An experimental study of surface coatings to limit the impact of frosting

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Master of Science Thesis

KTH School of Industrial Engineering and Management Energy Technology EGI-2018-711

Division of Applied Thermodynamics and Refrigeration SE-100 44 STOCKHOLM

An experimental study of surface

coatings to limit the impact of

frosting

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Master of Science Thesis EGI 2018:711

An experimental study of surface coatings to limit the impact of frosting

Carl Andersson Approved 2018-10-18 Examiner Björn Palm Supervisor Erik Björk

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Abstract

Heat pumps are commonly used as a way to efficiently meet heating demands. The efficiency and flexibility of Air-source heat pumps (ASHPs) have improved in recent years and is an attractive heating solution suitable for houses with lower heating demands, as it is inexpensive to purchase and install compared to other heating solutions. However, ASHPs have a significant drawback as frost builds up on the evaporator surface in certain conditions, reducing both the heating capacity and efficiency, and therefore requiring regular defrosting to restore performance. Moreover, improvements for heat exchanger designs allowing for more compact and efficient units have not been able to be fully utilized in frosting conditions, as they are more quickly blocked by the buildup of frost and have poor meltwater drainage during defrosting.

This thesis aims to experimentally investigate the potential of hydrophilic and hydrophobic surface coatings to minimize the negative performance impact of frosting in Air-source heat pumps. A literature study was performed as a basis for the experiments, covering previous research on how frosting affects the performance of heat exchangers and ASHPs, methods, and control strategies for defrosting as well as a theoretical background of the mechanisms governing condensation, frost formation and growth, wetting and intended working principles of the tested surface treatments.

A test rig consisting of a wind tunnel inside a climate chamber was modified, and an automated defrost control was implemented based on the reduction in air velocity. Seven different surfaces: one superhydrophobic, five hydrophilic (one superhydrophilic, four hydrophilic foils), and one uncoated aluminum surface were tested in frosting conditions over multiple cycles of frosting and defrosting. Test conditions were held stable at a climate chamber set-point of 2 °C, 84 % RH and an initial air velocity over the test plate of 2 m/s. Data was collected, and the performance was compared in terms of duty cycle, (defined as the quotient between time operating in cooling mode and the time for a full cycle) and observations were made regarding differences in behavior during frosting and defrosting.

Test results showed that there was a clear difference between the different types of surfaces. Over cycles 10 - 25 the five hydrophilic surfaces performed the best, having an average duty cycle of 0.83, compared to the uncoated aluminum surface (0.69) and the superhydrophobic surface performing the worst with a duty cycle of 0.56. A gradual drop in duty cycle was observed for all of the tested surfaces, both from a shorter runtime and increased defrosting time. The variance in defrosting time was small between cycles. However, there was a larger variation in runtime between individual cycles. Some visual observations of the behavior during frosting and defrosting on the surfaces, such as the buildup of remaining meltwater after several defrosting cycles were analyzed and discussed in relation to the measured performance.

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Sammanfattning

Värmepumpar används vanligtvis som ett sätt att effektivt uppfylla värmebehov. Effektiviteten och flexibiliteten hos luftvärmepumpar (ASHP) har förbättrats de senaste åren och det är en attraktiv

uppvärmningslösning som är lämplig för hus med lägre värmebehov, bland annat eftersom det är billigt att köpa och installera jämfört med andra uppvärmningslösningar. ASHPs har emellertid en betydande nackdel eftersom frost byggs upp på förångarens yta under vissa förhållanden, vilket reducerar både uppvärmningskapaciteten och effektiviteten, och därmed kräver regelbunden avfrostning för att återställa prestandan. Dessutom har förbättringar för värmeväxlare och förångare möjliggjort mer kompakta och effektiva enheter som inte kunnat utnyttjas fullt ut under förhållanden då frost bildas, eftersom de snabbt blockeras av den växande frosten och har dålig avrinning av smältvatten vid avfrostning.

Denna avhandling syftar till att experimentellt undersöka potentialen hos hydrofila och hydrofoba ytbeläggningar för att minimera den negativa påverkan av frostning på luftvärmepumpar. En

litteraturstudie utfördes som underlag för experimenten. Studien täckte tidigare forskning om hur frosting påverkar luftberörda förångare och luftvärmepumpar, metoder och kontrollstrategier för avfrostning samt en teoretisk bakgrund av mekanismerna för kondensation, frostbildning och frosttillväxt ,vätning samt avsedda ändringar i egenskaper för de testade ytbehandlingarna.

En provrigg bestående av en vindtunnel inuti en klimatkammare modifierades och en automatiserad avfrostningskontroll implementerades baserat på minskningen av lufthastigheten i vindtunneln. Sju olika ytor, en superhydrofob, fem hydrofila (en superhydrofil samt fyra hydrofila folier) och en obelagd aluminiumyta testades under frostningsförhållanden över flera cykler av frostning och avfrostning. Testförhållandena hölls stabila vid ett börvärde i klimatkammare på 2 ° C, 84% RH och en initial lufthastighet över testplattan av 2 m/s. Uppgifterna samlades in och prestanda jämfördes med avseende på intermittensfaktor (definierad som kvoten mellan tiden som körs i kylningsläge och tiden för en fullständig cykel) och observationer gjordes beträffande skillnader i beteende under frostning och avfrostning.

Testresultaten visade att det var en tydlig skillnad mellan de olika typerna av ytor. Under cyclerna 10 - 25 presterade de fem hydrofila ytorna bäst, med en genomsnittlig intermittensfaktor på 0,83; jämfört med den obelagda aluminiumytan (0,69) och den superhydrofoba ytan som hade den lägsta intermittensfakorn på 0,56. En gradvis minskning av intermittensfaktorn observerades för alla de testade ytorna, både på grund av en kortare körtid och en ökad avfrostningstid. Avfrostningstiden varierade relativt lite mellan

individuella cykler, medan det var en större variation i körtid i kylningsläge mellan individuella cykler. Vissa visuella observationer av beteendet under frostning och avfrostning på ytorna, såsom uppbyggnad av återstående smältvatten efter flera avfrostningscykler, analyserades och diskuterades i förhållande till den uppmätta prestandan.

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Preface

This master thesis was performed at the Division of Applied Thermodynamics and Refrigeration at the Department of Energy Technology at KTH Royal Institute of Technology. The subject of this thesis was part of a larger Effsys-Expand project, Effektivare avfrostning av luftberörda förångare headed by Professor Björn Palm and Erik Björk at KTH in collaboration with Electrolux AB with the aim of evaluating several different methods of increasing the efficiency of heat pumps operating in frosting conditions.

First of all I would like to thank my supervisor Erik Björk for giving me the opportunity to perform this master thesis and for taking time to discuss new ideas or concepts and answer the many questions I had, as well as your patience during the whole process. I would also like to thank Joachim Claesson, Peter Hill and all the others at the department for your discussions where you have shared your knowledge and given me invaluable tips during lunch and coffee breaks. Additionally, I would like extend another thanks to Peter Hill for the help with learning and using Agilent VEE, which was used for the data collection and defrost software. Furthermore, I would like to thank Benny Sjöberg for helping me use the equipment for manufacturing the test plates. I would also like to thank Mikael Järn, Kenth Johansson and Mikko Tuominen at RISE for manufacturing some of the tested surfaces as well as answering my questions regarding surface science.

Lastly, I would like to thank my family, my girlfriend Johanna and my closest friends for their continuous support and patience during the whole time, I truly appreciate it.

Stockholm, July 2018 Carl Andersson

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List of figures

Figure 2.1 Contact angle of a drop resting on a surface, modified from[29]. ...- 6 -

Figure 2.2 Representation of the cohesive forces behind surface tension in a drop of water[31]. ...- 7 -

Figure 2.3 A drop on an inclined plane showing the advancing and receding contact angle as well as Contact Angle Hysteresis, adapted from[37]. ...- 8 -

Figure 2.4 Schematic representation of two different wetting modes a) Homogeneous wetting and b) Heterogeneous wetting, adapted from[39]. ...- 9 -

Figure 2.5 Psychrometric representation of condensation, adapted from[57] ... - 12 -

Figure 2.6 Change in Gibbs free energy as a function of nuclei radius, adapted from [58] ... - 14 -

Figure 2.7 The different stages of dropwise condensation frosting, with each stage in chronological order. The diagram on the left side indicates the different stages that may occur and the conditions necessary for them to occur. Reprinted from[18]. ... - 18 -

Figure 2.8 Typical frost structures of a hydrophilic and a hydrophobic surface. ... - 21 -

Figure 2.9 Typical defrost temperature profile during a passive defrost. During active defrosting, there is also a vaporizing and dry-heating stage with much higher temperatures after the frost has melted. ... - 22 -

Figure 2.10 Frosting map; showing frosting regions based on temperature and humidity, constructed by Zhu et al.[79] ... - 23 -

Figure 2.11 Common defrosting methods, adapted from[85]. ... - 24 -

Figure 3.1 Schematic illustration of the climate chamber. The heating and cooling unit on the left side is mounted to the roof. ... - 26 -

Figure 3.2 Schematic illustration of the wind tunnel. ... - 27 -

Figure 3.3 Picture of the wind tunnel. ... - 27 -

Figure 3.4 Schematic illustration of the cooling module and test plate. ... - 28 -

Figure 3.5 Simplified flowchart of the data collection and defrost control program ... - 29 -

Figure 3.6 Test plate dimensions and features. ... - 30 -

Figure 4.1 Test plate temperature for three of the tested surfaces ... - 33 -

Figure 4.2 Percentage of time spent running for each of the 30 first cycles... - 34 -

Figure 4.3 Cycle times for the 30 first cycles ... - 35 -

Figure 4.4 Runtime for the 30 first cycles ... - 35 -

Figure 4.5 Defrost time for the 30 first cycles ... - 35 -

Figure 4.6 Duty cycle for each surface over cycles 10-25 with a standard deviation ... - 36 -

Figure 4.7 Retained water after defrosting for 4 of the tested surfaces, a) after 1 cycle, b) after 3 cycles, c) after 5 cycles, d) after 10 cycles, d) after 20 cycles. The image on the left shows a zoomed in view and the image on the right shows a view of the rightmost part of the test plate from top to bottom. ... - 38 -

Figure 4.8 Observation of different freezing behavior. Top row shows an image during freezing and the bottom row shows the uncoated and superhydrophilic surface 30 seconds later, and the superhydrophobic surface 5 minutes later. ... - 39 -

List of tables

Table 1 Contact angles of the tested surfaces ... - 31 -

Table 2 Test conditions during experiments ... - 31 -

Table 3 Test conditions and settings used during testing. ... - 31 -

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Nomenclature

Abbreviations

ASHP Air-Source Heat Pump

CAH Contact Angle Hysteresis

CNT Classical Nucleation Theory COP Coefficient of Performance

SAM Self-Assembled Monolayer

Symbols

𝐴 Interface area [m2_]

𝐴𝑙𝑣 Area of the liquid-vapor interface [m2] 𝐴𝑠𝑙 Area of the solid-liquid interface [m2]

𝐶𝑂𝑃1𝐶𝑎𝑟𝑛𝑜𝑡 Coefficient of Performance of heating for a Carnot cycle

𝑓 Solid surface area fraction 𝑔 Gravitational acceleration [m/s2_]

∆𝐺 Change in Gibbs free energy [J]

∆𝐺𝑐 Critical energy barrier for successful nucleation [J]

𝐼 Pre-exponential factor

𝐽 Embryo formation rate

𝑘𝐵 Boltzmann constant [J/K] 𝐿 Effective contact line length [m]

𝑚 Mass [kg]

𝑀 Molar mass [kg/mol]

𝑃𝑣 Local vapor pressure [Pa] 𝑃𝑣0 Saturation pressure of vapor [Pa]

∆𝑃 Pressure difference between the inside and the outside of the drop [Pa]

𝑟 Radius [m]

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viii 𝑟𝐹 Surface roughness factor

𝑅 Universal gas constant [J/mol∙K] 𝑅1−2 Radius of curvature [m]

𝑇 Temperature [K]

𝑇𝐶 Temperature at the cold side [K] 𝑇𝐻 Temperature at the hot side [K]

𝑉 Volume [m3_]

𝑊𝑎𝑑ℎ Work of adhesion required to remove a drop from a surface

𝛾𝑙𝑣 Liquid-vapor surface tension [N/m] 𝛾𝑠𝑙 Solid-liquid surface tension [N/m] 𝛾𝑠𝑣 Solid-vapor surface tension [N/m] 𝜃𝐴 Advancing contact angle [°] 𝜃𝑎𝑝𝑝 Apparent contact angle [°]

𝜃𝐸 Static contact angle or Young’s angle [°] 𝜃𝑅 Receding contact angle [°]

𝜃𝑇 Tilt angle of the plate [°]

𝜌 Density of the condensing water vapor [kg/m3_]

𝜎 Surface free energy [J/m2_]

𝜎𝑙𝑣 Liquid-vapor surface energy [J/m2] 𝜎𝑠𝑙 Solid-liquid surface energy [J/m2] 𝜎𝑠𝑣 Solid-vapor surface energy [J/m2]

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1 Introduction

1.1 Background

Condensation can occur on a surface if the temperature of the surface is below the dew point of the surrounding moist air. Additionally, if the temperature of the surface is below 0 °C, frost will start to form on the surface; either by condensing and then freezing (called condensation frosting), or by directly desublimating on the surface[1]. In many engineering applications involving heat transfer, condensation is often favorable since it can lead to significantly increased heat transfer. Frost, which is also commonly occurring is generally not preferable[2]. The accretion of frost and ice has a negative impact on the performance or safety in many different fields, for example, wind turbines, aviation, power lines, and refrigerant-to-air heat exchangers[3–6]. Although the mechanisms governing the formation of frosting and icing are different, they share many similarities and objects exposed to frosting conditions may experience icing from supercooled rain or fog as well.

For low-energy houses, air-source heat pumps (ASHPs) are an attractive heating solution because of the low installation cost and low heating capacity requirement. As the usability, efficiency and capacity of ASHPs improve and heating requirements decrease, heating solutions with a lower investment cost such as ASHPs are expected to become more attractive[7].

Despite being frequently used in other climates; air source heat pumps have one major problem during certain conditions. When the evaporator temperature is below 0°C, which happens with an outdoor temperature a bit over 0°C and especially during humid conditions there is a significant buildup of frost on the heat exchanger fins. This buildup of frost can cause several problems in the heat exchangers, leading to a reduced performance or even damage[8]. Frost buildup may reduce or obstruct the airflow over the heat exchanger, leading to a higher pressure drop and reduced air flow. This leads to a decrease in heat transfer[9]. The frost also acts as an insulating layer, lowering the heat transfer between the air and the evaporator. These two effects can lead to a heat transfer reduction in the heat exchanger by as much as 50 – 75 %, and a capacity decrease of 29 %[5,10]. The lowered heat transfer also leads to lower energy efficiency for the heat pump and unless defrosted, can make the heat pump unable to meet the heating demand.

Improvements in modern heat exchangers consisting of flat multichannel tubes and louvered fins have increased the heat transfer and have allowed heat exchangers to become more compact and efficient. In addition to this, microchannel heat exchangers require less refrigerant charge than conventional fin-and-tube heat exchangers, because of their much smaller refrigerant channels and more compact size [11]. One major drawback of these new heat exchangers is that they are much more susceptible to frosting for two major reasons. Firstly, frost builds up and obstructs the airflow between the fins more quickly because of the tight fin spacing. Secondly, heat exchangers with flat tubes and louvered fins generally have poor drainage of water during defrosting cycles which allow the remaining water to quickly freeze again[12–14]. Many areas of Sweden experience conditions where frosting occurs, with temperatures between 6 °C and -15 °C and over 50 % humidity during as much as 34 - 73 % of all hours annually [15]. In these areas, the reduction in efficiency of ASHPs with traditional heat exchanger designs during frosting conditions is around 10 %[16]. Using the modern design of heat exchangers with flat multichannel tubes and tightly spaced louvered fins the percentage of efficiency decrease during frosting is expected to be increased and may negate the possible efficiency improvements compared to traditional evaporator designs. Thus, reducing these problems allows manufacturers to use these new types of heat exchangers in environments where frosting may occur.

The majority of research on frosting has historically been focused on modeling the growth and properties of the frost layer thickness, and often ignored or simplified the different incipient modes of frosting. For example, the incipient stages of frost formation from dropwise condensation frosting, film condensation frosting and deposition differ and results in frost with different properties. A study by Sommers et al.

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showed that the frost density on hydrophilic surfaces was 20 - 26 % higher and hydrophobic surfaces had a 37 - 41 % reduced frost density compared to an uncoated aluminum surface[17]. The focus of many previous studies has been from an engineering standpoint of correlating environmental properties such as temperature, humidity and air velocity with properties of the frost such as thermal properties, density and growth rate to find useable models for predicting performance under frosting characteristics. However, many earlier models have ignored the incipient stage; condensation and the onset of freezing, as well as not included the surface wettability, focusing predominantly on modeling the properties during the frost thickness growth and the mature frost growth stage[17].

In recent years, with the breakthroughs in nanotechnology and ease of manufacturing functional surface coatings with hydrophilic or hydrophobic properties, more research has been done on the effect of surface coatings during frosting conditions. Older studies have mainly been on untreated surfaces, and often without taking surface characteristics into consideration.

The hydrophilic or hydrophobic characteristics of a surface affect the incipient stages of condensation and frost formation; before it is completely covered and the frost layer begins to grow in the thickness direction. There have also been some studies concerning the incipient stages of frosting in the last years focusing on the mechanisms governing the incipient stages of frosting[1,18,19].

1.2 Aims and Purpose

The aim of this thesis is to investigate the potential of surface treatments to minimize the impact of defrosting in heat pumps. This thesis is done as a part of a larger project in order to increase the efficiency of ASHPs in conditions where frosting can occur and in a broader perspective contribute to a reduced energy usage. Lastly, this thesis aims to contribute to the knowledge of what types of surface characteristics are desirable to minimize the impact of frost formation.

1.3 Methods

As a first step, a literature study was performed investigating how frosting affects ASHPs, what different methods for defrosting are used and different control strategies for initiating defrost cycles. The mechanisms governing condensation, frost formation, nucleation and frost thickness growth, as well as wetting and hydrophobic and hydrophilic surface treatments have been studied to gain a deeper understanding of the problem and the different approaches used to minimize the impact of frosting. Previous research in this area is also studied and compared.

Next, experiments were performed. A wind tunnel used for the experiments was modified with additional measurement probes, and a number of test runs were performed to ensure steady conditions could be achieved at the desired level. In addition to this, a program was created in the software Agilent VEE to collect the measurements and to automate the test procedure to ensure reliable initiation and ending of defrosting cycles. After this, seven different surfaces were tested in multi-cycle tests during frosting conditions and data was collected and evaluated.

In the end, the experimental results from the tests such as duty cycle, the time between defrosting and time spent defrosting as well as visual observations for the different surfaces was compared and analyzed.

1.4 Limitations

This degree project is conducted in one semester and has therefore been limited to correspond to this timeframe. The work has been limited to investigating only frost formation resulting from condensation frosting on a flat vertical plate in a wind tunnel and not on an actual evaporator surface of an air heat pump in operation. These experiments aim to demonstrate a general potential for mitigating the effect of frosting and reducing energy use for an air heat pump and for a more general result that can then be used as a basis for future studies on air heat pumps.

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A delimitation was made when the study only examines the kind of frost formation that occurs when the moisture first condenses on the surface and then freezes (condensation frosting). Other types of frost formation, by desublimation or ice formation coming from supercooled rain or fog, are not examined. The study was performed on seven different surfaces.

The size and scope of the research surrounding the various stages of frost formation, heat and mass transfer and thermal properties of frost, surface treatments, and strategies to minimize the impact of frosting are immense, and the research area is not exhausted. This is indicated by the fact that no practical passive solution to avoid frost formation has been found that doesn’t disrupt operation; despite the fact that the problem of frost formation has always existed, and been known in areas where the climate allows this to happen.

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2 Literature study

Several different concepts are of importance for understanding and characterizing the behavior during condensation frosting and defrosting. This chapter has been divided into different parts, covering different subjects related to the performance of different surfaces during frosting and defrosting and the connections between the different parts. The parts are mainly presented in chronological order, as they occur during frosting and then defrosting. In addition, the impact of surface characteristics during the individual stages of condensation frosting and defrosting is discussed.

2.1 Air source heat pumps

A heat pump works by extracting heat from a lower temperature source and rejects heat to a higher temperature heat sink. Air source heat pumps use the outside air as a low-temperature heat source to heat the inside of a house.

The main components of a heat pump operating a vapor compression cycle are the compressor, evaporator, condenser and an expansion device, usually a valve. The heat transfer is done by using an appropriate working fluid, often called a refrigerant that circulates between the hot and cold side of the heat pump.

The basic principle of a heat pump is that the compressor maintains two pressure levels and temperatures at either side of the heat pump. At the lower temperature and pressure side, the refrigerant is allowed to evaporate in the evaporator and thus absorb latent heat from the low-temperature source. The vaporized refrigerant is then compressed and enters the high-temperature side where it condenses and rejects the heat to the high-temperature heat sink. The refrigerant then passes through the expansion device and enters the low-pressure side to complete the cycle.

The maximum theoretical heating efficiency of an ASHP can be calculated by its Coefficient of Performance, (COP). 𝐶𝑂𝑃1𝐶𝑎𝑟𝑛𝑜𝑡= 𝑇𝐻 𝑇𝐻− 𝑇𝐶 ( 2-1 ) Where,

𝐶𝑂𝑃1𝐶𝑎𝑟𝑛𝑜𝑡 is the Coefficient of Performance of heating for a Carnot cycle

𝑇𝐻 is the temperature at the hot side in Kelvin. 𝑇𝐶 is the temperature at the cold side in Kelvin.

During frosting the frost acts both as an insulating layer evaporator increasing the thermal resistance and blocks airflow over the evaporator, further decreasing heat transfer[20]. The lowered heat transfer leads to a decrease in the rate of evaporation in the evaporator, and a decrease of the evaporator superheat; causing a pressure and temperature drop in the evaporator. This, in turn, causes a lower refrigerant flow and a lower compressor work; however, the decrease in evaporator heat transfer is much more significant than the reduction in compressor work[21]. In summary, this leads to a drop in both heating capacity and a lower COP of the system[20].

2.1.1 Evaporators

In an ASHP, as the name implies the evaporator uses air as a heat source. Evaporators are usually designed with the refrigerant flowing in tubes and the air passing over them. Since the heat transfer coefficient of air is much lower than the refrigerant flowing in the tube, fins are used to increase the air-side heat transfer area, and a fan is used to further increase the heat transfer by forced convection. The types of heat exchangers used are usually categorized by the shape of the section in which the refrigerant flows in, either a tube or a plate and the shape of the fins surrounding the tube or plate[22].

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To further increase the heat transfer, rather than having straight fins, modern heat exchangers fins are wavy or have strips cut and lifted in them; so called louvered fins to reduce the boundary air film thickness [23,24].

Older designs for ASHPs used in areas that may experience frosting conditions had evaporators with a fin spacing of around 5-6 mm to improve the time between defrosting, but modern designs utilizing a more effective defrosting process can have fin spacing as close as 1.3 to 2.5 mm[23].

In summary, heat exchangers with tighter fin spacing are more affected by frosting than fins with wider fin spacing. An experiment performed by E. Macchi et al. on fin-tube evaporators with different fin spacing (2, 4.5 and 7 mm) showed that the reduction in performance was more significant for the evaporator with closely spaced fins compared to the one with a wider fin spacing[25]. The most important factor behind the performance drop was the reduction in air velocity and mass flow over the evaporator from the frost which was more severe for the tighter spaced fins[25,26]. In line with this, compact microchannel evaporators were shown to be less effective than conventional fin-and-tube coil evaporators during frosting conditions[13,14].

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2.2 Wetting of a surface

Wettability describes the tendency of a liquid to spread out when placed on a solid or another liquid. This happens because of an imbalance of forces when two materials contact[27]. This imbalance causes the liquid drop to either increase the contact area by spreading out on the surface or balling up, minimizing the contact area with the surface. Theories relating to wetting and in particular the wetting of rough surfaces and droplet mobility are reviewed as well as the difference between different contact angles and their correlation with different properties such as droplet mobility. As such, the theory and concepts presented in this section are important in many different aspects that determine the performance of a surface during frosting conditions and defrosting. For example, a surface with high droplet mobility (low hysteresis) should have excellent drainage characteristics, allowing condensate droplets to slide off before freezing and leave less water on the surface after defrosting, whereas a surface with a low droplet mobility (large hysteresis) may retain a lot of meltwater after defrosting that quickly refreezes and reduces performance

2.2.1 Contact angle

In the case of a pure liquid on a perfectly flat surface, the liquid drop will have a particular angle at the intersection of the liquid-solid and liquid-vapor interface measured by the tangent line from the three phase contact line and along the liquid-vapor interface as shown in figure 2.1[28].

Figure 2.1 Contact angle of a drop resting on a surface, modified from[29].

This angle, 𝜃 called the static contact angle is an often used measurement to determine the wettability of a surface. Drops with a small contact angle (𝜃 < 90°) have a tendency to lay flat and spread over a large area, indicating low wettability while drops while drops with a large contact angle (𝜃 > 90°) will tend to not spread out and is said to have a poor wettability[28]. The angle is the result of a mechanical equilibrium of the different forces acting on the three-phase contact line. When stationary, in mechanical equilibrium the forces on the drop are described by Young’s equation [30].

𝛾𝑠𝑣− 𝛾𝑠𝑙− 𝛾𝑙𝑣cos 𝜃𝐸 = 0 ( 2-2 )

Where,

𝛾𝑠𝑣 is the solid-vapor surface tension

𝛾𝑙𝑣 is the liquid-vapor surface tension, often simply referred to as the surface tension 𝛾𝑠𝑙 is the solid-liquid surface tension

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2.2.2 Surface tension

The surface tension of the liquid mainly determines the shape of a droplet. In a single-component liquid such as pure water, each molecule in the interior of the droplet is pulled in by the surrounding molecules equally from all directions. But the molecules at the surface of the droplet are pulled in by the cohesive forces from the surrounding molecules towards the center, creating an internal pressure as shown in figure 2.2. Other external forces such as gravity also influence the shape of a drop, and as such, the contact angle is dependent on both surface tension (interfacial forces) and external forces[28].

Figure 2.2 Representation of the cohesive forces behind surface tension in a drop of water[31].

The increased pressure in a drop due to the surface tension is called Laplace pressure and is determined by the Young-Laplace equation, which for a spherical drop (𝑟 = 𝑅1= 𝑅2) becomes:

∆𝑃 = 𝛾𝑙𝑣( 1 𝑅1 + 1 𝑅2 ) =2𝛾 𝑟 ( 2-3 ) Where,

∆𝑃 is the pressure difference between the inside and the outside of the drop [Pa] 𝛾𝑙𝑣 is the surface tension of the drop [N/m]

A result of the Young-Laplace is that the pressure is larger in smaller drops as they have a smaller radius curvature than larger drops[32]. The effect provides an explanation for the ability of water vapor to supersaturate before a phase change is initiated. The phase change that occurs when water vapor condenses on a plate starts with microscopic droplets or clusters that then grow in size before they are visible to the human eye. The microscopic droplets have a large internal pressure and require a certain activation energy to form the surface of the new droplet[33].

2.2.3 Contact Angle Hysteresis

In the above examples, it has been assumed that the liquid droplets consist of pure water and are placed on an ideal, perfectly homogenous and flat surface without defects. In that case, the angle observed for a drop resting on the surface is the correct contact angle according to Young’s equation. However, in reality a surface has chemical or physical imperfections such as dirt or scratches. A drop resting on a non-ideal surface may show a contact angle greater or smaller than the theoretical contact angle. A drop resting on the real, non-ideal surface will show a changing contact angle without spreading or moving when water is added or removed from the drop or the drop is tilted. The drop will show a maximum or a minimum angle, known as advancing contact angle 𝜃𝐴 and receding contact angle 𝜃𝑅 (RCA) before spreading or

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contracting, or when resting on an inclined plane as seen in figure 2.3[32]. The difference between these angles is called the Contact Angle Hysteresis, CAH and both methods are used to determine advancing and receding contact angles. But, research has showed that the tilting plate method can result in different values for the advancing and receding contact angle. For example, the measured angles can depend on the initial angle of the plate when placing the drop and may on some surfaces be dependent on the amount of time the drop has rested on the surface[34–36]. As such, the tilting plate method may not be a suitable method for determining 𝜃𝐴 and 𝜃𝑅[30].

Figure 2.3 A drop on an inclined plane showing the advancing and receding contact angle as well as Contact Angle Hysteresis, adapted from[37].

2.2.4 Different wetting regimes on rough surfaces

There are two distinct ways a drop can wet a rough surface. The first way is the homogeneous wetting regime where the liquid thoroughly wets the rough surface, filling all the cavities, scratches and pits completely, shown in figure 2.4a. This wetting mode on rough surfaces leads to the apparent or observed contact angle being more extreme than on a flat surface. Drops on hydrophilic rough surfaces are wet more entirely than on similar smooth ones leading to even smaller contact angles. However, it also makes it harder for drops to wet hydrophobic surfaces, and may “pin” the contact line of the drop resulting in a large apparent contact angle [32]. This type of wetting is often referred to as the Wenzel state. The Wenzel equation relating the apparent contact angle with Youngs’ contact angle and surface roughness for this wetting regime is:

cos 𝜃𝑎𝑝𝑝= 𝑟𝐹∙ cos 𝜃𝐸 ( 2-4 )

Where,

𝜃𝑎𝑝𝑝 is the apparent contact angle,

𝑟𝐹 is the surface roughness factor, defined as the ratio of the true surface area to its projected flat area[38]. This equation can explain why droplets exhibit more extreme contact angles in the Wenzel state. Since 𝑟𝑓 = 1 for a perfectly smooth surface and 𝑟𝑓 > 1 for rough surfaces the apparent contact angle is greater than on flat surfaces for 𝜃𝑎𝑝𝑝> 𝜃𝐸> 90° and smaller when 𝜃𝑎𝑝𝑝< 𝜃𝐸 < 90°, with the effect being more pronounced at angles further away from 90°[32].

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Figure 2.4 Schematic representation of two different wetting modes a) Homogeneous wetting and b) Heterogeneous wetting, adapted from[39].

In the second mode of wetting a textured surface on which the droplet rests on is heterogeneous. Since the surface is a composite, i.e., from two or more materials (or air), each with their own corresponding Young’s contact angle, the apparent contact angle is a result of all of the different materials[32]. If a rough material is hydrophobic it is possible for liquid to not completely wet the surface; instead, pockets of air can become trapped in the cavities and pores of the surface forming a heterogeneous, composite solid-air interface. Droplets rest on the bumps of the surface and the trapped pockets of air as shown in figure 2.4b. Droplets in this wetting state typically exhibit very large contact angles and low contact angle hysteresis[30]. As such only a fraction of the contact is between the liquid and the solid surface, and the rest is between the liquid and the trapped air. This wetting regime is often referred to as the Cassie-Baxter state. The equation describing the apparent contact angle in this example is a particular case of an equation called Cassie’s law that applies to wetting of composite surfaces. When a liquid droplet rests on a composite interface of trapped air and a homogeneous solid surface the Cassie-Baxter equation becomes:[30]

cos 𝜃𝑎𝑝𝑝= 𝑓 ∙ cos 𝜃𝐸+ (𝑓 − 1) ( 2-5 )

Where,

𝑓 is defined as the solid surface area fraction.

As seen from this equation, a low solid surface area fraction leads to a significantly increased apparent contact angle. In some cases, the equation is also presented with the addition of a surface roughness factor similar to the one in the Wenzel equation added to 𝑓 ∙ cos 𝜃𝐸, to account for geometry and roughness factors on the structure[40,41].

A droplet resting on a rough surface can exhibit either of the two wetting states or a combination and can transition from one state to the other.

Surface roughness on hydrophobic materials leads to higher contact angles in both of the wetting modes. The highest contact angles reported on smooth surfaces is approximately 120°, surfaces exhibiting higher contact angles have some form of surface roughness that leads to a higher apparent contact angle[42].

2.2.5 Criticism of the Wenzel and Cassie-Baxter theories

Both theories by Wenzel and Cassie have been criticized in many papers as early as 1945 for the premise that the contact angle is a result of the solid-liquid contact area, and not the three-phase contact line[30]. A paper titled “How Wenzel and Cassie Were Wrong” published in 2007 by McCarthy and Gao aimed at bringing attention to the fact that the contact angle is determined by the forces acting on the three-phase line and employed an experiment designed to illustrate this[43]. The experiment was similar to a previous experiment done by Extrand in 2003, both using specially prepared surfaces with a different surface in a

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small area that would be entirely inside the contact area of the drop[30,44]. Extrand used two surfaces, one hydrophilic surface with a hydrophobic spot in the middle and a mildly hydrophobic surface with a mildly hydrophilic spot, and Gao and McCarthy used a mildly hydrophobic surface with a superhydrophobic spot inside the contact area of the droplet. Both experiments showed that the conditions at the three-phase line determined the contact angle and not the contact area[30]. From this, McCarthy and Gao argued that the knowledge that the contact area approach made by Wenzel and Cassie were wrong was nothing new; as shown by earlier publications. But, since nothing has changed in the field and that the belief that the characteristics of contact area determined contact angle still exist, they felt that it was necessary to try and correct this misconception[45,46].

However, most researchers agree that Wenzel’s and Cassie’s theories are of great importance in surface science and that they are useful, even if the derived equations are faulty, and in order to successfully use them their inaccuracies should be known[30,43,45,46]. Since then several different approaches have been proposed, such as using a modified version of the original Wenzel and Cassie-Baxter equations using the specific roughness or area fractions along the three-phase contact line[43].

2.2.6 Droplet mobility

An important aspect in wetting studies is the ability of a drop to resist movement. The amount of force needed for a drop to start moving or the tilt angle needed on an inclined plate for a drop to slide off is critical in many situations both in nature and in engineering applications, for example in the case of water drainage on evaporator surfaces. The force or tilt angle required to move a drop along a surface is a function of the contact angle hysteresis and have been expressed by many similar equations, where one of the notable early expressions were proposed in 1962 by Furmidge[45]. Below is a more recent example from a 2013 article by Wu et al. including a coefficient for the effective contact line length[47]

𝐹 = 𝑚𝑔 sin 𝜃𝑇 = 𝐿𝛾(cos 𝜃𝑅− cos 𝜃𝐴) ( 2-6 )

Where;

𝑚 is the mass of the liquid droplet 𝑔 is the gravitational acceleration 𝜃𝑇 is the tilt angle of the plate 𝐿 is the effective contact line length 𝜃𝑅 is the receding contact angle 𝜃𝐴 is the advancing contact angle

Here, L is dependent on the surface geometry of the surface roughness and determines the effective length on which surface tension forces are applied along the contact line[47]. This variable, the effective contact line length, exists in several variants and is also expressed as the drop diameter or radius times a geometry factor[36,48].

The work required to remove a drop from a surface is also important, often referred to as the work of adhesion. The work can be calculated by the Young-Dupré equation and relates the work of adhesion to Young’s contact angle. However, since drops resting on real surfaces exhibit hysteresis and the receding contact angle is the minimum contact angle drops exhibit when shrinking; the work of adhesion is sometimes expressed by the receding contact angle instead of the static contact angle[49]. Both versions continue to be used, and it seems that there is no clear consensus on which is correct as seen by a comment on and a subsequent reply on a recent publication[50–52].

𝑊𝑎𝑑ℎ= 𝛾(1 + cos 𝜃𝑅) ( 2-7 )

Where,

𝑊𝑎𝑑ℎ is the work of adhesion required to remove a drop from a surface.

In summary, these two equations (2-6 and 2-7) show that droplet sliding and adhesion are different mechanisms, and that a surface exhibiting a very high contact angle may not necessarily mean that

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droplets can slide off easily. Since only the static contact angle is used in almost all cases to define whether a surface is hydrophobic or hydrophilic, the terms may be misleading since there is no direct behavior related to the terms[53]. A hydrophilic surface with low contact angle hysteresis may very well be “slippery,” requiring a very low tilt angle or force for droplets to slide off and a hydrophobic surface can be “sticky,” pinning droplets in place[45]. Because of this, other terms have been proposed, for example, shear hydrophobicity, relating to the force required for a drop to slide contact angle hysteresis and tensile hydrophobicity, relating to the work required to remove a droplet from the surface to better describe and characterize surfaces[54].

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2.3 Condensation and Frost formation

Condensation is the process of the phase transition of vapor to liquid. It can take place on a surface if the temperature of the surface is below the dew point of the surrounding moist air. Additionally, if the surface temperature is below 0 °C the condensed vapor may freeze and form an incipient porous frost layer on the surface; this process is called condensation frosting. If both the surface temperature and the dew point temperature is below 0 °C, water vapor may directly desublimate on the surface as frost [1].

The change in chemical potential during a phase change can be described by the equation ∆𝐺 = 𝑛∆𝜇 = −𝑛𝑅𝑇 ln (𝑃

𝑃0) assuming the vapor to be ideal[2]. The expression can also be written as[33]:

∆𝐺 = −𝜌𝑉𝑅𝑇

𝑀 ln ( 𝑃

𝑃0) ( 2-8 ) Where,

∆𝐺 is the change in Gibbs free energy. 𝑃 is the local vapor pressure of water 𝑃0_{is the saturation pressure of vapor} 𝑅 is the universal gas constant

𝜌 is the density of the condensing water vapor 𝑉 is the volume of the condensing water vapor 𝑇 is the temperature of the condensing water vapor 𝑀 is the molar mass of water

For this transition to occur and for a cluster of atoms to form, a certain Gibbs energy barrier must be overcome; consisting of the energy required for the creation of new interfaces around the embryo [55]. To overcome this energy barrier, there must be a specific temperature difference ∆𝑇𝑠𝑢𝑝 or a supersaturation pressure ∆𝑃𝑠𝑢𝑝 between the dew point and the surface [2,33]. This means at the surface, the temperature of the moist air is below the dew point temperature and consequently, the local vapor pressure is supersaturated, it is often referred to as either supersaturated, subcooled or supercooled with respect to the saturated vapor pressure in the literature[56].

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This condensation process with supersaturated vapor over a flat plate can be represented in a psychrometric chart, shown in figure 2.5. Humid air (A) flowing over a cold plate is cooled down past the dew point (𝐴𝑠𝑎𝑡) until the free energy barrier is overcome, which happens at point (B). From (B) the supersaturated vapor condenses, i.e., the phase change from vapor to liquid takes place (B-C) and the liquid embryo forms. The travel between different points (A-B) and (B-C) represents the combined energy removal occurring during the process in terms of sensible heat (A-B) and latent heat (B-C)[57].

2.3.1 Nucleation

The amount of energy required for the creation of the new interfaces is dependent on the surrounding air and surface conditions. That is; the activation energy required for the formation of new interfaces depends on the surface energy for a given interface and the area of the interfaces, i.e., the surface area between the nucleating embryo and the air or the surface[55]. This is the basis for Classical Nucleation Theory (CNT) used to describe why supersaturated conditions are needed before nucleation occurs[55]. This applies to phase transitions in general; water can be subcooled before freezing and superheated before boiling for the same reason, that there exists a free energy barrier that must be surpassed in order for successful nucleation and a subsequent phase transition to occur[2].

An important distinction is that a phase transition initiated by the formation of a tiny particle (nuclei) of the new phase can happen in two different ways; either entirely within the surrounding environment of the parent phase called homogeneous nucleation or at a particle or surface acting as a nucleation site called heterogeneous nucleation[55]. Since the concept of homogeneous nucleation is more straightforward, it is used to describe the general concepts in classical nucleation theory even though heterogeneous nucleation is relevant in this thesis. Although the description in the following sections is from the perspective of condensation the same principle applies to the freezing of the droplets.

2.3.1.1 Homogenous nucleation

Because of the energy required for the creation of new interfaces in the case of nucleation, the expression ∆𝐺 for the phase transition must also include the surface free energy. In the case of homogeneous nucleation this becomes[33]:

𝑀 ln ( 𝑃

𝑃0) + 𝐴𝜎 ( 2-9 )

Where,

𝐴 is the area of the interface

𝜎 the surface free energy per unit area.

Assuming the nuclei to be a sphere with radius 𝑟 equation (2-9) gives[33]: ∆𝐺 = −4 3 𝜋𝑟3_𝜌𝑅𝑇 𝑀 ln ( 𝑃 𝑃0) + 4𝜋𝑟 2_𝜎 ( 2-10 )

The equation (2-10) has a maximum at one point for 𝑟 > 0 as 𝑟 increases since 𝑟2_{> 𝑟}3_{for small 𝑟, and} 𝑟2< 𝑟3for large 𝑟 as seen in figure 2.6.

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Figure 2.6 Change in Gibbs free energy as a function of nuclei radius, adapted from [58]

Figure 2.6 shows the change in the Gibbs free energy associated with a nucleating sphere with radius 𝑟. The volume free energy change is the driving energy in the phase transition and the surface free energy for the creation of the new interface is the hindering factor.

For a system to be in equilibrium the change in the Gibbs free energy is a minimum, and according to the second law of thermodynamics, all mechanical or chemical systems will tend to spontaneously proceed towards a state that results in a lower free energy of the system.

If a condensation drop has a radius smaller than 𝑟𝑐, then it is expected to get smaller and smaller until it disappears since spontaneous processes that minimize the Gibbs free energy is favored. Conversely, if the embryo has a radius greater than 𝑟𝑐 it is expected to grow indefinitely. This happens as at a critical supersaturation a nuclei of radius 𝑟𝑐 is in an unstable equilibrium with the supersaturated vapor, and if it were to increase in radius past 𝑟𝑐, then ∆𝐺 would decrease as it grows, favoring the further growth of the drop[2,33]. Using equation (2-10) and setting 𝑑∆𝐺/𝑑𝑟 = 0 the critical radius 𝑟𝑐 can be found:

𝑑∆𝐺 𝑑𝑟 = − 𝑟𝑐𝜌𝑅𝑇 𝑀 ln ( 𝑃 𝑃0) + 2𝜎 = 0 → 𝑟𝑐 = 2𝑀𝜎 𝜌𝑅𝑇 ln (_𝑃𝑃₀) ( 2-11 ) Substituting into equation (2-11) to find the minimum energy required for successful nucleation gives:

∆𝐺𝑐= 16𝜋 3 𝜎3 [𝜌𝑅𝑇_{𝑀 ln (}_𝑃𝑃0)] 2 ( 2-12 ) Where,

∆𝐺𝑐 is the critical, minimum energy barrier to be overcome for successful nucleation.

This can also explain why the vapor needs to be subcooled for a phase transition to first occur. Considering a bulk system, and thus without considering interfaces a phase transition might be favorable, however for a nucleus with 𝑟 < 𝑟𝑐, nucleation is unfavorable and only favorable for embryos larger than 𝑟𝑐[2].

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- 15 - 2.3.1.2 Heterogeneous nucleation

Heterogeneous nucleation is much more common and is the mode of nucleation happening when water vapor condenses on an evaporator surface. The reason for why heterogeneous nucleation is the prevailing mode of nucleation is that the surface energy for a heterogeneous nucleating site or surface is lower than for homogeneous nucleation; meaning the energy required for forming the new interface is lower and thus having a lower Gibbs energy barrier for successful nucleation[33]. This also means that for sites where heterogeneous nucleation is favored, (with a low Gibbs energy barrier) the critical supersaturation needed for successful nucleation is less. The required supersaturation is strongly dependent on the surface energy, which can be observed as the wettability of the surface and can be measured as the contact angle of a drop resting on the surface.

The embryo that forms during heterogeneous nucleation on a surface is in contact with both the surface and the surrounding air. The nucleating embryo needs to form an interface with both the solid surface and the surrounding vapor. In this case, the equation for ∆𝐺 becomes[55]:

𝑀 ln ( 𝑃

𝑃0) + 𝐴𝑙𝑣𝜎𝑙𝑣+ 𝐴𝑠𝑙(𝜎𝑠𝑙− 𝜎𝑠𝑣) ( 2-13 ) Where,

𝐴𝑙𝑣 is the area of the liquid-vapor interface. 𝜎𝑙𝑣 is the liquid-vapor surface energy. 𝐴𝑠𝑙 is the area of the solid-liquid interface. 𝜎𝑠𝑙 is the solid-liquid surface energy. 𝜎𝑠𝑣 is the solid-vapor surface energy.

Since the embryo favors a minimum energy state under thermodynamic equilibrium, the embryo will be in the shape of a spherical cap, similar to a droplet resting on a surface as shown in figure 2.1. Assuming that the surface is flat, inserting the equations for a spherical cap and using the fact that 𝜎𝑙𝑣cos 𝜃 = −(𝜎𝑠𝑙− 𝜎𝑠𝑣) into equation (2-13) gives[2]:

∆𝐺 = [−𝜌𝑅𝑇 𝑀 ln ( 𝑃 𝑃0)] 1 3𝜋𝑟 3_{(1 − cos 𝜃)}2_{(2 + cos 𝜃)}

+ 𝜎𝑙𝑣[2𝜋𝑟2(1 − cos 𝜃) − 𝑟2𝜋(1 − cos 𝜃2) cos 𝜃]

( 2-14 )

Which simplifies into:

∆𝐺 = [−1 3𝑟 𝜌𝑅𝑇 𝑀 ln ( 𝑃 𝑃0) + 𝜎𝑙𝑣] 𝜋𝑟2(1 − cos 𝜃)2(2 + cos 𝜃) ( 2-15 ) Similarly to homogeneous nucleation, the critical radius 𝑟𝑐 for heterogeneous nucleation can be found by using equation (2-15) and setting 𝑑∆𝐺/𝑑𝑟 = 0:

𝑑∆𝐺 𝑑𝑟 = −𝑟𝑐 𝜌𝑅𝑇 𝑀 ln ( 𝑃 𝑃0) + 2𝜎𝑙𝑣 = 0 → 𝑟𝑐= 2𝜎𝑙𝑣 𝜌𝑅𝑇 𝑀 ln ( 𝑃 𝑃0) ( 2-16 )

Substituting equation (2-16) into equation (2-15) gives the minimum energy required for successful heterogeneous nucleation on a smooth surface[2]:

∆𝐺𝑐 = 4𝜋 3 𝜎3 [𝜌𝑅𝑇_{𝑀 ln (}_𝑃𝑃₀)] 2(1 − cos 𝜃)2(2 + cos 𝜃) ( 2-17 ) Where,

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The resulting equation is similar to the one obtained for homogeneous nucleation, equation (2-12). The equation for homogeneous nucleation is larger by a factor of 4 but without the (1 − cos 𝜃)2_{(2 + cos 𝜃)} term which has a maximum value of 4 at 𝜃 = 𝜋. This shows that the energy barrier for successful nucleation is smaller for heterogeneous nucleation and that condensation can happen much earlier on high energy surfaces (high 𝜎𝑠𝑣) exhibiting a low contact angle, 𝜃.

The rate of steady state nucleation, i.e., the rate of nuclei of critical size formed can be written in the form of an Arrhenius-type equation[33]:

𝐽 = 𝐼 ∙ 𝑒

−∆𝐺𝑐

𝑘_𝐵𝑇 ( 2-18 ) Where:

𝐽 is the rate of embryo formation 𝐼 is a pre-exponential factor 𝑘𝐵 is the Boltzmann constant 𝑇 is the temperature

In this equation, ∆𝐺𝑐 is the activation energy, the free energy barrier for successful nucleation. Many different expressions and values for 𝐼 have been proposed, based on both Classical Nucleation Theory and other approaches and are beyond the scope of this thesis[2,33,59]. However, the exponential term has by far the most significant impact on the calculated nucleation rate[33]. A certain threshold value for 𝐽 before nucleation can be observed has also been proposed ranging from 106_{to 10}12_{, depending on if the} phase transition is boiling, condensing of freezing; but the value can be chosen rather arbitrarily as the function has such a large dependence on the supercooling or supersaturation. A change of temperature, 𝑇 by as little as 1 °C can increase or decrease the rate of formation by as much as three to four orders of magnitude[2,57]. This can also help explain why although the chance for successful nucleation to occur is a statistical phenomenon, the transition from no condensation being observed to when condensation can be observed occurs almost immediately at a very narrow range of temperature for any given vapor pressure[2].

2.3.1.3 Important considerations regarding nucleation

From the reasoning of classical nucleation theory, it is apparent why vapors may be supersaturated without condensation occurring. However, this only applies to the incipient stages of condensation on dry surfaces; as soon as a surface is wet, a vapor-liquid interface already exists, and condensation occurs at the saturation pressure. This would normally be the case for evaporator surfaces during operation as some moisture would be expected remain after defrosting.

An interesting result of the fact that supersaturation only occurs over dry surfaces is the fact that there can exist a vapor pressure gradient around condensing droplets and because of this gradient, which depends on the diffusion rate of water vapor there exists a critical distance from a droplet where new nucleation does not occur[60].

When condensate nucleates on normal structured superhydrophobic surfaces, the critical radius is so small that the droplets form in between the structures in a Wenzel state[61]. On normal superhydrophobic surfaces, this condensate layer stays in an impaled state as it freezes and shows a higher ice adhesion than compared to flat surfaces[62,63]. Ice adhesion is not of great importance in this study since the frost layer formed on an evaporator is not expected to detach under its own weight as it may be possible in other cases, such as rime or glaze ice on wind turbines or aircraft [42]. As the frost layer melts, the droplets stay impaled in a Wenzel state and do not transition into a Cassie-Baxter state even when mechanically vibrated, leaving impinged droplets after defrosting cycles[64]. On the other hand, superhydrophobic surfaces with multiple length scale (nano- and microscale) textures have shown to be able to shed

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meltwater formed from condensate in certain conditions[61]. As such, conventional superhydrophobic surfaces do not seem like a promising solution to the frosting problem in real-use, multi-cycle applications[63].

Additionally; in reality, dust particles or surface imperfections serve as nucleation sites leading to successful nucleation much earlier than what the presented examples of nucleation may suggest[2]. In almost all practical cases it is impossible to avoid these types of nucleation sites; especially during long-term use on surfaces that aren’t rigorously cleaned and maintained. In the application studied in this thesis; air-side evaporator surfaces in ASHPs it is unlikely that any significant long-term nucleation suppression effect can be observed, especially as any remaining moisture after defrosting will quickly freeze again and act as a nucleation site[61].

2.3.2 Different stages of the early condensation frosting process

The process of condensation frosting involves many steps, each with different mechanics and different characteristics. A more general description of the condensation frosting process has been made where it was divided into three stages, suitable both for dropwise and filmwise condensation. These three steps can be summarized briefly as, (1) condensation where droplets or a film form, grow and supercool over time, (2) a nucleation stage where the supercooled droplets or film freeze and (3) a crystal growth stage and frost growth in the thickness direction[1].

It has recently been shown that individual heterogeneous ice nucleation in each droplet is not the dominant mechanism of freezing during dropwise condensation frosting, where most droplets freeze via a process called inter-droplet ice bridging, where frozen droplets grow ice bridges towards neighboring liquid droplets which freezes upon contact with the ice bridge[1]. This, along with other recent advancements of our understanding of condensation frosting process was summarized in a recent review performed by Nath et al. where they present five different stages in the dropwise condensation frosting process and the mechanics that govern each stage[18]. These five stages occur during dropwise condensations and subsequent freezing which happens on hydrophobic surfaces. The frosting process that starts with film-wise condensation does not exhibit all of these stages, and although not all of the stages are of great importance in this thesis, they help explain the rationale behind some of the approaches towards achieving anti-icing surfaces.

The five stages are, (1) Supercooled condensation, (2) Onset of freezing, (3) Frost Halos, (4) inter-droplet ice bridging and dry zones and (5) Percolation clusters and frost densification[18]. These five stages are briefly described below and illustrated in figure 2.7.

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Figure 2.7 The different stages of dropwise condensation frosting, with each stage in chronological order. The diagram on the left side indicates the different stages that may occur and the conditions necessary for them to occur. Reprinted from[18].

2.3.2.1 Supercooled condensation

This step can be described in two stages, a heterogeneous nucleation of droplets on the surface and growth of the newly formed droplets. The newly formed droplets are supercooled (below 0°C) and grow from the ambient water vapor. As mentioned earlier the newly formed droplets can grow at saturated conditions since the vapor-liquid interface already exists, and because of this a vapor pressure gradient around each growing droplets forms[60]. This results in a rapid initial growth until the areas overlap and the vapor gradient around the droplets take on an essentially 1-dimensional profile perpendicular to the surface, and the growth of the droplets slows down. This continues until droplets grow sufficiently large and close to each other to coalesce, resulting in fewer but larger droplets and sometimes leaves space where new droplets can nucleate and grow[18].

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- 19 - 2.3.2.2 Onset of freezing

After condensation and successful growth, the supercooled droplets may freeze. The freezing of the droplet is also a nucleation event, as described in the above section and is thus a probabilistic event requiring a certain degree of subcooling. As the droplets are resting on the cold surface, they gradually cool from the bottom until the water near the surface reach a temperature where ice nucleation occurs[18]. Since droplets exhibiting a higher contact angle has less contact with the surface, and even less if they are resting in a Cassie state, the conductive heat transfer area from the cold surface is minimized, and they cool slower, resulting in delayed freezing of droplets[65]. The delayed freezing of the droplets also has an additional benefit since it may allow the droplets to grow large enough to slide off the surface before freezing[65].

The freezing itself starts with a rapid recalescence where the temperature of the drop jumps up to 0 °C, and the liquid in the drop becomes a slushy mix of water and ice followed by a much slower internal freeze front propagating through the drop, the speed of which depends on the heat transfer away from the freezing drop[66].

2.3.2.3 Frost halos

Since the temperature of the drop during recalescence jumps from its supercooled temperature to 0 °C, the droplet will evaporate so that the local vapor pressure around the droplet becomes the saturation pressure of water vapor over ice at 0 °C. If the vapor pressure required for nucleation is less than the saturation pressure of vapor over ice at 0 °C, a ring of newly nucleated condensate droplets will form around the freezing droplet[18,66].

2.3.2.4 Inter-droplet ice bridging and dry zones

When the droplet has frozen and cooled the saturated vapor pressure over itself (over ice at its temperature) is much lower than that around surrounding unfrozen droplets, since the saturation pressure over ice is lower than that over water[67]. Unless the surrounding condensate halo that formed during recalescence has frozen, it will evaporate, and be harvested by the larger frozen droplet[66]. This will also create a local dry zone around the frozen droplet where all the liquid droplets will evaporate[60].

The frozen drop will act as a local humidity sink, harvesting water from other nearby droplets[60]. When doing this the frozen droplet will form an ice bridge towards the liquid droplet, that will grow until it either touches the liquid droplet and freezes it, or entirely evaporates the liquid drop before the ice bridge can reach it, or the liquid droplet is frozen by another ice bridge growing towards it[1]. This is illustrated in the flowchart in figure 2.7, where 𝑆∗_{is a spreading parameter indicating successful ice bridging} when 𝑆∗_{< 1.}

This phenomenon is responsible for the dominant freezing mechanism of droplets formed during dropwise condensation, and is also why a “freezing front” can be observed moving over a plate of freezing condensate droplets, which would not happen if the droplets would freeze in isolation as a result of a nucleation event inside each drop[1].

This can help explain why superhydrophobic surfaces can retard frost formation for such an extended time in some instances. Superhydrophobic surfaces exhibiting easy and early droplet removal and a low droplet surface coverage can have unsuccessful ice bridging, significantly slowing the freezing process. The freezing process, (ice bridging) is usually started at the edges of a surface due to edge defects and freeze in towards the plate. A more deliberate approach towards anti-icing surfaces aims to exploit this phenomenon, either by tuning the distance between droplets by designing nucleation sites to achieve unsuccessful ice bridging or surrounding the nucleation sites with a film of antifreeze liquid to disrupt ice bridging[18].

An experimental study of surface coatings to limit the impact of frosting

An experimental study of surface

coatings to limit the impact of

frosting

Abstract

Sammanfattning

Preface

Table of Contents

List of figures

List of tables

Nomenclature

Abbreviations

Symbols

1 Introduction

1.1 Background

1.2 Aims and Purpose

1.3 Methods

1.4 Limitations

2 Literature study

2.1 Air source heat pumps

2.2 Wetting of a surface

2.3 Condensation and Frost formation