Frost self-removal mechanism during defrosting on vertical

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Frost self-removal mechanism during defrosting on vertical superhydrophobic surfaces: peeling off or jumping off Fuqiang Chu, Dongsheng Wen, and Xiaomin Wu Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03347 • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 26, 2018

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Frost self-removal mechanism during defrosting on vertical superhydrophobic surfaces: peeling off or jumping off Fuqiang Chu a, Dongsheng Wen a, Xiaomin Wu *,b aSchool of Aeronautic Science and Engineering, Beihang University, Beijing, China bKey Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing, China

Abstract Though a superhydrophobic surface has great potential to delay frosting, it tends to become frosted under humid conditions and needs to defrost periodically. So far, the exact mechanism of defrosting still remains unclear. Here we investigate the frost self-removal mechanism during defrosting on vertical superhydrophobic surfaces. Two self-removal modes are observed: peeling off and jumping off. When the frost thickness is larger than a threshold value, peeling off mode occurs; otherwise, jumping off mode takes place. Compared with the peeling off mode, the jumping off mode is less effective on self-removing frost as jumping is limited by energy transformation. A theoretical model based on frost melting – water permeation mechanism is proposed to determine the threshold value of frost thickness. According to this model, the threshold value of the frost thickness is dependent on the frost porosity and the surface temperature (or heat flux). For our particular experiments, the threshold value of the frost thickness predicted by the proposed model agrees well with our experimental results. Our work may advance the defrosting applications of superhydrophobic surfaces in related engineering fields. Keywords: superhydrophobic, defrosting, peeling, jumping, frost thickness, threshold value

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Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Introduction Frosting formation exists widely in engineering fields such as aviation, refrigeration and power generation, and causes numerous problems. The frost on an aircraft wing changes its aerodynamic configuration, reduces the wing lift, and even imperils the flight safety;1 the frost on heat exchanger fins blocks the flow channel, increases the thermal resistance, and deteriorates the heat transfer;2 the frost also changes the aerodynamic characteristics of a wind turbine and reduces its power generation efficiency.3 Over the past decade, many efforts have been made to restrain the frost formation using superhydrophobic surfaces with a contact angle larger than 150o and a contact angle hysteresis smaller than 10o.4-8 These studies demonstrated that a superhydrophobic surface has great advantages in delaying ice nucleation, reducing frost adhesion, and even self-cleaning subcooled droplets by a spontaneous jumping motion.9-15 It should be noted that although a superhydrophobic surface delays frosting to some extent, eventual frost growth is inevitable in chilled supersaturated environments due to inter-droplet ice bridging.12-14, 16-17 Therefore, periodic defrosting is very crucial for frosted superhydrophobic surfaces. Owing to its unique wettability, the superhydrophobic surface shows distinct defrosting characteristics. On horizontal superhydrophobic surfaces, our previous work showed that the frost meltwater films (ice-water mixtures) first dewet by edge curling and then by shrinking or coalescence, and finally dewet into isolated droplets.18 These droplets, which have been demonstrated to be in highly mobile Cassie-Baxter state, are able to roll down at very small titled angles.19-20 Similar to that occurred during condensation,21-22 self-propelled jumping, rotating and sliding movements during defrosting also take place frequently, making the defrosting process very dynamic and generating very low surface coverage on superhydrophobic surfaces.23-25 On vertical superhydrophobic surfaces, the defrosting process is more effective, because the melting frost usually departs from the superhydrophobic surface directly at the early stage of defrosting.26-28 Compared with conventional surfaces such as bare aluminum surfaces and hydrophobic surfaces, the retention water mass or fraction presents a much lower value.29-32 However, there are still some questions unclear for the defrosting on the superhydrophobic surface, and this limits its engineering applications. One of the key points is how the frost departs from a vertical superhydrophobic surface during defrosting. Different phenomena have been reported separately, such as slide down and peel off, but the exact mechanisms and the key influencing factors remain unclear. In this work, we aim to determine the frost departure mechanism during defrosting on vertical superhydrophobic surfaces by performing well controlled experiments on aluminum based superhydrophobic surfaces. Two self-removal modes, i.e. peeling off and jumping off, are observed. Their occurrences are dependent on frost parameters such as the frost thickness. We further develop a theoretical model to determine the threshold value of the frost thickness for these two frost self-removal modes. The present results not only deepen the scientific understanding of defrosting mechanisms on superhydrophobic surfaces, but also advance the defrosting applications of the superhydrophobic surfaces in related engineering fields such as aircrafts, heat exchangers, and wind turbines.

Experimental Section The experimental surfaces (4 cm × 4 cm) are Al-based superhydrophobic surfaces fabricated by the chemical etching-deposition method.33 The surface structures observed by a scanning electron microscopy are shown in Fig. 1. It can be seen that there are hierarchical micro-nano structures on the superhydrophobic surface with micro structures being aggregations of irregular nanoscale grains.33 Due to these hierarchical structures, the surface exhibits excellent superhydrophobicity. At room temperature, the measured static contact angle of a 2 μl droplet on this surface is 160.0±0.5o, and the measured advancing and receding contact angles using the titled plate method are 162.2±1.0o and 158.3±1.0o, respectively, as shown in Fig. 1. 2 / 16


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Figure 1. SEM images of the experimental superhydrophobic surface: hierarchical micro-nano structures evenly distributed on the superhydrophobic surface with micro structures being aggregations of irregular nanoscale grains. The static, advancing, and receding contact angles of the superhydrophobic surface are about 160o, 162o, and 158o, respectively.

The experimental system and apparatus for frosting used here were the same as those in our previous work.34 The superhydrophobic surfaces were vertically placed on the cold side of a thermoelectric cooler, and the experiments were performed in a closed laboratory. Before defrosting experiments, frosting experiments are needed to accumulate moderate frost. During the frosting experiments, the measured laboratory temperature was 18.0±1.0oC with a relative air humidity of 90.0±5.0%, and the cold surface temperature (means the interface temperature between the solid substrate and bottom frost/water) was −16.0±0.5oC. The frosting duration time was 10~30 min. We photographed frost profiles from the side and then extracted the average frost thickness using picture processing method based on Matlab programming (See supporting information Figure S1). After the frosting experiments, the power of the thermoelectric cooler was shut off and the heat flux was instantly transferred from the hot side of the thermoelectric cooler to the experimental surface and then to the frost. When the frost temperature rose above 0°C, the frost began to melt. We did not apply any extra heat source, and the selected the natural defrosting method is the same as what we used before. 18, 23

Results and Discussion Frost peeling off from surfaces Generally, during defrosting on a surface, frost melting and water permeation occur successively until the unmelted porous frost layer is saturated with water.35-36 Afterwards, meltwater (ice-water mixture) evolution stage (or called the accumulation stage) begins, during which some unique phenomena (such as edge curling) or self-propelled movements (such as jumping) may take place on superhydrophobic surfaces according to our recent works.18, 23 However, these stages during defrosting are not fixed, but will change with frost parameters such as the frost thickness, especially when defrosting on a vertical superhydrophobic surface. Figure 2(a) (See supporting information video S1 for multimedia) shows the defrosting process on vertical superhydrophobic surface when the frost thickness is about 0.6 mm (the frosting duration time is 20 min). Visually, as the defrosting goes on, the upper edge of the frost layer separates from the surface and the whole frost layer peels off from the surface by gravity completely. When the frost peels off from the surface, it has not melted completely. The mechanism of the frost peeling off is explained in Fig. 2(b). Because the heat flux transports from the hot side of the thermoelectric cooler to the surface and then to the frost, the frost close to the surface first melts, forming a water layer between the surface and the unmelted frost layer. Repulsed by the superhydrophobic surface with great water 3 / 16


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repellency and attracted by porous frost, water permeates into the frost layer quickly, separating the unmelted frost layer from the surface. As a result, the unmelted frost layer peels off from the surface just at the frost melting - water permeation stage but not at the meltwater evolution stage. If the frosting duration time is 30 min with a thicker frost of 0.84 mm thickness, the frost peeling off from the superhydrophobic surface during the frost melting - water permeation stage is more obvious (See supporting information Figure S2 and video S2). The defrosting experimental results reported by Kim et al. with much thicker frost (> 1 mm) also support our conclusions.31

Figure 2. Peeling off mode during defrosting on vertical superhydrophobic surfaces when the original frost layer is about 0.60 mm thickness. (a) Experiments: the upper edge of the frost layer separates from the surface and the whole frost layer peels off from the surface by gravity (See supporting information video S1 for multimedia); (b) mechanisms: water produced by frost melting permeates into the unmelted frost layer, separating the unmelted frost and the surface, then the unmelted frost peels off by gravity during the frost melting - water permeation stage (the meltwater evolution stage does not occur). The arc-shaped arrows represent peeling off behavior.

Frost jumping off from surfaces When the frosting duration time is 10 min with the measured frost thickness of 0.31 mm, the defrosting process on a vertical superhydrophobic surface is shown in Fig. 3 (See supporting information video S3 for multimedia). The frost layer breaks up and accumulates into many millimeter scale meltwater patches, which continue to evolve on surfaces by shrinking. As reported in the literature including our works, large amounts of surface energy can be released during the shrinking of meltwater with irregular shape, which easily triggers a self-propelled movement such as jumping.23-25 As seen in Fig. 3, the self-propelled jumping indeed occurs very frequently (the solid circles represent original meltwater patches, the dashed circles show clean surfaces after jumping, and the white arrows indicate shadows of jumping paths). These jumping movements are able to self-remove most meltwater patches, leaving an almost clean surface. As mentioned above, the defrosting stages will change with frost parameters such as the frost thickness on a 4 / 16


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vertical superhydrophobic surface. When the frost thickness is 0.31 mm, the defrosting process is quite different from that shown in Fig. 2 when the frost thickness is 0.60 mm. Easily understood, when the frost is thinner, the frost melting - water permeation stage would last for a shorter time, which means that the meltwater evolution stage comes sooner. Actually, when the frost layer of 0.31 mm thickness just begins to break up and accumulate (at about 12 s), the frost melting - water permeation stage is finished and the meltwater evolution stage begins, during which the jumping phenomena are triggered by meltwater shrinking.

Figure 3. Jumping off mode during defrosting on vertical superhydrophobic surfaces when the original frost layer is about 0.31 mm thickness (See supporting information video S3 for multimedia). Since the frost layer is very thin, the frost melting - water permeation stage is finished quickly. During the subsequent meltwater evolution stage, triggered by shrinking, the fragmentized meltwater patches jump off from the surface. The solid circles represent original meltwater patches, the dashed circles show clean surfaces after jumping, and the white arrows indicate shadows of jumping paths.

Although most meltwater patches jump off from the superhydrophobic surface, there are still some small droplets adhering on the surface, as shown in the image at 21 s in Fig. 3. This is because that jumping is an energy controlled phenomenon involving surface energy, viscous dissipation, work of adhesion, work of the retentive force and kinetic energy.37-39 Only when the released surface energy is enough to overcome the viscous dissipation and other negative energies, the jumping behavior would be triggered. The values of these energy forms are related to the size, the shape and the wetting mode of the meltwater, as well as the surface wettability. It means that not every meltwater patch could jump off from the surface and those without jumping would adhere on the surface. For the image at 21 s in Fig. 3, using proper image processing method,34 we extracted the profile of residual 5 / 16


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droplets, measured every droplet’s radius and calculated the total residual droplet volume. Figure 4 shows the profiles and statistical results of residual droplets. In total, 110 droplets (the total residual droplet volume is about 8.4 μL) were counted with their radii in the range of 0.15 to 0.45 mm. More than 76% of residual droplets locate in the radius range of 0.2~0.3 mm, only 7% of residual droplets whose radii are larger than 0.35 mm. The average radius (rave) was calculated to be 0.25 mm with a standard deviation of 0.06 mm. 60 5 mm

50 40

Count

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30 rave = 0.25 mm

20 10 0 0.15

0.20

0.25 0.30 0.35 0.40 Droplet radius, r (mm)

0.45

Figure 4. Profiles and statistical results of residual droplets on vertical superhydrophobic surface after defrosting when the frost layer is about 0.31 mm thickness. The radii range is from 0.15 to 0.45 mm with an average radius (rave) being about 0.25 mm. Most residual droplets (more than 76%) locate in the radius range of 0.2~0.3 mm.

For a water droplet adhering on a vertical surface, two forces are balanced including the gravity and the retentive force, as shown in Fig. 5. The gravity of the droplet is given by

G   water gV (1) where ρwater is the water density, g is the gravitational acceleration, and V is the droplet volume as

V

2  3cos  0  cos3  0 3  r (2) 3

where r is the droplet radius and θ0 is the surface static contact angle. The accessible maximum retentive force due to the contact angle hysteresis is calculated as 40-43

Fcah  kw lg  cos  r  cos  a  (3) where γlg is the liquid-gas surface tension, θa and θr are the advancing and receding contact angles, k is a dimensionless coefficient, and w is the maximum droplet contact width. For a droplet on a vertical surface, the real contact angle along the triple phase contact line varies with the azimuthal angle φ,44 i.e. When φ=0o, θ=θa; when φ=180o, θ=θr; when φ=90o, θ=θ0. Thus, the maximum droplet contact width, which corresponds to φ=90o, can be estimated as

w  2r sin  0 (4) Considering that the gravity and the accessible maximum retentive force are balanced, a critical droplet radius can be obtained as

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1

 6k lg  cos  r  cos  a  sin  0  2  (5) rcri   3    2  3cos  0  cos  0   water g  When the real radius of a droplet is larger than the critical value, the gravity dominates and the droplet rolls down from the surface; otherwise, the retentive force dominates, and the droplet adheres on the surface. For the Al-based superhydrophobic surface used here, the static, advancing, and receding contact angles of the superhydrophobic surface are measured to be 160.0±0.5o, 162.2±1.0o, and 158.3±1.0o. According to Eq. (5), with k being 2, 18 the calculated critical radius is 0.23±0.06 mm, which is consistent with the statistical average droplet radius (0.25±0.06 mm) with a relative deviation of 8%.

Figure 5. (a) Force analysis of a droplet adhering on vertical surfaces. G is gravity of the droplet, Fcah is the retentive force due to the surface contact angle hysteresis. (b) The triple phase contact line of the adhering droplet. w is the maximum droplet contact width, φ is the azimuthal angle along the triple phase line.

Threshold value of the frost thickness between peeling off and jumping off In above sections, we observed two self-removal modes, peeling off and jumping off, during defrosting on vertical superhydrophobic surfaces. Since both the frosting conditions (air temperature and humidity, surface temperature) and the defrosting method (natural defrosting) are the same in our experiments, we used frost thickness as a quantitative parameter to determine different frost self-removal modes. Our results show that when the frost is thick enough, the peeling off mode occurs; otherwise, the jumping off mode takes place. So, the question is, what is the threshold value of the frost thickness between peeling off and jumping off? To answer this question, a theoretical model was proposed based on frost melting – water permeation mechanism. It is known that when the surface temperature rises up to 0oC (melting point), the frost close to the surface begins to melt. In the model, we regard this moment as the initial time (t = 0). As shown in Fig. 6(a), assuming that when the original frost thickness is just the threshold value (hthr), after a period of time (Δt), xthr thick frost melts and the resulting water just completely permeates into the unmelted frost with a thickness of ythr, forming a meltwater (ice-water mixture) layer whose thickness is ythr. It is important to noted that, at the time t = Δt, the unmelted frost layer is saturated with water, indicating that the frost melting – water permeation stage is just finished. Note that hthr = xthr + ythr, and according to the mass conservation, xthr and ythr satisfy the following equation,

ice (1   )xthr   water ythr

(6)

where ρice is the ice density, ρwater is the water density, and ε is the frost porosity. Thus, the threshold value of the frost thickness is given by Eq. (7). To calculate hthr, we should determine ythr at time t = Δt. 7 / 16


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    hthr  1+ water y (7) ice (1   )  thr  As shown in Figure 6(b), at any given time t, after infinitesimal time dt, dx thick frost melts and the resulting water permeates into dy thick frost layer, forming a saturated meltwater layer with thickness of dy. According to the energy and mass conservation,

q '(t ) d t  ice (1   )Qlatent d x (8)

ice (1   ) d x   water d y

(9)

The left hand side of Eq. (8) is the transferred heat to the frost during dt time period, where q’ is the heat flux; the right hand side is the latent heat for dx thick frost melting, where Qlatent is melting latent heat of unit mass ice. If the heat flux is known, Eq. (8) and Eq. (9) can be solved simultaneously. However, sometimes, such as in our natural defrosting experiments, the heat flux is not known. But the surface temperature, which varies over time, is measured. For the meltwater layer, based on the Fourier’s law,

q '(t )  kmeltwater

T (t )  T0 (10) y (t )

where T0 is the interface temperature between the meltwater layer and the unmelted frost layer, which is approximately 0oC; kmeltwater is the weighted thermal conductivity, given by

kmeltwater  kwater  kice (1   ) (11) Substituting Eqs. (9) ~ (11) into Eq. (8) gives

y (t )

d y (t )  cT (t ) (12) dt

where, the coefficient c, which relates to the properties of frost, ice and water, is equal to

c

kwater  kice (1   ) (13)  water Qlatent

With the initial condition that t = 0, y = 0, Eq. (12) can be solved to obtain the solution y(t). If we can determine the time Δt, we can calculate the threshold value of the frost thickness according to Eq. (7). Next, based on our experiments, we will figure out y(t), determine Δt, and finally find the threshold value of the frost thickness, hthr.

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Figure 6. (a) Schematic of the threshold value of the frost thickness based on the frost melting – water permeation mechanism. During the whole frost melting – water permeation stage whose duration time is Δt, xthr thick frost melts and the resulting water completely permeates into the unmelted frost with a thickness of ythr, forming a meltwater (ice-water mixture) layer whose thickness is ythr, then the threshold value of the frost thickness, hthr, is equal to the sum of xthr and ythr. (b) Schematic of the frost melting – water permeation mechanism during infinitesimal time, dt. dx thick frost melts and the resulting water permeates into dy thick frost layer, forming a saturated meltwater layer with thickness of dy.

Mohs and Kulacki said in their book that the transition between the frost melting – water permeation and the meltwater evolution was less defined but they conjectured that the transition appeared to occur when the surface temperature is about 2.5oC.35 In our experiments, we measured the surface temperature variations, which is shown in Fig. 7(a). When the temperatures are near 2oC, there are obvious turning points while there is not near other temperatures. Figure 7(b) shows some picture evidences (magnifying defrosting figures when the original frost thickness is 0.31 mm). When the surface temperature is near 2oC (the third picture), tiny cracks appear on the frost layer and the frost begins to accumulate, indicating that meltwater evolution stage begins; when the surface temperature is about 2.7oC (the fourth picture), the cracks are more obvious that some isolated meltwater patches are already formed. Therefore, we assume that when the surface temperature is 2oC, the frost melting – water permeation stage is finished and the transition to the meltwater evolution stage occurs. As the partial enlarged drawing in Fig. 7(a) shows, it takes about 2 s for these surface temperatures to rise from 0oC to 2oC. So, we assume a linear function, T(t)=t, to approximately describe the surface temperature variations in this narrow range (0oC ~ 2oC). Then, the duration time Δt for the frost melting – water permeation stage is determined to be 2 s.

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Figure 7. (a) Surface temperature variations during defrosting process for different frost thickness. When the temperatures are near 2oC, there are obvious turning points while there is not near other temperatures. As the partial enlarged drawing shows, it takes about 2 s for these surface temperatures to rise from 0oC to 2oC, therefore, regarding the time when the surface temperature is 0oC as initial time (0 s), we assume a linear function, T(t)=t, to approximately describe the surface temperature variations in this narrow range (0oC ~ 2oC). (b) Defrosting figures showing real-time surface temperatures when the original frost thickness is 0.31 mm. When the surface temperature is near 2oC (the third picture), tiny cracks appear on the frost layer, indicating that frost begins to accumulate and the meltwater evolution stage begins; when the surface temperature is about 2.7oC (the fourth picture), the cracks are more obvious that some isolated meltwater patches are already formed.

With T(t)=t and the initial condition that t = 0, y = 0, y(t) is obtained by solving Eq. (12) as

y (t )  ct (14) Generally, the frost porosity is influenced by the surface wettability, the frosting conditions as well as the frost time, 45 but for convenience here, we assume that the frost porosity does not vary over frosting time. For the defrosting experiments when the original frost thickness is 0.84 mm, we collect the self-removed frost and measure its weight (0.272 g) by an electronic balance. Then, the porosity of original frost layer (ε) is calculated to be about 0.77. Substituting the frost porosity and other thermal properties of ice and water at 0oC temperature (See supporting information Table S1 for the parameter value we used) into Eq. (13), the coefficient c is calculated to be 3.6×10-9. Consider that the duration time Δt for the frost melting – water permeation stage is 2 s, the threshold value of the frost thickness is calculated to be 0.56 mm according to Eq. (14) and Eq. (7). In our experiments, peeling off mode occurs when the frost thicknesses are 0.60 mm and 0.84 mm which are larger than 0.56 mm, while jumping off mode takes place when the frost thickness are 0.31 mm. The calculated threshold value of the frost thickness agrees with the experimental results well, as shown in Fig. 8. According to our model, the threshold value of the frost thickness is related to the frost porosity and the surface temperature variation (or heat flux). Figure 8(a) shows the relation between the threshold value of the frost thickness and the frost porosity when the surface temperature variation satisfies T(t) = t. As the frost porosity increases, the threshold value of the frost thickness increases. Figure 8(b) shows the relation between the threshold value of the frost thickness and the heat flux when the frost porosity is constant. As shown, the threshold value almost increases linearly with increasing heat flux. Figure 8 also shows the predicted self-removal mode (peeling off or jumping off) during 10 / 16


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defrosting on a vertical superhydrophobic surface for a given frost thickness when the frost porosity and the heat flux are changed. These results could allow one to know how long to wait prior to defrosting to achieve the more effective peeling off mode. However, limited by our experimental conditions, we did not obtain frost layers with various porosity and did not apply various heat flux, so there are not large amounts of experimental points to further validate our model. We will work on it in our future work.

Figure 8. Relation between the threshold value of the frost thickness and (a) the frost porosity when the surface temperature variation satisfies T(t) = t or (b) the heat flux when the frost porosity is constant, as well as the predicted self-removal mode (peeling off or jumping off) during defrosting on a vertical superhydrophobic surface for a certain frost thickness.

Conclusions We conducted defrosting experiments on vertical Al-based superhydrophobic surfaces and investigated the frost self-removal mechanisms. Under the same frosting and defrosting conditions, when frost layer is relatively thick, the frost self-removes from the superhydrophobic surface completely by a way of peeling off during the frost melting – water permeation stage; when the frost is not thick enough, it breaks up and accumulates with the fragmentized meltwater patches jumping off from the surface at the meltwater evolution stage. As the jumping is influenced by many factors and limited by energy transformation, not every meltwater patch would jump and those without jumping would adhere on the surface after defrosting. It means that the jumping off mode is not as effective as the peeling off mode. Since both the frosting conditions and the defrosting method are the same in our experiments, we used frost thickness as a quantitative parameter to determine different frost self-removal modes. We proposed a theoretical model based on the frost melting – water permeation mechanism with the threshold value of the frost thickness determined. When the frost thickness is larger than the threshold value, the peeling off mode occurs during defrosting on vertical superhydrophobic surface; otherwise, the jumping off takes place. For our particular experiments, the predicted threshold value of the frost thickness agrees well with our experimental results. However, with some assumptions and approximations used, the predicted threshold value by our model is not precise, and limited by our experimental conditions, we did not obtain enough experimental points to further validate the model; therefore, there is still plenty of work to do in future.

Associated content Supporting information 11 / 16


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Frost thickness extraction process from side-view images of frost profiles using proper image processing method; defrosting process on vertical superhydrophobic surfaces when the original frost thickness is 0.84 mm (frosting time is 30 min); some thermal properties of water and ice at 0oC. (PDF) Video S1. Peeling off mode during defrosting on vertical superhydrophobic surfaces when the original frost thickness is 0.60 mm (frosting time is 20 min). (MP4) Video S2. Peeling off mode during defrosting on vertical superhydrophobic surfaces when the original frost thickness is 0.84 mm (frosting time is 30 min). (MP4) Video S3. Jumping off mode during defrosting on vertical superhydrophobic surfaces when the original frost thickness is 0.31 mm (frosting time is 10 min). (MP4)

Author information Corresponding author *E-mail: [email protected]; Tel: +86-10-62770558. ORCID Fuqiang Chu: 0000-0002-4054-143X Dongsheng Wen: 0000-0003-3492-7982 Xiaomin Wu: 0000-0001-7703-0038 Notes The authors declare no competing financial interest.

Acknowledgements This work was supported by the National Postdoctoral Program for Innovative Talents of China (No. BX20180024) and the National Natural Science Foundation of China (No. 51476084).

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Frost self-removal mechanism during defrosting on vertical

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