modified with fluorinated and polysiloxane coatings have low water wettability and surface energy, resulting in icephobic behavior under subzero temperatures 298,299 . However, this approach is limited under many technical circumstances: for example, when a cold surface encounters supercooled water droplets in a humid atmosphere, icing is ultimately inevitable. In this situation, ice adhesion hinders the effort to rid a surface of the ice. As a result, several engineering attempts to prevent ice/frost formation or prolong machinery operation in ice-promoting environments have concentrated on ice/frost delay, ice adhesion reduction or both. An even more severe technical challenge is the design of surfaces that maintain machinery performance in the presence of ice or frost. The density of the ice/frost is a function of temperature, humidity, thermal conductivity and wettability of the surface. Therefore, while it is desirable that a surface delay ice/frost nucleation, if ice/frost cannot be prevented, a surface that produces a dense phase is preferred in refrigeration systems for mitigating the heat transfer reduction due to icing.
The present section describes engineering attempts to produce surfaces that delay ice/frost nucleation and reduce ice adhesion. Studies that focus on ice removal are not within the scope of this review.
Surface chemistry and texture affect ice nucleation: Ice nucleation rates were found to be one order of magnitude higher on smooth hydrophobic surfaces compared to smooth hydrophilic surfaces 300 , where water microdroplets formed on flat, solid surfaces by an evaporation and condensation process. The first study of freezing on textured superhydrophobic surfaces was conducted by Saito and co-workers, and showed less snow accumulation on nanostructured superhydrophobic surfaces than on smooth surfaces 301 . Hydrophobic textured stainless steel surfaces functionalized with polyelectrolyte polymer brushes showed lower freezing temperatures than polished untreated steel for supercooled liquid droplets under slow cooling conditions 302 . Increased freezing delays and lower ice adhesion strength with decreasing contact angle hysteresis were observed by Arianpour et al. 303 , who studied small water droplets cooled on nanostructured composite coatings consisting of vulcanized silicone rubber and various amounts of carbon-black, titania or ceria nanopowders as fillers. A recent condensation-frosting study made on superhydrophobic surfaces with enhanced self-propelled jumping of condensed water microdroplets, showed significant delay in frost initiation even at very low (subzero) temperatures and high degree of supersaturation 304,305 . Another recent study 306 on superhydrophobic surfaces made of zinc oxide nanowires showed significant retardation in frosting as well as considerable delay in freezing of condensed liquid droplets on nanowires with smaller diameters. Condensed droplets on these surfaces were formed at temperatures well below 0°C and showed very high contact angle, even at smaller length scales (~50 µm). The mode of initial condensation also determined the freezing delay. When initial condensation occurred in filmwise mode, the freezing temperature was higher and freezing duration was an order of magnitude lower compared to dropwise condensation in 307 , where nanostructured surfaces consisting of ZnO nanorod arrays were employed in an evaporative closed cell. Sessile water droplets freezing on surfaces with different wettabilities -ranging from superhydrophilic to superhydrophobicwere also studied by Yin et al. 308 under continuous substrate cooling. Ice accretion was tested by spraying supercooled water to samples at different horizontal inclination angles. Their results did not show any correlation of ice formation with surface wettability and revealed the greater role of surface texture in anti-icing performance. On micro/nanotextured superhydrophobic surfaces, the time delay in ice nucleation of sessile droplets was found to be extended, as was the total time of freezing 307,309 .
Controlling ice adhesion with surface hydrophobicity and texture: Several studies on shear force of ice adhesion on multiscale-texture hydrophobic/superhydrophobic surfaces have shown ice adhesion force reduction between a factor of 2 to 6 compared to the respective control surfaces [310][311][312][313][314] . Under axial stresses, the reduction factor was even higher (5-10). 310 Saleema et al. 315 318 extensively studied ice adhesion on many smooth surfaces of representative wettabilities and hysteresis. Their results showed strong relationship between the average ice adhesion strength and the practical work of adhesion, which is a function of receding contact angle on those smooth surfaces. Humid conditions led to higher ice adhesion due to the anchoring effect 319,320 . Studies have been carried out in an attempt to understand the role of surface roughness on ice adhesion using superhydrophobic surfaces. Since the contact area between the ice and the solid on superhydrophobic surfaces is very low (typically less than 5% of the entire surface), such surfaces are expected to feature significantly lower ice adhesion force. Fibrous superhydrophobic surfaces with their increased robustness and resistance to condensation-induced wetting would also seem to be ideal for resisting ice adhesion, assuming they can be made robust enough not to be damaged 320,321 .
Wind turbine blades coated with highly porous superhydrophobic coating made from PTFE showed significant reduction in ice accretion rate 322 . Highly re-entrant surface structures reduce solid liquid contact area, and thus the low heat transfer rate may be responsible for their observed superior anti-frost performance 320 .
Hydrophobicity affects frosting/defrosting: Jing et al. 323   for water at -20°C, r c = 2.2nm), shown in Figure 20a, the freezing delay time is independent of roughness (see 105 ). The classical heterogeneous nucleation theory is shown by the dotted curve in Figure 20a and deviates significantly from the experimental data (symbols). A similar discrepancy was reported by Gorbunov et al. 331 . An extension to the classical theory was formulated in 105 taking into account the reduction in excess entropy of water in the proximity of a surface, as compared to bulk liquid. Figure 20b shows the freezing delay vs. roughness with measured contact angle for the smooth surfaces (average roughness ≤ critical nucleus size). The adjusted model (solid curve in Figure 20b  In the situation of impacting droplets, it seems reasonable to assume that the risk of icing increases with Frosting: Compared to icing, frosting directly from the gas phase (desublimation) onto superhydrophobic surfaces is much more challenging and has not been investigated extensively yet. An initial study 20 in this area indicated that superhydrophobic surfaces retard frosting via metastability of the triple point line 334 .
Other anti-icing surfaces: Besides superhydrophobic surfaces, a new kind of surface, called liquid suffused solid (SLIP) surface, with very low contact angle hysteresis has also been proposed 111 and evaluated to effectively address the issue of icing and frosting. SLIP surfaces also inhibit ice nucleation in supercooled liquid very effectively due to their ultra-smooth texture and high degree of surface homogeneity 335 which act in tandem to lower the temperature for ice nucleation initiation. Though these surfaces have shown promising results, they currently have drawbacks, such as cloaking 336 . The entropy reduction of the crystalline phase near a charged solid surface also influences the heterogeneous nucleation rate of ice at the interface. Recently, zwitter-wettability surfaces (which rapidly absorb molecular water from the environment, but simultaneously appear hydrophobic when probed with water droplets) made from molecular water absorbing polymeric molecules were reported to display frost resisting capability 337 .
Biphilic surfaces: Frosting/icing studies on biphilic surfaces have been almost entirely lacking, and only recently started to appear in the literature. Mishchenko et al. 194 used functionalized, hydrophilic polymers and particles deposited on the tips of superhydrophobic posts to induce precise geometrical control over water condensation and freezing at the micrometer scale. Control of freezing behavior was demonstrated via deposition of ice-nucleating AgI nanoparticles on the tips of these structures. The hydrophilic polymer with AgI particles on the tips was used to achieve templating of ice nucleation at the micrometer scale.
They presented preliminary results indicating that control over ice crystal size, spatial symmetry, and position might be possible with this method.

Technology sustainability: energy, economic and environmental benefits
Advanced surface engineering for phase change heat transfer will impact, among many others, three important industries: (a) manufacturing, (b) electricity generation, and (c) automotive.
Energy savings in manufacturing: Thermal transfer and energy storage processes directly impact chemicals, petroleum refining, as well as the plastic and rubber industries. These industries collectively consume more than 10% of the total energy used in the United States, which represents 97.3 quadrillion Btu in 2011 338 . For comparison, the total energy consumption per capita in Japan represents half that in the USA. For shell-and-tube vapor generators, a 20-50% improvement of global heat transfer coefficient using engineered surfaces would reduce by a corresponding amount the surface areas (and likewise size and material costs) of heat exchangers needed in the chemical and manufacturing industry, and facilitate process integration 339 .
Energy savings in the thermal generation of electricity: Figure 22 shows that electricity production represents more than 40% (40 Quad) of the total energy used in the United States. Electricity is overwhelmingly produced via phase change thermal processes involving devices such as condensers, evaporators, steam turbines. The conversion losses, from heat to electricity, account for more than 25% (25 Quad) of the total US energy consumption. Advanced surface engineering for phase change heat transfer would significantly reduce conversion losses by minimizing exergetic losses 339 . Also, heat exchangers with engineered surfaces for dielectric fluids would improve by about 15% the efficiency of low-T Rankine cycles used in refrigeration, solar power, and air conditioning. Economic and energy impact to the automotive industry: Electric and hybrid vehicles use energy in a more sustainable manner than vehicles with thermal combustion engines. Engineered surfaces for phase change heat transfer will make hybrid and electric drive vehicles more affordable, thereby increasing their market share. It has been estimated that power electronics constitute 40% of the total cost of the traction drive system in hybrid vehicles 340 . Recent work at the US National Renewable Energy Laboratory (NREL) has demonstrated that two-phase immersion cooling systems can significantly improve thermal performance by reducing the total thermal resistance (junction-to-liquid/coolant) of an automotive power electronics module by more than 50%, compared to the conventional single-phase automotive cooling system 341 .
Importantly, micro and nano-engineerd surfaces for phase change heat transfer represent an enhancement process that could be implemented either by retrofitting existing heat exchanger equipment or in manufacturing newer-generation heat exchangers.

Summary and outlook
The present review illustrates the rationale, techniques and challenges of engineering the texture and chemistry of surfaces for phase change heat transfer. While the idea of engineering surfaces for enhancing phase change heat transfer is not new 208 , the degree of sophistication with which surfaces can be engineered today-owing to advances in micro-and nano-fabrication methods over the last two decades-has caused a resurgence of interest in the subject. Examples of the variety of methods available to the "surface engineer" have been presented, and a large choice of modifications of surface energy and textures is possible, from the nanoscale to the centimeter scale.
Based on several examples described in this review, it is the conviction of the authors that optimum surfaces for phase change heat transfer need to address the specificities of phase change heat transfer, in a similar way as a key matches its lock. In that sense, surfaces specifically need to be engineered as:  Possessing multiscale texture, to address the multiple scales of phase change  Featuring non-homogeneous wettability, to address the biphasic nature of phase change  Adaptive, to address the transients and various regimes associated with phase change.
Very recently, several surfaces featuring multiscale textures and spatial variations of wettability have shown improved boiling 38,58 , condensation 288 and frost-avoidance performance 333 . Few surfaces currently possess the ability to adapt their features to the various regimes associated with phase change, but such strategies are feasible (e.g. using either passive thermal sensitive liquid crystal coatings 342 , or magnetophoretic assembly of nanoparticles into nanofins for on-demand hot spot cooling 343 ).
While this review has exposed the related fundamentals and state of the art techniques to fabricate such surfaces, we identify below several remaining challenges important to the design, manufacturing and widespread use of engineered surfaces for phase change heat transfer There is a need for design rules. Phase change heat transfer covers such a wide range of length scales, There is a need for better physical understanding of the physical aspects of phase change. In boiling, the evolution of the microlayer thickness and its contribution to the boiling heat transfer is still poorly quantified 62 and a subject of continued debate 347 . While the influence of wettability (static and dynamic) on nucleation has been studied from the field's inception, its influence on nucleate and critical phase change heat transfer is still an open question. For instance, Dhir et al. 47 state that, "In spite of all the advances in the computational techniques for solving boiling problems, the one variable that has still not been modeled correctly is the contact angle (static or dynamic)." Moreover, a recent report redefines the threshold angle for wettability transition (from wettable to non-wettable), and makes a case for its dependence on surface tension (eg. for hexadecane this transition occurs at 125 o , which is far removed from the 90 o value applying for water). 348 There is also a need to study how surface coatings modify the thermal conductivity of surfaces. The physics behind DwC nucleation and its dependence on wetting are poorly understood, as the temperature difference involved in the process is often in the range of the instrumentation error. In frosting, boiling and condensation there is a strong need for experimental and theoretical studies on the poorly understood transition between the nucleation-driven high HTC phase change heat transfer and the single phase heat transport.
Another challenge is extending the knowledge base and techniques mostly developed for water to technical fluids such as refrigerants, used in the heating, ventilation and air conditioning industries. Due to the very low surface tension of refrigerants, it is difficult to fabricate surfaces that are not wetted by them. A recent investigation of DwC of low surface tension fluids motivates further studies on development of ultra-low-surface-energy modifiers and lubricant-impregnated surfaces compatible to fluorinated refrigerants to achieve a major breakthrough in this area. 349 Also, technical applications call for surfaces that are durable and stable over time. Nanostructures with very small cross-sections are prone to failure under stress as shown in frost formation studies 319,350,351 .
The longevity of a surface enhancement feature is important. Indeed, simple surface enhancements like sandblasting can dissipate "within a day" 49 , mostly because the additional cavities degas slowly, or hydrophobic spots could delaminate. Chemical stability is also a challenge for several superhydrophilic patterning techniques, as is the case with UV-irradiation of TiO 2 containing coatings which revert to their original hydrophobic state when stored 352 . Thermal stability is critical for surfaces for phase change heat transfer. Additionally, micro and nanostructures may exhibit different thermal behavior compared to bulk materials 353 . The resistance to fouling 354 of these surfaces also needs to be investigated. It is difficult to claim a priori that enhanced surfaces are more or less prone to fouling than other enhanced surfaces or flat surfaces. Interestingly, low surface energy has also been shown to reduce and prevent fouling 182 , and nanostructures with pitches and features significantly smaller than the typical size fouling particles have been shown to mitigate fouling [355][356][357] , for both superhydrophobic and superhydrophilic samples 3 .
There are several obstacles that need to be addressed to produce commercially viable surfaces for controlling phase change heat transfer. These issues have been reviewed in 3,49,355,[358][359][360] .