Investigation of the Interface Effects and Frosting Mechanism of Nanoporous Alumina Sheets

Abstract

Nanoporous alumina sheets can inhibit the growth of the frost layer in a low-temperature environment, which has been widely used in air-conditioning heat exchangers. In this study, nanoporous alumina sheets with pore diameters of 30 nm, 100 nm, 200 nm, 300 nm, and 400 nm were prepared by using the anodic oxidation method with the conventional polished aluminum sheet as the reference. A comprehensive and in-depth analysis of the frosting mechanism has been proposed based on the contact angle, specific surface area, and fractal dimension. It was found that compared with the polished aluminum sheet, the nanoporous alumina sheets had good anti-frost properties. Due to its special interface effects, the porous alumina sheet with a 100 nm pore diameter had strong anti-frost performance under low temperatures and high humidity. In an environment with low surface temperature and high relative humidity, it is recommended to use hydrophilic aluminum fins with large specific areas and small fractal dimensions for the heat exchange fins of air source heat pump air conditioning systems.

1. Introduction

Air conditioning systems are widely used to adjust the comfort of a building environment. While enjoying a comfortable indoor environment, people are also worried about the high energy consumption of buildings and serious environmental pollution. Studies have shown that building energy consumption accounts for 30–40% of the total social energy consumption [1]. Moreover, air conditioning energy consumption accounts for 40–60% of building energy consumption [2,3]. Air source heat pumps constitute the most widely used air conditioning equipment in domestic residential buildings due to their energy saving, environmental friendliness, short investment return period, and low operating cost. However, in severely cold winter, when the surface temperature of the fins of the outdoor heat exchanger of the air source heat pump air conditioning system is lower than the ambient dew point temperature and is lower than the freezing temperature of the condensate water, the surface of the fins will be frosted [4], which reduces the heat transfer efficiency of the heat exchanger by 50–75% [5]. This is energy waste and environmentally unfriendly. Therefore, the optimization of air source heat pump air conditioning systems and the improvement of anti-frosting performance is a hotspot of current research, attracting many researchers’ attention [6].

Inspired by the superhydrophobic “lotus effect” [7], a passive defrosting method was proposed by creating a surface that can prevented the condensation/frosting of water molecules on the surface or promoted the shedding of condensate/frost on the cold surface [8]. The passive method requires low energy consumption and is environmentally friendly. Both hydrophilic and hydrophobic fins on the heat exchanger meet the requirements of passive defrosting. Liu et al. [9] demonstrated the delayed formation of the frosting layer on hydrophilic heat exchange fins by at least 15 min compared to the ordinary heat exchange fins with a reduced amount of frost by 40%. Okoroafor et al. [10] found that due to the reduced water adsorption, the aluminum sheets coated with hydrophilic layers showed good anti-frosting properties in humid air. Their frosting rate and the thicknesses of the frost layers were 10–30% lower than that of an ordinary aluminum sheet. Lee et al. [11] compared the frost formation on the surfaces with different dynamic contact angles (DCA) of 23° and 88°. The results showed that low-DCA surfaces had lower frost thickness and higher frost density than high-DCA surfaces. Yang et al. [12] developed a nanoporous hydrophilic aluminum sheet with an improved anti-frosting performance at −15 °C by reducing the frosting rate by a factor of 3. Meanwhile, Wang et al. [13] found that the superhydrophobic surface also had good anti-frosting performance under high humidity conditions. A superhydrophobic aluminum surface with hierarchical micro–nano structures was created via a combination of chemical etching and sandblasting [14]. The frosting delay time was more than 10 times that of the bare substrate, and the frosting area was significantly smaller. Lei et al. [15] used the spray coating method to prepare a superhydrophobic coating based on silica nanoparticles and room-temperature vulcanized silicone rubber. The experimental results showed that the superhydrophobic coating had a strong ability to prevent frost growth. Fan et al. [16] prepared a transparent hydrophobic surface by using a sol–gel method with the frost formation time increased by 4.5 times that on the unmodified surface at a propagation speed of 47.5 μm/s, which was 29.6% lower than that of the unmodified surface.

Hydrophilic/hydrophobic surfaces produced by surface coating have some shortcomings. The surface coating could be structurally fragile with poor adhesion, easily falling off, and showing poor durability [17]. The preparation of a nanoporous surface via anodization method can avoid such shortcomings because this way, the nanoporous surface is directly formed, giving it better durability. Wilson et al. [18] found that nanoporous surface coating could reduce the nucleation temperature of condensed water, and the freezing property of the coating surface was not damaged after 150 cycles of freezing/melting. Kim et al. [19] conducted experimental tests on a nanoporous surface and found that it can promote the condensation of water droplets and the falling off of the frost layer from the surface under the action of its gravity, which makes up for the limitations of the hydrophobic surface in a high-humidity environment.

The anti-frosting properties of nanoporous alumina sheets have been studied, but their anti-frosting mechanism is seldom studied. To further study the mechanism of surface frosting and provide a reference for the subsequent preparation of anti-frosting surfaces, many researchers have conducted studies based on the contact angle and surface energy of a surface. Huang et al. [20] prepared a surface with a contact angle of 96.2°~154.9° by using solution immersion. Under natural convection conditions, a comparative experiment of frosting on the surface of ordinary copper was carried out. The results showed that the delayed frosting time on the surface was directly proportional to the surface contact angle. The larger the contact angle was, the better the surface anti-frosting performance was. Piucco et al. [21] found that the initial frosting area of the surface was inversely proportional to the surface contact angle. As the contact angle increased, a lower surface temperature was required to produce frost crystals. Mangini et al. [22] observed the frost layer morphology on a surface with different contact angles by using infrared thermal imaging cameras. They found that a dense ice layer was formed on the surface with a small contact angle while a sparsely distributed ice layer was formed on the surface with a large contact angle. This indicated that the contact angle would affect the shape and density of the surface frost layer and have a certain effect on the long-term frost formation on the surface. Na and Webb et al. [23] found that a low-energy surface required a much higher supersaturation degree for frost nucleation than a high-energy surface. Liu et al. [24] proposed that the retarding frost nucleation on a low-energy surface is due to a smaller area of contact with the condensed water nuclei than on high-energy surfaces.

It is generally considered that frosting is a continuous problem and cannot be limited to the initial stage of frosting. However, the contact angle and surface energy mentioned above can only be used to study the initial frosting performance at the interface. The effects on the growth of the frost layer also need to be investigated, and these have important effects on the frosting process [25]. The growth structure of the frost layer directly affects the density of the frost layer, the effective diffusion coefficient of water vapor in the frost layer, and the thermal conductivity of the frost layer [26]. These three physical parameters will adversely affect the frost structure. Due to the complexity of frosting, most current studies are still limited to experimental tests and simple theoretical analyses. Limited studies have been conducted on the mechanism of frosting on surfaces.

In this study, nanoporous alumina sheets were prepared by using the anodic oxidation method with averaged pore diameters of 30 nm, 100 nm, 200 nm, 300 nm, and 400 nm. The mechanism of frosting on the nanoporous alumina sheet surfaces was explored. Focusing on the frost layer morphology at the initial frosting stage of the nanoporous surface, the experimental results were analyzed for Gibbs free energy, specific surface area, and fractal dimensions, and the theoretical morphology was compared with the actual morphology through visual observation. The subsequent research will further quantitatively analyze the frosting properties of a nanoporous surface by combining the thickness and density of the frosting layer. This research will help analyze the mechanistic factors that affect surface frosting with provided performance parameters for preparing surfaces with high anti-frosting properties. The results promote applying nanoporous material as the anti-frost material in air source heat pumps with a potential energy-saving technology.

2. Sample Preparation and Characterization

The nanoporous alumina sheets were prepared by using an anodization process. The pore diameters could be manipulated by controlling the intensity of the oxidation current and the hole expansion treatment. The surface morphology, contact angle, surface energy, and fractal dimension were observed and measured.

2.1. Preparation of the Nanoporous Alumina Sheets

The preparation process mainly involved 4 steps. Firstly, aluminum sheets (99.99% purity) were ultrasonically cleaned in the acetone/ethanol solution for 10 min to remove the residual grease before being dried and used as substrates. The samples were immersed in the 1 M sodium hydroxide solution for 5 min to remove the surface oxide film. After that, the substrate was electrochemically polished in a 400 mL 1:9 ratio perchloric acid in ethanol solution for 2 min, using graphite as the cathode and an aluminum sample as the anode. Finally, the electrolyte was replaced with 0.3 M oxalic acid solution for the anodization to form nanoporous material under a DC bias. It should be mentioned that after each step was finished, the substrate was thoroughly washed with deionized water.

A nanoporous surface with different apertures could be obtained by changing the current amplitude, and the relationship between the surface structure parameters and the anodization current is presented in

Table 1. Surface structure parameters and fabrication craft.

Simple	Diameter	Spacing	Depth	Current	Size
1	0 nm	0 nm	0 μm	0 A	20 × 20 × 0.2 mm
2	30 nm	65 nm	60 ± 5 μm	0.2 A
3	100 nm	100 nm		0.5 A
4	200 nm	450 nm		1.2 A
5	300 nm	450 nm		1.2 A
6	400 nm	450 nm		1.2 A

(‘diameter’ refers to the diameter of a nanopore, and ‘spacing’ refers to the distance between the centers of two adjacent nanopores). The nanoporous samples with 300 nm and 400 nm pore diameters (Samples 5 and 6) were obtained using the hole expansion treatment by immersing the aluminum sheet with a 200 nm pore diameter in 5 wt% phosphoric acid solution for 30 min and 60 min. Alongside this, the polished aluminum sheet (simple 1) was prepared for comparison.

2.2. Surface Topography

A scanning electron microscope (SEM, S-3400N, Hitachi, Tokyo, Japan) was used to study the surface morphology, as shown in Figure 1. Uniformly distributed nanopore structures with relatively uniform pore sizes were observed for all samples. Sample 2 has a higher density of nanopores than sample 3. Samples 4, 5, and 6 have similar hole spacings, while the pore diameters are increased accordingly, with the wall gradually becoming thinner. The images below have been enlarged 50,000 times.

The number of nanopores and the specific surface area for each sample could be calculated according to its pore diameter, depth, and spacing (the number of nanopores on the abscissa can be obtained by dividing the length of the surface by the spacing of the pores, and the same method obtains the number of nanopores in the ordinate; their product is the total number of nanopores. Specific surface area refers to the ratio of the total microscopic area of the surface of a nanoporous alumina sheet to the macroscopic area). The calculation results are listed in

Table 2. The parameters of the prepared samples.

Sample	2	3	4	5	6
Number of nanopores	9.5 × 1010	4 × 1010	1.98 × 109	1.98 × 109	1.98 × 109
Specific surface area (m2/m2)	1342.5	1697.5	187.5	282.5	375

.

2.3. Contact Angle and Surface Energy

Static contact angle and surface energy were measured using an optical contact angle measuring instrument (ZJ-7000, Shenzhen, China), with the contact angle range being 0–180°, accuracy ±0.1°, surface energy range 0–1000 mN/m, and accuracy ±0.01 mN/m. It should be mentioned that surface energy is defined as the extra energy generated by the surface of a material relative to its interior. Water droplets are spherical on surfaces with low surface energy because low surface energy is not sufficient to break the surface tension of water droplets. The results are shown in Figure 2 and

Table 3. The parameters of the prepared aluminum sheets.

Sample	1	2	3	4	5	6
Contact angle (degree)	87	40	37	31	36	56
Surface energy (mN/m)	50	142	147	157	149	111

.

2.4. Surface Fractal Dimension

The fractal dimension reflects the effectiveness of the space occupied by a complex form, which is a measure of the irregularity of a complex form. It can be used to analyze the space occupancy efficiency of nanoporous surfaces, i.e., how many nucleation active points water molecules have on their surfaces.

The fractal dimension was analyzed using Photoshop, Matlab, and the Fraclab toolbox from the SEM images. The Photoshop software (Photoshop CC) was used to convert the SEM images of the nanoporous alumina sheets into grayscale images, which were then converted into binary images represented by binary numbers. After that, the Matlab software (Matlab 2020) was used to convert the binary data into Fraclab-identifiable double-precision numerical data. Finally, the Fraclab toolbox was used to calculate the box dimension to obtain the fractal dimensions of the surfaces of the nanoporous alumina sheets. The surface fractal dimensions of nanoporous alumina sheets are shown in

Table 4. The surface fractal dimension of nanoporous alumina sheets.

Sample	2	3	4	5	6
Fractal dimension	2.8788	2.8084	2.8643	2.7684	2.8247

.

3. Theoretical Analysis

The heat transfer relationship between the water vapor and the solid surface and the morphological characteristics of the frost layer affect the frosting rate and frosting quantity on a solid surface. The frosting mechanism of the prepared nanoporous alumina sheets will be analyzed from their surface heat, mass transfer, and interface effects—that is, using surface contact angles, fractal dimensions, and specific surface areas.

3.1. Thermodynamitical Analysis

The frosting nucleus is formed from a vapor embryo through condensing water molecules. Although the saturated air is in direct contact with a cold surface whose temperature is below 0 °C, the nucleation begins only after overcoming the energy barrier.

The model representing the homogeneous and heterogenous nucleation on a surface is shown in Figure 3a,b [21] (Reproduced with permission from Hermes, Experimental Thermal and Fluid Science, published by ELSEVIER, 2008). The vapor transformation into nucleation is accompanied by a transition from a saturated state to a supersaturated state. The following equation shows the free energy difference, ΔG, between the supersaturated and saturated states [23,27].

$$\Delta G=V\Delta g_{\mathrm{v}}+{\gamma }_{\mathrm{se}}{A}_{\mathrm{se}}+{\gamma }_{\mathrm{ew}}{A}_{\mathrm{ew}}-{\gamma }_{\mathrm{sw}}{A}_{\mathrm{ew}}$$

(1)

Here, V is the volume. A_ew and γ_ew are the surface area and surface energy at the embryo–wall interface. A_se and γ_se correspond to the surface area and surface energy at the surroundings–embryo interface. γ_sw is the surface energy at the surroundings–wall interface. Δg_v is the volume-specific Gibbs free energy deviation between the supersaturated and saturated states, which is described in Equation (2) [21].

$$\Delta g_{\mathrm{v}}=\Delta h_{\mathrm{lat}}-TS=\frac{\rho \mathrm{R}T}{M}\ln \left(\frac{{\omega }_{\mathrm{s}}}{{\omega }_{\mathrm{sat},\mathrm{e}}}\right)$$

(2)

Here, ω_s and ω_sat,e are the humidities of the surrounding air and the air at the embryo surface, respectively. T is the embryo temperature and R is the ideal gas constant. ρ and M are the embryo density and molar mass, respectively. Hence, the total free energy difference can be expressed in Equation (3).

$$\Delta G=\frac{\rho V\mathrm{R}T}{M}\ln \left(\frac{{\omega }_{\mathrm{s}}}{{\omega }_{\mathrm{sat},\mathrm{e}}}\right)+{\gamma }_{\mathrm{se}}{A}_{\mathrm{se}}+{\gamma }_{\mathrm{ew}}{A}_{\mathrm{ew}}-{\gamma }_{\mathrm{sw}}{A}_{\mathrm{ew}}$$

(3)

Fletcher [28] assumed that the shape of the parent phase for nucleation is a spherical segment as shown in Figure 3b. The embryo size significantly affects the Gibbs free energy deviation. As Bai [29] mentioned, at a critical radius, r′, the Gibbs free energy to be overcome for the initiate nucleation will be minimized. Using the Fletcher model, the critical Gibbs free energy deviation (ΔG′) can be obtained at the critical embryo size (r′).

$$\Delta {G^{\prime }}_{\mathrm{tot}}=\frac{4\pi }{3}\frac{{\gamma }_{\mathrm{se}}{}^3}{{\left[\frac{\rho \mathrm{R}T}{M}\ln \left(\frac{{\omega }_{\mathrm{sat},\mathrm{e}}}{{\omega }_{\mathrm{s}}}\right)\right]}^2}{\left(1-\cos \theta \right)}^2(2+\cos \theta )$$

(4)

$$r^{\prime }=2{\gamma }_{\mathrm{se}}{\left[\frac{\rho \mathrm{R}T}{M}\ln \left(\frac{{\omega }_{\mathrm{s}}}{{\omega }_{\mathrm{sat},\mathrm{e}}}\right)\right]}^{-1}$$

(5)

Becker and Doring [30] proposed the following equation for the embryo formation rate on a unit surface area for heterogeneous nucleation:

$$I=I_0\exp (-\frac{\Delta G^{\prime }}{\mathrm{k}{T}_{\mathrm{w}}})$$

(6)

Here, I is the embryo formation rate at temperature T_w. ΔG′ is scally by Volmer and Flood [31]. I₀ = 10²⁵ embryo/(cm² s) is the kinetic constant and k is the Boltzmann constant (1.381 × 10⁻²³ J/K) [28].

It could be concluded from Equations (4)–(6) that the nucleation rate of frost crystals is inversely proportional to the surface contact angle in a certain thermal system.

3.2. Fractal Dimension Analysis

Both the nucleation rate and the macroscopic morphology of the frost layer can affect the formation of frost on cold surfaces. The fractal dimension is a quantitative reaction of self-similarity and can reflect the complexity of surface microstructure [32]. The larger the fractal dimension of the surface is, the more complex the surface structure will be, with a more active surface containing more edges and angles and thus increasing the number of attachment points for the initial liquid nuclei. Hou [33] and Mei [34] have discussed the effects of a cold surface having different fractal dimensions on surface condensation and frosting. They realized that differentiation in frost layer morphology significantly affects the heat transfer between the frost crystals, the cold surface, and the surrounding environment. Ding et al. [35] proposed that the smaller the fractal dimension of the surface was, the more regular the surface morphology would be and the fewer active points the initial liquid nucleus would need to survive, leading to a smaller number of condensing droplets and thus reducing the surface frost crystal coverage.

3.3. Surface Adsorption

The essence of frosting is that water molecules contact a cold surface and the liquid phase turns into frost crystals exothermically. Free collisions of water molecules and active adsorption on the surface are involved. Physisorption is the main adsorption mechanism at low temperatures, involving the Van der Waals forces between molecules. Studies have shown that the Van der Waals force can be affected by the specific surface area of a surface. The larger the surface area is, the greater the Van der Waals force is [36]. The active adsorption of water molecules on the surface will increase the probability of water molecules contacting the surface. Strong, active adsorption will enhance the initial frosting on the surface. However, the long-term frosting on the surface needs to be further analyzed because the strong adsorption force will also affect the shedding of the frost layer and the heat transfer efficiency of the surface.

4. Experiment and Discussion

The frosting morphologies of nanoporous alumina sheets were observed and analyzed. The influence of the interface effects (contact angle, specific surface area, and fractal dimension) of nanoporous surfaces on their frosting properties was analyzed.

4.1. Experimental Test

The experimental test setup, shown in Figure 4, included a computer, microscope, and semiconductor cooler. The frost topographies of the fronts and sides of the aluminum sheets were photographed. Frontal shooting was performed with a wind speed of 0.1 m/s, an ambient temperature of 28 °C, a relative humidity of 62%, and a surface temperature of −10 °C. Lateral shooting was performed with a wind speed of 0.1 m/s, an ambient temperature of 16 °C, a relative humidity of 58%, and a surface temperature of −15 °C.

The microscope and computer were connected with a CCD, the frosting process on the surface of each aluminum sheet was transmitted to the computer through a video cable image, and the pictures of different aluminum sheets were taken at the same multiple. The experimental results are shown in Figure 5 and Figure 6.

The following phenomena can be obtained by analyzing Figure 5.

On the surface of the polished aluminum sheet, the water molecules first condensed into hemispherical water droplets, next, they gradually froze, and then, frost crystals appeared on the frozen water droplets. On the surface of the 30 nm pore diameter alumina sheet, the water molecules condensed into droplets without obvious shapes, the spreading area was large, the heights of the droplets were smaller than the heights of the water droplets condensed on the surface of the polished aluminum sheet, and a dense frost layer was generated on the surface of the droplets after freezing. The surface of the 100 nm pore diameter alumina sheet first condensed into a water film and then froze, forming frost crystals on the surface of the frozen water film. The frosting processes of the 200 nm, 300 nm, and 400 nm pore diameter alumina sheets were similar, and frost crystals were generated directly on their surfaces. The amount of frost on the surface of each aluminum sheet in the early stage of frosting could be preliminarily judged thus: polished >30 nm > 100 nm; 200 nm > 400 nm > 300 nm.

From the results in Figure 6, the following conclusions could be obtained.

When ice was formed on the surface of each polished aluminum sheet, dendritic frost crystals continued to grow on the surface of the ice block, and the dendritic frost crystals increased the contact area with air and promoted the subsequent frosting process. The surface frost crystals of the 30 nm pore diameter alumina sheet were tree-shaped. The frost crystals grown on the surface of the 100 nm and 200 nm pore diameter alumina sheets were needle-like, and the frost crystal density on the surface of the 100 nm pore diameter alumina sheet was greater than that on the 200 nm pore diameter alumina sheet; from the results of the long-term experiment, it was found that the dense needle-like frost crystals would play a role in heat insulation and hinder the subsequent frosting process of water molecules. The dendritic frost crystals on the surface of the 300 nm pore diameter alumina sheet reduced the obstruction of heat exchange with water molecules and enhanced the subsequent frosting process. A flat frost layer on the surface of the 400 nm alumina sheet would hinder the subsequent frosting process.

4.2. Interface Effect of Nanoporous Alumina Sheets

The effects of contact angle, specific surface area, and fractal dimension on frost morphology, supercooling degree, and embryo formation rate in the alumina sheet surfaces were analyzed. The interface parameters of different nanoporous alumina sheets are shown in Figure 7, Figure 8 and Figure 9 (the data in Figure 7, Figure 8 and Figure 9 corresponds to Table 2, Table 3 and Table 4. Each contact angle is measured by using the optical contact-angle-measuring instrument at 3 random points on the surface and selecting their average value. The specific surface area is calculated by combining the surface pore size and pore spacing. The fractal dimension is calculated, by using the MATLAB software, based on the surface topography).

The initial frosting phenomenon was analyzed with the interface parameters of the nanoporous alumina sheets. Morphology models representing the formations of initial frost crystals on different aluminum sheet surfaces were built, as shown in Figure 10, based on the photographs at the beginning of the frosting in Figure 11.

(1) The surface contact angle of the polished aluminum sheet was much larger than those of the other prepared aluminum sheets, resulting in a larger Gibbs free energy barrier and a longer phase transition time. More water molecules would condense on its surface before they froze. After freezing, the water molecules in the air would subject phase changes on the ice crystals exothermally, generating frost crystals.

(2) The specific surface areas of the 30 nm pore diameter alumina sheet and 100 nm pore diameter alumina sheet were similar and much larger than those of the other aluminum sheets. At the beginning of the frosting process, water molecules in the moist air would be trapped with a larger molecular adsorption force. This process would be very rapid, and the captured water molecules would not have time to transform into ice, forming a liquid water film first. Since the surface fractal dimension (i.e., active surface points) of the 30 nm pore diameter alumina sheet was larger than that of the 100 nm pore diameter alumina sheet, the spreading area of the water film on the 30 nm pore diameter alumina sheet would be larger. Since the contact angle on the surface of the 30 nm pore diameter alumina sheet was greater than that on the 100 nm alumina sheet, the phase transition was more difficult than that on the 100 nm pore diameter alumina sheet, leading to a thicker liquid water layer.

(3) The specific surface areas of the 200, 300, and 400 nm pore diameter alumina sheets were similarly low. The adsorption of water molecules depended on the probability of free collision between water molecules and the nanoporous alumina sheet surfaces. Therefore, after contacting these nanoporous alumina sheet surfaces, the adsorbed water molecules would directly form ice crystals rather than liquid. Their fractal dimensions followed the order of 200 nm > 400 nm > 300 nm, and so, the number of formed frost embryos would also show 200 nm > 400 nm > 300 nm. The contact angle of the surface of the 400 nm pore diameter alumina sheet was greater than those of the 200 nm and 300 nm pore diameter alumina sheets. Hence, the phase transition of water molecules on the 400 nm pore diameter surface was more difficult and slower. Therefore, the height of the frost crystal embryos would be smaller than that of the 200 nm and 300 nm pore diameter alumina sheets. Since the contact angles of the 200 nm and 300 nm pore diameter alumina sheets were similar, their frost crystal embryo heights were also comparable.

By comparing Figure 10 and Figure 11, it can be seen that the frost crystal morphology model can reflect the initial frost crystal morphology on the surface of an aluminum sheet.

Analyzing the frost crystal morphology model, one could draw the following conclusions:

(1)

The polished aluminum sheet has the best thermal conductivity. The contact area of the surface ice crystal with air is large. Therefore, the polished aluminum sheet has the highest average frosting rate when compared to the other aluminum sheets.

(2)

The formed frost crystals on the 100 nm pore diameter alumina sheet are distributed relatively and sparsely due to the sparsely distributed surface-active points. During the initial stage of frosting, the ice crystals play the role of overhead insulation on the cold surface to prevent frost formation. Hence, the 100 nm pore diameter alumina sheet offers good anti-frosting performance even in high humidity environments.

5. Conclusions

In this study, nanoporous alumina sheets with pore diameters of 30, 100, 200, 300, and 400 nm were prepared by using the anodic oxidation method with a polished aluminum sheet as a reference. The mechanism of surface frosting was established based on the contact angles, specific surface areas, and fractal dimensions. Based on the influence of mechanism parameters on frost performance, the frost morphology model in the early stage of surface frosting was established, and the reliability of the frost morphology model was verified by comparing it with the actual observation; moreover, the surface performance parameters of high frost resistance were introduced to the frost morphology model to provide a reference for the preparation of high-frost-resistance surfaces.

The alumina sheet with a 100 nm pore diameter has strong anti-frost performance at low temperatures in a high humidity environment due to its hydrophilic surface with a large specific area and small fractal dimension. Sparsely distributed ice crystals appear on its surface first, and then, frost crystals grow on the ice crystals. The ice crystals form an insulation layer limiting the growth of frost crystals.

Through theoretical analysis, in the environment of low surface temperature and high relative humidity, it is recommended to use hydrophilic aluminum fins with a large specific area and small fractal dimension for the heat exchange fins of air source heat pump air conditioning systems.