morphology patterned surfaces

Accepted Manuscript Frost Spreading on Microscale Wettability/Morphology Patterned Surfaces Yugang Zhao, Chun Yang PII: DOI: Reference:

S1359-4311(16)33838-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.04.063 ATE 10212

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

2 December 2016 13 April 2017 17 April 2017

Please cite this article as: Y. Zhao, C. Yang, Frost Spreading on Microscale Wettability/Morphology Patterned Surfaces, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.04.063

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Frost Spreading on Microscale Wettability/Morphology Patterned Surfaces Yugang Zhao and Chun Yang* School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 * E-Mail address: [email protected]

Abstract: Frost on a solid surface spreads essentially via building up ice bridges between condensed droplets. Modulation of condensate droplet distributions is thus an effective approach to control frost spreading. Here, we investigate the effects of both surface wettability and morphological patterns on the frost spreading velocity for various substrate surface temperatures. Our experimental results showed that the morphological patterned surfaces drastically retard frost spreading while the effect of the wettability patterned surfaces is not significant. The frost spreading velocity increases with decreasing substrate temperature on the smooth surfaces and the wettability patterned surfaces. The morphology patterned surface effectively resists frost spreading over a wide range of subcooled temperatures. A simple model is proposed to elaborate the effects of wettability, morphology, and temperature on the frost spreading velocity and the model is found to be in reasonable agreement with our experiments. Additionally, microphotography reveals ice bridging regimes in different cases. Our findings facilitate understanding of the frost spreading dynamics which can lead to the novel designs of frost-free surfaces. Keywords: Frost spreading; Morphological patterns; Wettability patterns; Substrate temperature; Ice bridging.

1. Introduction Condensate frosting may be considered as one of the most pervasive types of ice that is associated with numerous industrial applications, such as air conditioning, refrigeration, heat pump, and cryogenics systems [1-4]. Many detrimental effects result from the frost accretion. Particularly, heat exchanger performance in such systems deteriorates drastically due to additional thermal resistance induced by the 1

frost layer [5, 6]. In view of the highly unsteady nature of condensation processes, the droplet interaction mechanisms and ice nucleation mechanisms, condensate frost formation and its dependence on substrate properties, thermal history and other environmental parameters are still not well understood [7, 8]. Thus, effective, efficient solutions are needed to limit condensate frost accretion. Deicing technologies specially designed for solving condensate frosting problems have been studied extensively in the past decade [9-11]. There has been a great deal of research on the study of superhydrophobic surfaces [12-14]. Despite superhydrophobic surfaces being identified by many researchers as potential candidates for icephobic surfaces, contradictory results were been reported with superhydrophobic surfaces not always having good icephobicity [15-17]. Instead, a rational surface design to overcome condensate frosting needs to consider the effects of both wettability and roughness.

Typical condensate frosting on solid surfaces can be conceptually categorized into four sequential stages [18], (i) condensate nucleation, (ii) droplet growth and coalescence, (iii) ice nucleation and spreading, and (iv) the last stage of dendritic frost growth which creates the porous nature of frost layers. Historically, the condensation [19-22] and dendritic frost growth [23, 24] stages have received the most attention with extensive studies to characterize their behaviors and to model their growth. However, the mechanism of frost spreading has remained elusive until very recent works showing that frost spreads via interdroplet freezing propagation waves once ice nucleation is triggered at neighboring edge defects [25, 26]. Since the frost spreads among the condensate droplets, the substrate wettability and/or morphology can be tailored to modulate the size and distribution of the condensate droplets as effective ways to control and thus suppress frost spreading and, thereby, promote the heat transfer. Numerous recent experimental studies have shown that micro/nano engineered substrates can drastically reduce the frost spreading velocity [27-29]. Surfaces are needed to suppress the ice bridging network which is of great importance for frost spreading and determines the characteristics of the resultant frost layer [30-32].

Here, we report a systematic study of frost spreading on various types of substrate surfaces, including a smooth hydrophilic surface, a smooth hydrophobic surface, a surface with wettability patterns, a surface with morphological patterns, and a surface with dual (wettability and morphological) patterns. The frost spreading was investigated on these surfaces for a range of substrate temperatures from -5 oC and -30 oC. Special focus is placed on the relationship between the condensate droplet distribution and the frost spreading velocity. The frost spreading velocity is found to be up to 8 times slower on morphology patterned surfaces than on smooth surfaces due to the confined droplet distribution, while the wettability 2

patterns have little effect on the frost spreading velocity. The results also show that the combined effect of the surface properties and the substrate temperature controls the formation of ice bridges and, thus, the frost spreading velocity. These findings improve our current understanding of frost formation and pave the way for the design of novel anti-frosting surfaces.

2. Experimental 2.1 Surface fabrication and characterization In this work five types of silicon-based surfaces were fabricated using 500 µm thick one-side polished <100> orientation silicon wafers as the substrate base material. The sample surfaces were cleaned following a standard protocol consisting of rinsing with acetone, IPA, and DI water and then drying in dry nitrogen gas flow. All five types of surfaces were cleaned in the same way to ensure that the surface properties were consistent before the next fabrication step. The smooth hydrophilic surfaces (surface_1) were the original silicon wafers cut into 2  2 cm squares with a diamond cutter. The smooth hydrophobic surfaces (surface_2) were created using chemical vapor deposition of a hydrophobic monolayer of Trichloro 1H, 1H, 2H, 2H-perfluorooctyl silane (Sigma-Aldrich). Right before the chemical vapor deposition, an intensified oxygen plasma treatment of 10 mins was applied to facilitate the functionalizing of the hydrophobic groups. Surfaces with wettability patterns (surface_3) were obtained by combining UV photolithography, chemical vapor deposition, and wet etching. An AZ photoresist layer of dense-square-array circular patterns was fabricated on the pre-cleaned silicon wafer. The subsequent chemical vapor deposition of a silane monolayer and wet etching to remove the photoresist residuals made a surface with wettability contrast features of circular hydrophilic areas on the hydrophobic background. Surfaces with morphology patterns (surface_4) were produced using photolithography, deep reactive ion etching of the silicon, wet etching, and chemical vapor deposition. The resultant surface_4 had hydrophobic cylindrical micropillar patterns. The fabrication procedure for the dual surface (wettability and morphology) pattern (surface_5) was similar to that for surface_4, except for reversing the wet etching and chemical vapor deposition sequence. Thus, the resultant surface_5 also had cylindrical micropillar patterns with hydrophilic pillar top surfaces and hydrophobic pillar side and bottom surfaces.

Both of the topographical and wettability features were characterized for the five types of fabricated surfaces. The topographies of the fabricated surfaces were characterized using a field emission scanning 3

electronic microscope (FESEM, JEOL7600). Surfaces_1, 2, and 3 were smooth in submicrometer or even nanometer scales. Surfaces_4 and 5 show no significant difference in roughness, with both having the pre-designed patterns with 50 µm pillar diameter and pitch (edge to edge). Figure 1(a) shows the wellordered cylindrical micropillars on surface_4 and 5. The wettabilities of the fabricated surfaces were characterized by measuring the static contact angle for sessile droplets on the surfaces. A high-resolution optical tensiometer (Attension Theta) was used for the measurements. A 5 µL deionized water droplet was gently put onto the sample substrates with the resultant static contact angles for surfaces_1, 2, 3, 4, and 5 being θ= 67.5 ± 2.2o, 109.2 ± 1.4o, 107.6 ± 1.7, 152.3 ± 5.1o, and 148.6 ± 4.9o, respectively, as shown in Figure 1(b). The macroscopic wettability of the wettability contrast patterned surface was determined by the hydrophobic background as indicated by the contact angle for surface_3. A similar result was seen when comparing surface_4 and 5 with no noticeable difference.

4

Figure 1

Characterization of the five types of fabricated silicon wafer substrate surfaces. a) Schematic

illustration (surfaces_1, 2 and 3) and FESEM snapshots (surfaces 4 and 5). b) Wettability characterization by static contact angle measurements on the surfaces. c) Typical condensate droplet distributions on each surface for a constant substrate temperature of -10oC after cooling for about 100 s. Reference bars in the inserts represent a length of 50 μm.

Figure 2

Schematic diagram of the experimental setup. The substrate temperature was controlled by a dual

stage thermal control unit (the 1st stage was a heat sink with a coolant circulator and the 2nd stage was a Peltier element controlled by LabVIEW data acquisition modules). The chamber was filled with a mixture of water vapor and nitrogen gas with a preset humidity. High-speed microphotography was used to observe the condensation and frost spreading processes. The insert shows a typical frost spreading process captured in the present work with the frost moving inwards from the boundaries.

2.2 Experimental setup A sample substrate was put into a customized cooling system and then thermally bonded onto the Peltier element using thermal paste (Silicone grease, Omega Engineering). The cooling system included a condensate chamber, a temperature control unit and a direct high-speed microscope for visualization as shown in Figure 2. The condensate chamber was enclosed with the side and top surfaces made of acrylic and filled with a mixture of nitrogen gas from a high-pressure gas tank and water vapor from a 5

commercial humidifier. The in-chamber humidity was controlled by adjusting the nitrogen gas and water vapor flowrates. The pressure inside the condensation chamber was balanced with the ambient pressure through a check valve. The thermal control unit contained a heat sink and a Peltier element (Ferrotec, 9500/127/060B) for two-stage control of the substrate temperature. The heat sink was an aluminum block connected to a coolant circulator (JULABO, Bath Fluid Thermal-H5). The Peltier element and the heat sink were bonded together using thermal paste to minimize the thermal contact resistance. Three thermocouples were inserted between the sample substrate and the Peltier element to measure the substrate temperature. The substrate temperature was adjusted by varying the temperature or the flow rate of the coolant circulator and the electrical current to the Peltier element. In each experiment, a constant substrate temperature was maintained by a proportional-integral-derivative (PID) controller using the LabVIEW data acquisition input & output modules (National Instrument, NI 9219 & NI 9264). The condensation and subsequent frost spreading on the substrates were recorded by a high-speed camera (M310, Phantom) connected to a personal computer.

All the experiments were conducted in this chamber with various substrate temperatures (from -5oC to 30oC) while maintaining the same in-chamber temperature of 20  0.2oC and relative humidity of 40  5%. Prior to each experiment, the sample surface was rinsed in deionized water for 1 minute and then dried in a nitrogen gas flow to avoid undesired heterogeneous nucleation on dust particles on the surface.

3. Results 3.1 Heterogeneous condensate droplet distribution Since the frost spreads among the condensate droplets by the building of ice bridge networks, the variation of the condensate droplet distribution is expected to be an effective approach to control the frost spreading velocity. Both the wettability and the surface morphology were varied in the present work where the wettability patterned surfaces provide preferential condensate nucleation sites while the morphology patterned surfaces altered the growth rate of the condensate droplets. According to classical 

nucleation theory, the energy barrier, G , for heterogeneous condensate nucleation is,

G 

6

16 ( Tm )3 f ( ) 3(H v T )2

(1)

where σ is the surface tension of liquid water in air, Tm is the equilibrium dew point, ΔT is the subcooling represented by the temperature difference between the substrate temperature and the equilibrium dew point, ΔHv is the enthalpy change due to the phase change per unit volume and f(θ) is a geometrical factor that is a function of θ, the equilibrium contact angle. Increasing the hydrophobicity increases f(θ) and, 

thus, the energy barrier, G . Condensate nucleation is more likely to occur on hydrophilic regions at a fixed substrate temperature. For the surfaces with wettability patterns (surface_3 and 5), the condensate nuclei first appear on the hydrophilic region and then on the hydrophobic background. For stationary ambient air conditions, the growth rate of the condensed droplets is determined by the water vapor mass diffusion rate in the air which is proportional to the vapor concentration gradient. Hence, for surfaces with morphological patterns (surface_4 and 5), the micro droplets grow faster on the tops of the pillars and slower on the other surfaces.

Representative condensate droplet distributions on the five fabricated surfaces are shown in Figure 1(c) for a condensation duration of 100 s at a substrate temperature T= -10 oC (before ice nucleation occurs). Random distributions of condensate droplets are observed on surface_1 and surface_2 as expected due to the sequential processes of condensate nucleation, droplet growth, and coalescence. The condensate droplets on surface_3 with the wettability pattern have a similar distribution to those on surface_2, with slightly more droplets aligned on the hydrophilic regions. Thus, the background wettability (instead of the hydrophilic regions) mainly determines the final condensation result. The condensate droplets on surface_4 with the morphological pattern accumulate on the pillar tops and the upper portions of the pillar side walls, showing a follower-like structure with a prime central droplet surrounded by a few siding droplets. The condensate droplets on surface_5 with both patterns appear only on the pillar tops (hydrophilic posts) with a patterned distribution of constant sizes and intervals.

3.2 Ice initiation and spreading Ice nucleation occurs on the intentionally fabricated hydrophilic edges of the chip surfaces. These hydrophilic edges together with the cavities along the chip edges further reduce the energy barrier for heterogeneous ice nucleation, so the ice phase always begins from the edges and propagates inwards. As shown in the insert in Figure 2, the observation window is focused adjacent to the chip edge to allow observation of unidirectional frost spreading. A square 1500  1500 μm observation window was set 200 μm from the chip edge to reduce the effect of excess condensation due to geometric singularities. The 7

average frost spreading velocity was obtained by measuring the time taken for the freezing phase front to move across the observation window. Figure 3 shows the effect of the substrate temperature on the ice nucleation time. The ice nucleation time is independent of the surface characteristics and depends only on the substrate temperature in these experiments. The time from when the substrates were loaded onto the cryostage until the emergence of an appreciable ice phase drastically decreases from over 400 s for the highest substrate temperature of -5oC to less than 5 s for the lowest substrate temperature of -30oC. The direct phase change from vapor to ice (i.e. desublimation) was not observed in the present work even for the lowest hydrophilic surface temperatures.

Ice nucleation time (s)

500

Surf_1 Surf_2 Surf_3 Surf_4 Surf_5

400

300

200

100

0 -30

-25

-20

-15

-10

-5

Substrate temperature (oC)

Figure 3

Ice nucleation time (time from when the substrate was loaded onto the cryostage until the

appearance of an appreciable ice phase) as a function of substrate temperature. The error bars were obtained from four independent measurements.

3.3 Frost spreading velocity on various types of surfaces The frost spreading within the selected observation window is shown in Figure 4 for five different surfaces. The ice and water phases have different reflective indexes, so the freezing front can be readily detected. The frost spreading characteristics vary on these surfaces mainly due to the different condensate droplet distributions. The observations show three characteristic frost spreading stages, (i) the emergence of the ice phase within the observation window denoted by time t 0, (ii) the middle stage when the region is partially covered with ice and (iii) the completed stage when the entire region is covered with ice. The left, middle, and right columns represent these three stages for each surface. The frost spreading velocity can be obtained using u  s /  t , where s is the length of the observation window and t is the time taken for the ice phase to pass across the observation window. The frost spreads on the smooth 8

hydrophilic surface (surface_1) with a maximum velocity of 17.5 ± 1.8 μm/s, with the velocity reduced to 11.3 ± 1.5 μm/s on the smooth hydrophobic surface (surface_2). The wettability patterns on surface_3 slightly alter the condensate droplet distribution which has a minor effect on the frost spreading velocity. Thus, a similar spreading velocity of 9.1 ± 1.1 μm/s occurs on surface_3. The morphological patterns on surface_4 have a significant effect on the frost spreading process with the frost spreading velocity on surface_4 being only 3.7 ± .5 μm/s, which is less than ¼ of that on surface_1. For surface_5 with both patterns, the condensation is promoted on the pillar tops (compared to the case of surface_4) resulting in larger droplets with smaller intervals, so the frost spreading velocity on surface_5 is slightly larger, 3.9 ± .4 μm/s.

Figure 4

Frost spreading across the observation window (shown in Figure 2) on the five surfaces (a-e) at

the constant substrate temperature of -10oC. t0 is the time when the ice phase enters the observation window. The middle and right columns show a middle state and the completed frost spreading.

3.4 Effect of substrate temperature 9

Figures 5 and 6 show snapshots of the frost spreading on surface_1 and surface_5 at various substrate temperatures. For frost spreading on the smooth hydrophilic surface, since the total condensation time is much shorter with decreasing substrate temperature as shown in Figure 3, there is not enough time for droplet growth and coalescence at low substrate temperatures. Hence, the condensate droplet number density increases dramatically with decreasing substrate temperature and the average droplet size is reduced. The maximum frost spreading velocity occurs at the lowest substrate temperature and the frost spreading velocity increases dramatically with decreasing substrate temperature. The resultant frost spreading velocities on surface_1 is 13.7± 1.5 μm/s at the substrate temperatures of -5oC, 19.6 ± 2.6 μm/s at -15oC and 60.3 ± 4.9 μm/s at -25oC. In contrast, the frost spreading on the surface with both patterns (surface_5) is quite different at the various substrate temperatures. The frost spreading velocity does not change much even though the condensation states are quite different over such large temperature range. However, undesirable ice nucleation also occurred on individual pillars as a result of surface cavities due to fabrication. Thus, unidirectional frost spreading no longer occurs at substrate temperatures of -25oC and below. Reasonable estimates of the frost spreading velocities were obtained from measurements taken in carefully selected regions.

Figure 5

Frost spreading across the observation window on a smooth hydrophilic surface (surface_1) at

three substrate temperatures of -5oC (a), -15oC (b) and -25oC (c).

10

Figure 6

Frost spreading across the observation window on a surface with both wettability and

morphological patterns (surface_5) for three substrate temperatures of -5oC (a), -15oC (b) and -25oC (c).

4. Discussion 4.1 Simple analytical model describing the effects of wettability, morphology, and temperature on frost spreading A simple analytical model was developed to explain the observed effects of wettability, morphology,

and temperature on the frost spreading. The model is based on several commonly used assumptions [28] that 1) the temperature at the freezing front (a mixture of water and ice) is the equilibrium freezing point, Tmi, 2) the condensate droplets are truncated spheres, and 3) the ambient air is stationary (without convection). The frost spreading results from the freezing of individual droplets and the building of ice n

n 1

i 1

i 1

bridges between the droplets. Then, the frost spreading time is t   tintra,i   tinter,i , where tintra,i is the time for freezing of the i-th individual droplet and tinter,i is the time for building an ice bridge connecting the i-th droplet and the i+1-th droplet. For the i-th droplet with a contact area of radius r and contact angle of θ, tint ra ,i can be calculated through an energy balance between the released latent heat and the ice heat conduction. A scaling analysis shows that tint ra ,i 

11

VhL , where V is the droplet volume, ak T

a is the contact area, h is the height of the truncated sphere, L is the latent heat per unit volume, k is the thermal conductivity of the ice and T  Tmi  TS is the subcooling. The geometry of the truncated sphere leads to tint ra ,i  g (r, )

L r 2   1  cos   1  cos  with g (r, )   3     k T 6   sin    sin   2

4

  being a geometric factor 

related to the shape and size of a condensate droplet in the shape of a truncated sphere.

The time for building the ice bridge connecting the i-th droplet and the i+1-th droplet can be evaluated as

tint er ,i 

Vb Mv

, where  is the ice density, Vb is the ice bridge volume, and M v is the mass transfer rate

for water vapor diffusion from the i+1-th (water) to the i-th (ice) droplet. The ice bridge geometry can be simplified to a truncated circular cone with its base area as the projected area from the target droplet (i+1th, water) onto the source droplet (i-th, ice) with the cone length/height ratio based on the distance between

droplets

from

center

to

center.

The

volume

can

then

be

expressed

as

Vb   {(r cos )2 [l  r (1  sin  )]  r 3 (2  sin  )(1  sin  ) 2}/ 3 , where r is the contact radius of a condensate droplet, θ is the apparent contact angle, and l is the distance between two adjacent droplets (center to center). Mv 

The

mass

transfer

Mv

rate,

DM r 2  Pvapor , water  Pvapor ,ice    sin  cos  RT l

,

assuming

1D

water

vapor

diffusion

is

[31, 33], where D is the diffusion coefficient for water vapor

molecules in air, M is the molar weight of water, Pvapor ,ice and Pvapor ,water are the saturated vapour partial pressures at the ice/air and water/air interfaces, T  Ts is the substrate temperature, and R is the universal gas constant. The experimental results indicate that

tint ra ,i

tint er ,i

is around 0.2 for surfaces_4 and 5 at -5oC or less for

the other cases. Hence, the frost spreading velocity is mainly determined by the time to build the ice bridge, which is also consistent with the study by Petit and Bonaccurso [32]. The actual frost spreading velocity is, thus, related to the average time to build the ice bridges and the spatial density of the ice bridges.

4.2 Effect of surface wettability and morphology

12

The wettability and morphological patterns affect the frost spreading through their influence on the building of the ice bridges. The frost spreading velocity is mainly dependent on the spatial distribution of the ice bridges and the time required to build individual ice bridges. Analytically, for a typical ice bridge between two adjacent droplets, the time to build the ice bridge can be estimated using t 

Vb mA

where 

is the ice density, m is the water vapor mass flux and A is the projected area [31]. From the model in section 4.1, m 

1 , with l being the center to center distance between adjacent droplets. A larger ice l

bridge will take longer to form, thereby, leading to a smaller frost spreading velocity. Similarly, a larger projected area or a smaller interval will give rise to a faster frost spreading velocity. Figure 7(a) illustrates the usual condensation and ice bridge process on the smooth surfaces, surfaces_1 and 2. The condensation is more developed on the hydrophilic surface_1 due to the smaller energy barrier for heterogeneous condensate nucleation. Thus, surface_1 is covered with larger condensate droplets resulting from the droplet growth and coalescence, while hydrophobic surface_2 is covered with a larger number of moderately sized droplets as shown in Figure 1. Since the projected area from a neighboring water droplet to an ice droplet (i.e. the base area of the ice bridge) increases significantly with contact angle θ, each ice bridge on surface_1 is smaller than those on surface_2. Another important factor is the contribution of the second generation of condensate droplets formed around an initial large droplet. As shown in Figure 7(b), the presence of a second generation of condensate droplets leads to the formation of multiple small ice bridges which speeds up the frost spreading drastically. This second generation of condensate droplets is more likely on hydrophilic regions as shown in Figure 4(a). Consequently, hydrophilicity reduces both the size of the ice bridges and the number density of the ice bridges which promotes the frost spreading. The wettability patterns on surface_3 are a combination of hydrophilic and hydrophobic regions. The frost spreading on surface_3 is still mainly determined by its hydrophobic background.

13

Figure 7

Illustrations and experimental snapshots of the ice bridging modes on smooth surfaces 1 and 2. (a)

Illustration showing ice bridging between two large (primary) droplets; (b) Illustration showing ice bridging between two large droplets with a small droplet in-between; (c) and (d) are the corresponding experimental snapshots of (a) and (b), respectively. The times to form the ice bridges in (c) and (d) were 27.2 s and 4.5 s, respectively.

For surfaces_4 and 5 with the surface morphology patterns, the ice bridges mainly formed from pillar top to pillar top as illustrated in Figure 8(a). Thus, the scenario observed for surfaces_4 and 5 can be simplified to the previous analysis with condensate droplet arrays having uniform distances between them on a smooth surface with varying contact angles. Instead of the constant contact angle for the condensate droplets on the smooth surfaces, the contact angle of the condensate droplets formed on the pillar tops increases as the condensation progresses up to a maximum. Then, each ice bridge is much larger than on the smooth surfaces and the frost spreading is slowed. When the pillar tops are made hydrophilic as on surface_5, the condensation is enhanced on the pillar tops. The mass transport of the water vapor is promoted as the surface to surface distance between adjacent droplets reduces. However, the volume of the ice bridges also increases as the projected area increases. These two effects tend to balance each other which explains why the frost spreading rates on surfaces_4 and 5 are very similar. In addition, small condensate droplets were also found on the pillar sides of hydrophobic surface_4 as shown in Figure 1 with the ice bridging mode then changed to the case illustrated in Figure 8(b) which promotes the frost spreading to some extent, but not significantly.

14

Figure 8

Illustrations and experimental snapshots of ice bridges formed on surfaces_4 and 5 with the

patterned pillars. (a) Illustration showing ice bridging between two droplets on the pillar tops; (b) Illustration showing ice bridging between two side droplets; (c) and (d) are the corresponding experimental snapshots of (a) and (b), respectively. The times for building the ice bridges in (c) and (d) were 38.3 s and 31.9 s, respectively.

4.3 Effect of substrate temperature As shown in Figure 3, the substrate temperature has a significant effect on the condensate rate and the condensation time for all the surfaces tested in this work. For smooth surfaces_1, 2 and 3, the energy barrier for heterogeneous condensate nucleation is drastically reduced by lowering the substrate temperature which significantly increases the nucleation site number density. The average ice bridge size is then effectively reduced, which accelerates the frost spreading. This effect is more significant on the hydrophilic surfaces as expected from classical nucleation theory. For surfaces_4 and 5 with the morphological patterns, the condensate droplet distributions are mainly dependent on the pillar geometries; hence, the ice bridging and the resultant frost spreading are less dependent on the substrate temperature. This can also be explained using our model which shows the direct effect of the substrate temperature on the vapor diffusion and, thus, the building of the ice bridges is trivial.

15

4.4 Comparison of experimental and analytical results Figure 9 shows the frost spreading velocity versus substrate temperature for all five types of fabricated surfaces. The figure compares the predictions of the analytical model in section 4.1 with the experimental data. The analytical model catches most of the observations. The freezing front propagation velocities also agree reasonably well with two literature studies [25, 26]. For example, in ref. 28 the freezing front propagation velocity on a smooth hydrophobic surface at -10oC is 7.8 ± 1.1 µm/s and at -20oC is 12.4 ± 1.5 µm/s, which are quite close to the current results of 11.2 ± 0.9 µm/s and 14.8 ± 1.2 µm/s on a smooth hydrophobic surface at these two temperatures (surface_2). However, most studies have focused on the retardation of the freezing front propagation using superhydrophobic surfaces with nanoscale or hierarchical roughness. To the best of our knowledge, there is no data on freezing front propagation on microscale patterned surfaces. Figure 9 shows that the frost spreads faster at lower substrate temperatures on smooth surfaces and wettability patterned surfaces (surfaces_1, 2, and 3). On the smooth hydrophilic surface_1, the frost spreading velocity increases drastically with decreasing substrate temperature. The frost spreading velocity is less dependent on the substrate temperature for the smooth hydrophobic and wettability patterned surfaces (surfaces_2 and 3) than on surface_1. No noticeable variation of the frost spreading velocity with substrate temperature is observed on the morphology patterned and dual patterned surfaces (surfaces_4 and 5).

80

Surf_1 Surf_2 Surf_3 Surf_4 Surf_5

Frost spreading velocity (m/s)

70 60 50 40 30 20 10 0 -30

-25

-20

-15

-10

-5

o

Substrate temperature ( C)

Figure 9

Measured and predicted frost spreading velocities for various substrate temperatures for the five

fabricated surfaces. The solid symbols represent the measurements while the open symbols represent the predictions of the analytical model in section 4.1. The error bars were based on four independent measurements.

5. Conclusions 16

This paper reports on the effects of wettability and surface morphology as well as substrate temperature on the frost spreading velocity. The frost spreading was investigated at a constant substrate temperature on five types of fabricated surfaces, including a smooth hydrophilic surface, a smooth hydrophobic surface, a surface with a wettability pattern, a surface with a morphology pattern, and a surface with both morphology and wettability patterns. The results showed that the morphology patterned surfaces effectively retard the frost spreading by providing a controlled droplet distribution pattern, while the wettability patterned surface showed similar performance as the smooth hydrophobic surface. The frost spreading on these surfaces at different substrate temperatures was also studied. The frost spreading velocity drastically increased with decreasing substrate temperature on the smooth surfaces and the wettability patterned surfaces due to the larger number of condensate droplet nucleation sites, so the ice bridges were smaller. A relatively stable frost spreading velocity was achieved on the morphology patterned surface and the dual patterned surface. This finding shows that surfaces with morphology patterns are promising candidates for anti-icing applications over a wide range of substrate temperatures. An analytical model was developed to describe the building of the ice bridges that accounts for the effects of wettability, morphology, and temperature on the frost spreading. The model predictions agree well with the experimental data.

Acknowledgements We acknowledge financial support from the Ministry of Singapore through the Academic Research Fund (MOE2016-T2-1-114) to CY, the Nanyang Technological University PhD Scholarship through the Nanyang Environment & Water Research Institute (NEWRI) to YZ. We are also grateful to Professor David M. Christopher at Tsinghua University for his critical proof reading of the revised manuscript.

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Graphical abstract

Frost spreading on microscale wettability/morphology patterned surfaces

Hydrophilic

200 μm

Wettability patterned

Dual patterned

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Highlights 

Effects of wettability and morphology patterns on frost spreading;



Frost spreading at varying substrate temperature;



Demonstration of morphology patterned surface with anti-frosting performance;



A simple analytical model for describing frost spreading;

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