Fog Collection on Polyethylene Terephthalate (PET) Fibers: Influence

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Fog collection on polyethylene terephthalate (PET) fibers: Influence of cross-section and surface structure Md. Abul Kalam Azad, Tobias Krause, Leon Danter, Albert Baars, Kerstin Koch, and Wilhelm Barthlott Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b00478 • Publication Date (Web): 05 Mar 2017 Downloaded from http://pubs.acs.org on March 7, 2017

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Fog collection on polyethylene terephthalate (PET) fibers: Influence of cross-section and surface structure M. A. K. Azad†*, Tobias Krause†‡, Leon Danter§, Albert Baars§, Kerstin Koch£& Wilhelm Barthlott† †

Nees Institute for Biodiversity of Plants, Rheinische Friedrich-Wilhelms-University, Bonn, Germany ‡

Department of Mechanical Engineering, Westphalian University of Applied Sciences, Bocholt, Germany

§

Department of Biomimetics, Faculty of Nature and Technique, Bremen University of Applied Sciences, Bremen, Germany

£

Faculty of Life Sciences, Rhine-Waal University of Applied Sciences, Kleve, Germany

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ABSTRACT

Fog collecting meshes show a great potential to ensure the availability of a supply of sustainable fresh water in certain arid regions. In most cases, the meshes are made of hydrophilic smooth fibers. Based on the study of plant surfaces, we analyzed the fog-collection of different polyethylene terephthalate (PET) fibers with different cross-sections and different surface structures with the aim of developing optimized biomimetic fog collectors. Water droplet movement and the onset of dripping from fiber samples were compared. Fibers with round, oval, and rectangular cross-section with round edges showed higher fog-collection performance than other cross-sections. However, other parameters, e.g., width, surface structure, wettability etc. also influenced the performance. Directional delivery of collected fog droplets by wavy/v-shaped microgrooves on the surfaces of the fibers enhances the formation of a water film as well as their fog collection. A numerical simulation of the water droplet spreading behavior strongly supports these findings. Therefore, our study suggests the use of fibers with round cross-section and microgrooved surface, and an optimized width for an efficient fog collection.

INTRODUCTION

The United Nations Conventions to Combat Desertification (UNCCD) reports that by 2025 around 2.4 billion people will be living in the areas with an absolute water scarcity 1. The report also indicates the scarcity of water as a trigger for conflicts as well as population displacement. Fog, being ubiquitous in certain arid regions, e.g., Namib and Atacama Desert, may be a sustainable fresh water resource to alleviate water scarcity. Different biological role models – the ‘living prototypes’ are the inspiration for biomimetic applications due to their structural


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principles and functionalities

2, 3

. Each of the existing species has gone through evolutionary

change in response to particular environmental conditions and thereby developed an optimized technical solution. 2 Marloth, a pioneer of fog-collection research used reeds (grass-like plants) bundles to measure the fog precipitation on Table Mountain in South Africa 4. Based on the idea, numerous fogcollection projects were conducted by exploiting mainly wire and fiber meshes

5, 6, 7, 8

. Fog

collectors made of polyolefin meshes have been used for decades 9, 10, 11. These fog collectors are of low efficiency (~20%) 8. However, by modifying the meshes, usually used in the fog collectors, their collection efficiency can be optimized. For example, development of a threedimensional fabric has been reported 10, the use of a multi-funnel fog collector has been proposed 12

, water collection and release behavior of a temperature sensitive polymer coated cotton fabric

has been demonstrated 13, some design rules of fiber network, e.g., theoretical width of the fiber, gap length between the fibers, low contact angle hysteresis (CAH) of the fiber surface with a contact angle of ~100° 14, and a design for an optimized biomimetic fog collector based on the hierarchical surface architecture of a plant model 15 were proposed. The potential of artificial silk fiber 16, 17, 18, 19 and electrospun nanofibers 20, 21 to collect fog and dew was shown. Conical wires, a hydrophilic-hydrophobic cooperative system and/or patterned structures etc., have been demonstrated in the aim of better fog-collection efficiency 22, 23, 24, 25, 26, 27, 28, 29, 30, 31. Plants capable of fog collection in different foggy regions have structured leaves, needle shaped leaves, spine shaped structures etc.

15, 32, 33, 34, 35, 36

. For example, Namib dune bushman

grass (Stipagrostis sabulicola) was demonstrated to collect a higher amount of fog than the Namib beetle (Onymacrys unguicularis) 37. Pines, redwoods and firs with needle shaped leaves have shown a good fog-collection ability 7. Their leaf morphologies are being considered as


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potential models for developing efficient fog collecting meshes. The needles or needle like structures of the plants have different cross-sections, e.g., round, triangular, rectangular, rectangular with round corners and/or edges etc., and they have different surface microstructures as well. In contrast, the surfaces of the ribbons or fibers of the meshes that have been used for the last few decades to collect fog are usually smooth 38. However, the influences of different fiber cross-sections have thus far not been studied. Therefore, fog droplet behavior on 14 PET fibers with different cross-sections and surface structures, e.g., microgrooves, is analyzed to investigate their influence on fog-collection efficiency. Efficient fog collection largely depends on the effective transport of captured fog droplets.

15

In this case, anisotropic wetting or directional wetting phenomenon can be implemented as a mode of droplet transport by either patterning surface free energies or designing geometrically anisotropic structures

39, 40

. Wenzel and Cassie-Baxters’ contact angle models reported the

wettability behavior of the surfaces comprised of asperities and grooves of different shapes, randomly distributed on them as well as textured/grooved surfaces 41, 42. According to Wenzel’s model, the droplet liquid wets and fills surface grooves completely. Whereas Cassie-Baxters’ model assumes an interface composed of both solid and ambient gas under the liquid droplet. Many other physical insights of the grooves on the surfaces during fog droplet impact and directional spreading of liquids have been extensively analyzed in previous studies 48, 49, 50, 51, 52

43, 44, 45, 46, 47,

. Therefore, they are intentionally not a focus of this study; rather the droplet

dynamics and transport on the fibers, and their implications for fog collection are studied here.

EXPERIMENTAL SECTION


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Fiber samples: 14 different polyethylene terephthalate (PET) fibers (Nextrusion GmbH Bobingen, Germany), referred to as profiles in the text, with different cross-sections were used. They have widths between 317 µm and 2300 µm. They were grouped into two categories. Category A: consists of the profiles 1–7 with width less than 1 mm and Category B: consists of the profiles 8–14 with width larger than 1 mm. Sample preparation: Long fibers were cut into pieces of 2 cm in length and they were used as single fiber samples. Multiple fiber samples were also used. Fibers of 2 cm in length were aligned vertically, parallel to each other, wherein the distance between the adjacent fibers was as identical as possible for every 2x2 cm2 sample (Figure 1a). The gap between two fibers was approximately equal to their widths. Samples were prepared in such a way that they have an equivalent effective surface area for fog collection. About ~55% surface area of each sample was occupied by the fibers and the rest was free to prevent the impedance of the fog flow. The surface area coverage of the samples was calculated from their images by Photoshop CS3. Light- and scanning electron- microscopy: Samples were analyzed by a Keyence VHX-1000 digital microscope (Keyence Corporation, Japan) and a Stereoscan 200 SEM (Scanning Electron Microscope) (Cambridge, U.K.). Specimens were coated with gold for 30 s at 60 mA (sputter coater, Balzers Union SCD040, BAL–TEC AG, Liechtenstein) prior to SEM analysis. Contact angle (CA) measurement: Contact angle measurements were performed by a goniometer (DataPhysics OCA 20, Filderstadt, Germany). The difference between advancing and receding contact angle is contact angle hysteresis (CAH). CAH was measured by increasing the volume of a demineralized water droplet from 2 to 5 µl and decreasing from 5 to 2 µl at a rate of 0.1µl/s. The delay time was 5 s. All measurements were taken at room temperature (21°C). Because all fibers are composed of PET, a CA of a 5 µl of water droplet on a fiber with smooth


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surface and large width (profile 14) was measured. Average and standard deviation from 10 measurements were calculated. Experimental setup: Droplet deposition behavior on the surfaces of the fibers as well as their fog-collection was analyzed by the setup shown in Figure 1b. Samples were mounted vertically at 17 cm (Figure 1b) from the outlet of an ultrasonic humidifier (Honeywell, BH–860E; outlet diameter 3.2 cm, fog output maximum 0.4L/h). Fog flow velocity was ~1.6 m/s at 17 cm from the outlet (velocity measured by Testo 416 anemometer, Lenzkirch, Germany). The temperature was 19–20°C and the relative humidity was 75–85%. For documentation a digital SLR camera (Nikon D 90 with a medical Nikkor lens) was used. The amount of water dripped down the samples in the container placed under the samples as well as with the remaining water on the samples was measured (by KERN EMB 200–3, KERN & Sohn GmbH, Germany) over 30 min to determine their efficiency. Water collected in the container together with the remaining water on the fibers is referred to as total collected water. Control experiments (5 times each of 30 min) without the samples were also conducted.

a

b

Figure 1. (a) Schematic of a multi-fiber sample; the width of a fiber in the sample as well as the gap between two consecutive fibers is approximately identical. (b) Schematic of the setup for fog-collection experiment (adapted with permission 38, Copyright IOP 2015).


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Simulation: Fog droplet behavior on fiber surfaces was investigated also by a numerical simulation. Different surface parameters, e.g., contact angles; dimensions of the grooves etc. were set up in the simulation. To analyze the behavior of the droplet with time, the continuity and momentum equation, as well as an additional transport equation for the phase fraction gas/liquid, have been solved using the interDyMFoam algorithm of the open source software OpenFOAM (Version 2.3.1). To determine the gas-liquid interface OpenFOAM applies the Volume–of–Fluid–Method (VOF). Figure 2 shows a schematic of a grooved fiber surface, the initial position of the water droplet, as well as values for the geometry, surface and fluid properties. The discretization schemes are of second order in time and first/second order in space.

ρl = 1000 kg/m3

ρg = 1.0 kg/m3

vl = 1 x 10-6 m2/s

vg = 1.48 x 10-5 m2/s

σ = 0.072 kg/s2

θ = 62°

h = 15 µm

λ = 113 µm

d = 100 µm

L = 1000 µm

Figure 2: Schematic of a wavy microgrooved surface (wave length λ, amplitude h/2, length in z direction L) and initial position of a spherical water droplet (diameter d). Densities ( and viscosities (ν) are given for the liquidand gas phase indexed with l and g, respectively. The contact angle on the surface is θ and the surface tension is . The gravitational force is pointing in the negative z direction.

The basic mesh (simulation parameter) consists of 75600 hexahedral cells with an average non-orthogonality of 8.26°. During calculation an increase in number of cells took place; every 7 ACS Paragon Plus Environment

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second time step a mesh refinement at both sides of the liquid/gas interface led to an improved interface capturing.

RESULTS

Fog-collection by the fibers with different cross-sections, widths and surface structures is analyzed in this study. A negligible amount of fog water (14 ± 4 µg) was collected in the container by the control experiment. In the following section findings from the study are discussed. I

II

640 µm

III

439 µm

570 µm

IV

VI

V

988 µm

556 µm

VII

490 µm

IX

VIII

317 µm 1337 µm

1277 µm

X

XII

XI

1243 µm

FOG FLOW

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1503 µm

1372 µm

XIV

XIII

2289 µm

2122 µm


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Figure 3: Cross-sections of 14 fiber profiles used. Average values of their widths are given. The directional placement with respect to fog flow during the fog-collection experiment for both single and multi-fiber samples is indicated at the right side of the figure.

Cross-sections of the fibers: Cross-sections and dimensions of 14 different fibers are given in Figure 3(I–XIV). Roman numbers (I-XIV) are used to indicate the figures to make them consistent with the fiber profile numbers. Widths of the fibers are given in Table 1. Table 1: Widths (average ± standard deviation) of the fiber profiles 1-14. Profiles in Category A Widths (µm) Profiles in Category B Widths (µm)

a

d

1

2

3

4

5

6

7

640 ± 2

570 ± 1

439 ± 1

556 ± 1

988 ± 2

490 ± 2

317 ± 2

8

9

10

11

12

13

14

1277 ± 1

1337 ± 1

1243 ± 4

1372 ± 2

1503 ± 2

2289 ±2

2122 ± 3

b

c

e

Figure 4: (a-e) Scanning electron micrographs (SEMs) of structured surfaces of fiber profiles 2, 8, 10, 11 and 12, respectively. Microgrooves can be seen on the surfaces of profile 2 in (a), profile 8 in (b) and profile 11 in (c). Facets/angular faces on the surfaces of the fiber profiles 10 in (d) and 12 in (e) (marked with the arrows).


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Surface structures: Surface structures of profiles 1–14 were analyzed with scanning electron microscope. Microgrooves can be seen on the surfaces of fiber profiles 2, 8 and 11, shown in Figure 4a-c, respectively. Facet (angular faces) like structures, due to their polygonal shapes/cross-sections, on the surfaces of fiber profiles 10 (Figure 4d) and 12 (Figure 4e) can be seen. Other fiber profiles have smooth surfaces (Figure S1a-i in Supporting Information). Wavy microgrooves on the surfaces of profiles 2 and 8, and v-shaped microgrooves on the surface of profile 11 are schematically illustrated in Figure 5a-b, respectively. Characteristics of the microgrooves have been summarized in Table 2.

a

b

Figure 5: Illustration of the characteristics of (a) wavy microgrooves of profile 2 and 8, and (b) V-shaped microgrooves of profile 11. The ridges are also marked on the right side of the figures. Here, λ is the peak to peak distance of the grooves, h is groove depth and θ is the angle between the walls of the grooves.


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Table 2: Characteristics of the microgrooves on fiber profiles 2, 8 and 11. The values represent average ± standard deviation. Characteristics

Profile 2

Profile 8

Profile 11

Groove depth (h in µm)

15 ± 0.6

28 ± 0.7

111 ± 0.6

Peak-peak distance (λ in µm)

117 ± 1.4

260 ± 0.8

686 ± 2

Angle between the walls of a groove (θ in degrees)

130 ± 1.3

126 ± 1

146 ± 1.4

Surface wettability: Contact angles were measured on a smooth PET fiber (Profile 14). Advancing contact angle (θadv) was 78° ± 2, receding contact angle was (θrec) 45° ± 3 and contact angle hysteresis (CAH) was 34° ± 2. Influence of cross-section and surface structure on fog collection: The amount of water dripped down as well as the amount of total collected water (dripped down + remaining on the fibers) by the samples was measured (Figure 6). In category A, profile 2 (rectangular crosssection with round edges (Figure S2 in Supporting Information) and microgrooved surface) collected the highest amount of fog water (2121 ± 156 µg) followed by profile 7 (1772 ± 118 µg) with an oval cross-section and smooth surface. Profiles with rectangular cross-sections with round corners and smooth surfaces were not as efficient (1109 ± 221 µg, and 1203 ± 226 µg by profile 3 and 4, respectively) as profiles 2 and 7. Profiles 1 (elliptical cross-section) and 6 (round cross-section) showed higher efficiencies (1534 ± 130 and 1349 ± 116 µg, respectively) than profiles 3 and 4. Profile 1 has a larger width than profile 3 and 4; and profile 6 has a larger width than profile 3 (Figure 3 and Table 1). Profile 5, though has an elliptical cross-section but due to a larger width (988 µm ± 2) and smooth surface, showed one of the lowest efficiencies in this


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category. Profile 3 (rectangular cross-section with round corners and smooth surface) showed the lowest fog collection ability.

a

b

Figure 6: Amount of water dripped from multi-fiber samples made of 14 fiber profiles, and total water (dripped down + remaining on the fibers) collected by the samples over 30 min. (a) Category A: profiles 1–7, (b) Category B: profiles 8–14.


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In category B profile 11, having round cross-section and v-shaped microgrooves, was shown to be the most efficient fog collector (1431 ± 120 µg) followed by profile 8 having similar crosssection but wavy microgrooves. It is to be noted that profile 11 has a larger width than profile 8 (see Table 1). However, the difference in their collection efficiency can be explained by deeper grooves of profile 11 than those of profile 8 (Table 2). Profiles 9 (triangular cross-section) and 10 (polygonal cross-section) collected higher amount of water than profiles 12 (hexagonal crosssection) and 13 (parallelogrammatic cross-section) due to their smaller widths (Table 1) compared to the latter two. Profile 14 contains hooks (Figure S3) that improved the capture of fog droplets as well as the transport through the channels. That’s why Profile 14, though has a larger width than profile 12, had a higher water collection than the latter one. Profile 13 showed the lowest fog collection because of its largest width among the profiles. Water collection efficiency is also related to a fast directed movement of the deposited water on the fiber surfaces. Time required for the first droplet to move to the bottom of single fiber samples and the onset of dripping of water drops from the single fiber of each profile was recorded and the data are shown in Figure 7a–b. In category A (profiles 1–7), profile 2 and 5 took about the same time (38 ± 8 and 41 ± 2 s, respectively) for the 1st droplet to move to the bottom, while a large difference occurred in their onset of dripping (98 ± 10 and 151 ± 8 s correspond to profile 2 and 5, respectively). Profile 2, which was proved to be the most efficient in fog collection, took shorter time (38 ± 8 s) for the 1st droplet to move to the bottom than profile 7 (62 ± 8 s), the second most efficient, but both took about the same time for their onset of dripping (98 ± 10 and 94 ± 6 sec, respectively). This is because of the smaller width of profile 7 (~317 µm) than profile 2 (~570 µm). Similar results can be seen in category B too.


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a

b

Figure 7: Time required for the first droplet to move to the bottom of single fiber samples, and onset of dripping of water drops from a single fiber of each profile of (a) category A (profiles 1-7) and (b) category B (profiles 8-14).

It took 61 ± 9 and 31 ± 1 s for profile 8 and 11, respectively for the 1st droplet to move to the bottom. They both have microgrooves on their surfaces. But they took a longer time (171 ± 23 and 159 ± 10 s for profile 8 and 11, respectively) than profile 2 (98 ± 10 s) for the onset of dripping. However, profile 11 proved to be efficient on both cases, i.e., droplet movement and 14 ACS Paragon Plus Environment

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onset of dripping, in this category due to the larger depth of the grooves than profile 8 (Table 2). Other profiles of this category (category B) took much longer time as shown in Figure 7b. Channels in the shorter sides of the rectangular fiber profile 14 (Figure S3 in Supporting Information) improved the transport compared to profiles 9, 10, 12 and 13. Fog droplet behavior on different fiber profiles: Fog droplet behavior on the surfaces of all fiber profiles was analyzed. In single fiber samples, except profile 2, 8 and 11, the deposition of tiny fog droplets followed by the enlargement by the coalescence of the neighboring fog droplets was observed. Then adjacent droplets merged and a water droplet with an elongated shape was observed to form. The fusion of water droplets caused a slight downward movement along the fiber. In the resulting gaps, small water drops were formed again. This was a continuous process, leading to a fiber surface completely covered by large water droplets. A large droplet, while slipping downward, collected all the droplets on its way down. This caused free space for new droplets to form, though the time for the process, i.e., movement of droplets and their onset of dripping varied depending upon their cross-section profile and width (Figure 7a–b). However, a difference with the above described phenomenon was observed on the microgrooved fiber profiles (2, 8 & 11), where water film formation on their surfaces and faster onset of dripping were found. Nevertheless, fog droplet behavior and/or water dripping on the surfaces of sample profiles, e.g., profile 2, profile 4 and profile 7 is described and compared in Figure 8a–x. Profiles 2 and 7 were chosen because of their higher efficiency, as well as profile 4 for its lowest efficiency.


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b

n

o

c

d

p

e

q

f

r

g

h

s

t

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i

j

u

k

v

w

l

m

x

Figure 8: Fog deposition and movement on the surfaces of 3 fiber profiles: (a–j) profile 2 (in green), (k–r) profile 4 (in red) and (s–x) profile 7 (in brown). Scale bar 1 mm. Microgrooves on profile 2 improved film formation shown by the dotted line in (c). Arrows in (f) shows the downward movement of droplets following the film. Figures (g–h) show the increase of size of the droplet at the bottom by the movement of water through the film. A droplet is about to fall down (j). Rectangular marks in (m–r) show the fusion of neighboring droplets. Fusion of neighboring droplets (s–w), and downward movement of droplets are indicated by arrows in figures u, w, x. Time scales (seconds) can be seen on respective images.


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Profile 2 (rectangular cross-section with round edges, microgrooved surface): Tiny droplets were observed to fuse with neighboring droplets, resulting in the formation of elongated drops only after 12 s (Figure 8a–b). Subsequently, elongated droplets on the surface tended to fuse together (Figure 8c) due to the continuous droplet impact on the fiber surface as well as capillary action 48. Two elongated droplets on two points of the fiber surface were seen to increase in size (Figure 8d), resulting in the downward movement (Figure 8e–f). All of a sudden one droplet appeared at the bottom of the fiber (Figure 8f) in about 38±8 s. During this transport a fast flowing film from the elongated droplet to the bottom was observed. Therefore, it is assumed that there were already liquid (water) fingers or filaments on the grooves that facilitated the film formation. It should be noted that the two droplets of same age can appear in different sizes because of the different size distribution of the fog droplets (2–50 µm). The water from the second droplet, anywhere at the top of the fiber, was transported via the film and accumulated with the droplet (Figure 8g) at the bottom. The increase of the size of the droplet at the bottom over time (37 s – 41 s in Figure 8g,h), while there was no droplet movement from the top to the bottom, proved the transport of water via the film on the surface of the fibers. Therefore, no blocking of the free flow space on the multi-fiber sample, known as ‘clogging effect’, was observed. Another droplet (Figure 8i) anywhere in the middle of the fiber was large enough about to move to the bottom. Finally, after enough accumulation with the droplet at the bottom, it was about to fall down (Figure 8j) and at 107 s the droplet dripped, while an average onset of dripping was 98 ± 10 s (Figure 6). Profile 4 (rectangular cross-section with round corners, smooth surface): In addition to the deposition of lots of tiny droplets, elongated droplets were formed (Figure 8k–l). However, even after 40 s significant fusion of droplets was not observed (Figure 8l). After 53 s, two large


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neighboring droplets only in one point fused together (Figure 8m–n). The droplets were then too far away to fuse together (Figure 8n–q). However, over time other neighboring droplets fused (Figure 8o–r) and increased in size also by the deposition of new droplets as well as fusing with the droplets of neighboring fibers of a multi-fiber sample, resulting in clogging and thereby hindrance of fog flow. The droplets started moving downwards gradually and when large enough at the middle of the fiber (Figure 8r) a droplet moved to the bottom resulting in a hanging droplet. The cycle continued until the hanging droplet is large enough to drip. Similar results of droplet behavior were observed on all the smooth fiber profiles having width of more than 430 µm. However, due to different cross-sections and widths, their fog-collection efficiency varied. Profile 7 (oval cross-section, smooth surface): On the surface of the fiber, half circle shaped droplets were observed. They were increasing by fusing with the neighboring droplets (Figure 8s–t). At around 66s a droplet moved to the bottom all on a sudden collecting other tiny droplets on its way down (Figure 8u). New droplets deposition continued, followed by the accumulation and movement of new droplets to the bottom to cause dripping (Figure 8v–x). However, no film formation was observed on the surface of profile 7 but oval cross-section and smaller width helped improve the transport. Relatively smaller droplets moved downwards along the fibers collecting all the drops on its way down because of the smaller width of the fibers. Moreover, the diameter of the 1st droplet at the bottom was measured over time from 51 – 74 s when there was no droplet movement to the bottom but the increase was negligible (Figure 8v,w). Transport or drainage of the deposited fog water: The ratio of dripped water to total collected water signifies the transport or drainage of the deposited water.


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a

b

Figure 9: Ratio of dripped water to total collected water (in percentage) by 14 fiber profiles over 30 min; (a) category A (profiles 1–7) and (b) category B (profiles 8–14).

It indicates how much water drained from the fibers to the collector under the sample. Based on the analysis, the results (Figure 9a–b) showed that in each category separately, profiles with microgrooved surfaces (Profiles 2, 8 and 11) showed higher transport efficiencies than other samples with smooth surfaces. The result is in consistent with previous studies.

53, 54

However,

profile 7 having oval cross-section and the lowest width showed better transport efficiency than the rest of the samples except profile 2; even though its surface is smooth. Furthermore, the size and volume of the drop, dripping down from the fibers of profile 2 was larger than that of profile


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7 (Figure 8j,x). Therefore, both parameters, i.e., smaller width and microgrooves on the fiber surface played important role in water transport.

Simulation: A numerical simulation was conducted to validate the droplet behavior on the surface of a microgrooved fiber. Experimental microgrooved surfaces with the characteristics based on the fiber profile 2 shown in Table 2 were generated. Due to the highest fog-collection efficiency among the samples the dimensions of profile 2 were used in the simulation. The behavior of the droplet from an initial state to the preliminary spreading in the grooves at time 16.6 x 10-4 s is displayed in Figure 10a–f. At the beginning, a droplet was located on the top of a ridge (Figure 10a). With time the droplet started to wet the grooved surface and spread into two neighboring grooves (Figure 10b). After 1.8 x 10-4 s the droplet split up into two parts. During the splitting a few tiny droplets detached from the main volume (Figure 10c). Most of them reunited or left the numerical domain, while one tiny drop can still be seen in the left view in Figure 10c (marked by an arrow). After the split the droplet reunited and moved around the ridge (Figure 10d). The droplet volume tended to fill the grooves rather than rested on the ridge. Therefore, the droplet spread over the two adjacent grooves (Figure 10e). Finally, the droplet moved into a single groove (Figure 10f).


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a

b

c

d

e

f

Figure 10: Droplet behavior in simulation at different times t (in seconds). Water and grooved surface are shown in blue and gray, respectively. On the left side an isometric view of the entire numerical domain is given. Right side presents a view along the direction of gravity (z axis). Coordinate systems for both views are given at the bottom. Pixelated, i.e., unsmooth surface of water droplet (a) is marked with arrows.


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DISCUSSION

Different cross-sections of the fibers, their widths and surface structures, e.g., grooves, and their influences on fog-collection were tested. Microgrooved hydrophilic fiber surface as well as a smaller fiber width (317 µm) of the fiber was found to be the most advantageous. Directional delivery of collected fog droplets by the microgrooves and a thinner boundary layer of the surfaces caused by the surface asperities55 enhance the fog-collection. Directional spreading of liquids is inherent for grooved reliefs, as has been elaborately discussed in previous studies 44, 45, 46, 47, 49, 50, 51

. Moreover, hydrophilic surface property of the grooved surface, due to the capillary

action, might enhance the anisotropic behavior as reported by Xia et al

56

and Kubiak and

Mathia.48 Both the spreading and receding of the impacting fog droplets are dictated by the grooves, e.g., formation of liquid fingers or filaments along the grooves due to this surface asperity is reported.

44, 57

In a microgrooved surface the energy barrier is lower in the direction

parallel to the grooves than that in the direction vertical to the grooves

45, 58

. Consequently, the

hydrophilic microgrooved fibers demonstrated higher transport efficiency compared to fibers with smooth surfaces (Figure 9a–b). Furthermore, the continuous impact of droplets on the fiber surface provides sufficient momentum to push elongated water droplets, followed by the film through the grooves

44, 46, 47, 59

. Therefore, a fast or effective water transport on microgrooved

hydrophilic fiber surface (θadv = 78° ± 2, θrec = 45° ± 3) results from the difference in energy barriers in different directions of the grooves. This also explains how the multi-fiber samples with microgrooved fiber profiles can overcome the clogging effect whereas those with smooth hydrophilic surface or even the hydrophobic surface cannot, as reported before14, 38. The numerical simulation (Figure 10a–f) also validates directional spreading, thus leading to the film formation on a microgrooved surface. Due to the coarse basic mesh (the term ‘mesh’ 22 ACS Paragon Plus Environment

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refers to a simulation parameter) at the initial state the surface of the droplet appears pixelated, i.e., unsmooth surface water droplet at time, t = 0 s in Figure 10a. With time, mesh refinement sets in and leads to smoothing of the surface. Up to time = 16.6 × 10 s a quite dynamic behavior of the droplet can be observed which is determined by a permanent conversion of kinetic energy into potential surface energy and vice versa, as well as into internal energy by dissipation, leading to a decay of the conversion process. Finally, a single droplet with an elongated shape remains inside a single groove. The grooves show more resistance to the spreading of the droplet perpendicular to the grooves, thus leading to the final shape elongation perpendicular to the grooves. These findings are in agreement to the previous studies

44, 60

. The

phenomenon results from the hydrophilic property of the microgrooved surface.48 The influence of gravity on the shape can be assumed negligible due to small Bond number of =

= 1.36 × 10

Fog Collection on Polyethylene Terephthalate (PET) Fibers: Influence

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