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Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229

Contents lists available at ScienceDirect

Colloids and Surfaces A: Physicochemical andEngineering Aspects

j ourna l h om epa ge: www.elsev ier .com/ locate /co lsur fa

nhancement of fog-collection efficiency of a Raschel mesh usingurface coatings and local geometric changes

ithun Rajaram, Xin Heng, Manasvikumar Oza, Cheng Luo ∗

epartment of Mechanical and Aerospace Engineering, University of Texas at Arlington, 500 West First Street, Woolf Hall 226, Arlington, TX 76019, Unitedtates

i g h l i g h t s

In this work, we explored the pos-sibility of enhancing fog-collectionefficiency of typical Raschel meshes,which have been widely used to col-lect fog in a few countries, such asChile.We found that a superhydropho-bic coating resulted in about 50%enhancement in the collection effi-ciency, and developed a simple modelto explain the reason behind thisenhancement.We also observed that the reduc-tion of pore size, together with theincrease of the distance between twoinclined filaments, yielded another50% enhancement, and found thatdifferent pathways of drops resultedin this enhancement.After the surface modification andlocal geometric changes, the result-ing mesh has collected water about 2times that of a typical Raschel mesh.In addition, we also developed a newpunching process to fabricate mesh-like structures out of polymer sheets.

g r a p h i c a l a b s t r a c t

r t i c l e i n f o

rticle history:eceived 2 June 2016eceived in revised form 18 August 2016ccepted 20 August 2016vailable online 22 August 2016

a b s t r a c t

In a few countries, such as Chile, Raschel meshes are widely used in the field to collect fog. In this work, weexplored the possibility of enhancing fog-collection efficiency of typical Raschel meshes. We found thata superhydrophobic coating resulted in about 50% enhancement in the collection efficiency, and that thereduction of pore size, together with the increase of the distance between two inclined filaments, yieldedanother 50% enhancement. After the surface modification and local geometric changes, the resultingmesh has collected water about 2 times that of a typical Raschel mesh.

eywords:og collectionaschel meshuperhydrophobic coatinghade coefficientunchingenzel state

∗ Corresponding author.E-mail address: chengluo@uta.edu (C. Luo).

ttp://dx.doi.org/10.1016/j.colsurfa.2016.08.034927-7757/© 2016 Elsevier B.V. All rights reserved.

© 2016 Elsevier B.V. All rights reserved.

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M. Rajaram et al. / Colloids and Surfaces A:

. Introduction

In addition to energy, the issue of water shortage and scarcity isne of major global concerns, since about one billion people living

n rural areas of African, Asian, and Latin American countries do notave access to clean water sources [1]. A water shortage has been

major problem faced by the modern civilization in both arid andumid environment [2]. In an arid environment with little rainfallvery year, fog may be an important water source to some desertlants and animals, such as the cactus Opuntia microdasys [3], whichriginates from Chihuahua Desert, the Namib dune bushman grasstipagrostris sabulicola [4], the species Tillandsia landbecki in coastaltacama [5], mesophytic geophytes in Namaqualand and the Lit-

le Karoo [6], and the Namib tenebrionid beetle Stenocara [7,8]. Aew artificial fog collectors have been recently developed [7,9–24].

ost of them mimic the fog-collection mechanisms of the afore-entioned cactus [9–16] and beetle [7,17–21]. On the other hand,

hese collectors appear still at the stage of laboratory research, andave not yet been applied in the field.

For the last two decades, in at least five countries, such as Chile,he most commonly used large fog collector in the field employs aaschel mesh that is vertically oriented between two poles to col-

ect water from fog [25–28]. The Raschel mesh has meter-scaledengths and widths, and it also has mm-scaled pores and filamentsFig. 1(a)). The pores of a Raschel mesh have approximately trian-ular shapes, and some filaments are inclined with lengths close to

cm (Fig. 1(b)). The filaments are about 20 �m thick, while theiroints are 200–400 �m thick. Fog is composed of tiny water drops

ith diameters in the range of 1–40 �m. The fog collection includeswo steps. Tiny drops that are carried in a wind hit and accumulaten filaments. Under gravity, large drops, which are formed due tohe coalescence of the tiny drops, may drain off from the filamentso an underneath gutter. Raschel meshes are effective in fog collec-ion. Their fog collection rates are typically 1–10 L/m2 per day [28].lso, the presence of light rain with the fog has produced collec-

ion rates as high as 300 L/m2 per day for a wind speed of 10 m/s28]. On the other hand, there is a large room to improve their fog-ollection efficiency. According to recent experimental results, onlyround 2% of water drops that pass by a typical Raschel mesh haveeen collected by this mesh [24]. In contrast, an optimal mesh withectangular pores has shown a five-time enhancement in the fog-ollection efficiency of a typical Raschel mesh [24]. Meanwhile, itas already been demonstrated that Raschel meshes are effectiveo harvest water in the field. Therefore, a Raschel mesh should havets unique advantages in collecting fog.

Using woven polyolefin Raschel meshes (Fig. 1), Schemenauer,ereceda, and their co-workers have conducted numerous pilot-cale studies that demonstrate the feasibility of collecting fog28–32]. However, as commented in ref. 24, most studies on

esh-based fog harvesters have been performed in the field usingncontrolled natural fog conditions, and systematic studies of these

og harvesters under laboratory conditions have been rare [27–32].nder controlled laboratory conditions, Azad et al. have recentlyxplored the effect of wettability on the fog collection of a doubleayered polyolefin Raschel mesh [12]. They found that the amountf water collected by superhydrophilic mesh was about 5 time thatf a hydrophilic (untreated) mesh, and that a hydrophobic meshollected 2.5 times higher amount of water than the hydrophilicne. Their results indicate that the enhancement of either surfaceydrophilicity or hydrophobicity may increase fog-collection effi-iency. The superhydrophilic mesh has been previously shown toe effective in fog collection [12]. In this work, we consider the

ffect of surface hydrophobicity, with particular attention to thatf superhydrophobic coating. We also explore the influence of thehanges in filament dimensions and orientations. Although doubleayered Raschel meshes are usually used in the field, our investi-

cochem. Eng. Aspects 508 (2016) 218–229 219

gation is focused on a single layered one. A good understanding ofits fog-collection behavior may lead to a better application of thedouble layered ones.

2. Theoretical background, and comparison tests

2.1. Theoretical background

The collection efficiency, �, of a mesh depends on aerodynamiccollection efficiency (�ace), capture efficiency (�cap), and drainingefficiency (�dra) [27]:

�= �ace�cap�dra. (1)

All of these three efficiencies are not larger than 100%. �ace isthe fraction of the unperturbed water flux heading towards a meshthat would collide with the mesh filaments. �cap is the fraction ofthe collided water drops that actually deposit on filaments from thefog flow initially headed toward the filaments. �dra is the fraction ofthe deposited water that would drain off from the filament, whichis subsequently collected through a gutter located at the bottom ofthe mesh.�ace is related to shade coefficient (SC), which is the ratio of the

filament area over the total mesh area. �ace does not necessarilyincrease with the decrease in the pore area. The expression of �ace

is [27]

�ace = s

1 +√

CoCd

, (2)

where s represents SC, Cd is the drag coefficient for the overall struc-ture and approximately equals 1.18 for a Raschel mesh, and Co isthe pressure loss coefficient. Co is related to s by [27]

Co = 1.62[1.3s + s2

(1 − s)2]. (3)

According to Eqs. (2) and (3), �ace is only 9% for a solid plate,which has no pores. It is 20% for a typical Raschel mesh, whose SCranges from 35 to 37%. However, �ace can be easily improved to themaximum value of 24.5% if SC is 55%, when the filament area of atypical Raschel mesh is increased relative to the pore area.

Langmuir and Blodgett have previously derived an empiricalexpression of �cap for a circular cylinder [33]. This expression,together with Eq. (2), was adopted in ref. 24 to optimally designrectangular meshes, which have circular filaments. Since the fila-ments of a Raschel mesh have rectangular cross-sections, instead ofcircular ones, the empirical expression of �cap may not be applicableto the Raschel mesh. In addition, we have not seen any theoreticalmodels for �dra. Thus, we would like to have a good understandingabout these two efficiencies through experiments.

2.2. Comparison tests

Fog-collection experiments were performed on differentmeshes using an experimental setup shown in Fig. 2. Each testis conducted at room temperature (24 ◦C ± 1 ◦C). Two humidi-fiers (model: EE- 5301, Crane USA Co., and AOS 7135 Ultrasonic,BONECO USA Co.) are connected together to generate enough mistto cover a tested sample. A plastic pipe is employed to guidethis mist flow. A fan (model: Breeze color USB Desktop fan, Arc-tic USA Co.) is used at 800 rounds per minute to increase themist flow speed. At the end of the pipe, the mist flow speed is1.1 m/s, which is measured using a wind speed meter (model:

WM-2 Handheld Weather meter, AmbientWeather USA Co.). Theentire process is conducted in a closed chamber with dimensions of74 × 31 × 30 cm3 (length × width × height). 100% humidity is main-tained inside the chamber, and a humidity meter (model: Hydro-

220 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229

Fig. 1. (a) Front view of part of a Raschel mesh (optical image), and (b) dimensions of its pores and the filament (schematic). The unit in (b) is millimeter.

F idifierp lose-uf e who

TUcad

Utrrth3ntt

oeTrtb1ttd

ig. 2. (a) Experimental setup for fog collection: vapors are generated by two humipe (tests are not started yet, and no mesh is hanged at the sample location). (b) C

unnel was put at the end of the plastic pipe to ensure that the mist flow covered th

hermometer Humidity Alert with Dew Point- 445815, EXTECHSA Co.) is used to monitor the humidity throughout a processycle. A tested mesh is placed 5 cm away from the exit of the pipe,nd a glass container is put below the mesh to collect water thatrains down.

Two rectangular stainless steel meshes (McMaster-Carr Co.,SA) and a polyethylene Raschel mesh (Marienberg Co., Chile) were

ested (Fig. 3). The fiber diameter and pore spacing of the firstectangular mesh are 0.34 and 0.9 mm, respectively. The secondectangular mesh has thicker fibers and larger pores. Their diame-er and spacing are 0.89 and 2.3 mm, separately. The Raschel meshas the same dimensions as the ones shown in Fig. 1(b). Its SC is7%. It is currently being used in a double layer by FogQuest Orga-ization to collect fog in developing countries.34 All of the threeested meshes, as well as the other tested meshes of this work, hadhe same length of 3.3 cm and width of 2.0 cm.

Receding and advancing contact angles were also measuredn each mesh. In this work, three measurements were taken forach contact angle with an error of 2◦. Their mean was given inable 1. The receding contact angles of the first rectangular, secondectangular, and Raschel meshes were 45◦, 45◦ and 98◦, respec-ively. The corresponding advancing contact angles were found toe 72◦, 56◦, and 113◦. The contact hystereses were 17◦, 11◦, and5◦, respectively. Since the rectangular meshes had different con-act angles from the Raschel mesh, we did not specifically compare

he amounts of water collected by them. Instead, we focused on theifference in their fog-collection mechanisms.

s, and a fan is used to drive these vapors towards a hanged mesh through a plasticp view of the sample location during a test (a mesh was hanged over there, and ale mesh sample).

The two rectangular meshes have a main draining path differentfrom that of the Raschel mesh. In the case of these rectangu-lar meshes, every fiber is cylindrical with circular cross-sections.Accordingly, tiny drops were initially seen around a fiber, andthese drops then grew along all the directions to form small drops(Fig. 3(a1)). A large drop was formed on a pore due to the coa-lescence of the small drops on the neighboring fibers (Fig. 3(a2)),and the large drop fell down when it was above a threshold size(Fig. 3(b1) and (b2)). The threshold sizes for the first and secondrectangular meshes were, respectively, 3.2 and 3.9 mm in diameter.There are two problems associated with this main draining path.The first one is that the large drop clogs the pore area (Fig. 3(a2),(b1) and (b2)). This means that SC is close to 100% as in the case of aplate without any pores. Thus, �ace actually decreases to the lowestvalue of 9% during the collection process. In addition, the drops onthe side surfaces of a fiber are directly exposed in the wind, and theyare lack of strong support of their substrate (Fig. 3(a1)). These mayresult in the second problem. That is, although we did not observein our tests (the flow speed was 1.1 m/s), such drops may be blownoff by a high-speed wind (e.g., 10 m/s) [24], resulting in the decreaseof �dra.

In contrast, the Raschel mesh does not have these two prob-lems. It has rectangular fibers. Initially, tiny drops mainly appearedon the front surface of a filament, since this surface was directlyexposed in the fog flow (Fig. 3(c1)). Only few drops were seen on

the side surfaces of the filament. The tiny drops on the front surfaceof an inclined filament then merged into a small drop (Fig. 3(c1)).The small drop subsequently moved towards the joint of the fila-

M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 221

Fig. 3. (a) Illustration and (b) experimental results of mist flow (optical images) on two rectangular meshes with cylindrical fibers. (a1) Small drops appear on the sidesurfaces of fibers, and (a2) these drops merge into a large one. (b1) small and (b2) large rectangular meshes. (c) Illustration and (d) experimental results of mist flow on aRaschel mesh: (d1) tiny drops first appear on the surfaces of filaments; (c1, d2) these drops merge to form small drops, which subsequently move down to the joint of themesh and form a large drop; and (c2, d3) the large drop detaches from the joint when it is above a threshold size. In (d), circles denote drops, and scale bars in (b) and (d)represent 2 mm.

Table 1Contact angles measured on samples before the start of fog tests.

Type Receding contact anglewith an error of 2◦

Advancing contact anglewith an error of 2◦

Contact angle hysteresis

First (small) rectangular mesh 45◦ 72◦ 17◦

Second (large) rectangular mesh 45◦ 56◦ 11◦

As-received Raschel mesh 98◦ 113◦ 15◦

Teflon-coated Raschel mesh 120◦ 125◦ 5◦◦ ◦ ◦

m(sdtsodwadic

paijtai

NeverWet-coated Raschel mesh 154Hydrobead-coated Raschel mesh 156◦

ZnO nanowires-coated Raschel mesh 112◦

ents, coalescing with other drops at this joint to form a large dropFig. 3(c2)). During this process, due to the support of the filamenturfaces and the pinning effect of the filament edges, drops wereifficult to get blown off from a filament by a wind, or to move out ofhe filament along the direction perpendicular to this filament. Con-equently, in our tests, no water drops were visibly seen to bounceff from a filament, and they just moved down along the longitu-inal direction of an inclined filament. Accordingly, almost all theater drops that hit the filaments should be captured. The same

pplied to the case when the mesh was covered with a superhy-rophobic coating (the coating and testing results will be detailed

n Section 3). Thus, the Raschel mesh should have a value of �cap

lose to 100%.Furthermore, the inclined filaments in a Raschel mesh, in com-

arison with vertical fibers in a rectangular mesh, enable drops thatre located on these filaments to merge at their joint (Fig. 3(c2)),ncreasing the rate of generating a large drop. When the drop at the

oint became large enough, it overcame the adhesion force overhere and fell down into the underneath water container (Fig. 3(c2)nd (d3)). This drop did not clog much of the pore area. Hence,n comparison with a rectangular mesh, the Raschel mesh should

156 2158◦ 2◦

138◦ 26◦

have a higher �dra, and its �ace does not decrease during the fog-collection process.

The flow speed in our tests was about 1.1 m/s. It is expectedthat, at a much higher wind speed (e.g., 10 m/s), water drops maybe bounced off or blown away from the filaments. In addition, it isnoted that, in the case of rectangular meshes [24], the hydrophobiccoating was the most effective in collecting water, while the super-hydrophobic one was not. They found that the adhesion was notstrong between water drops and superhydrophobic coating, whichmay cause a re-entrainment problem to reduce the collection effi-ciency. However, due to the support of the filament surfaces, theadhesion is not a major concern in the case of a Raschel mesh, unlessthe wind speed is high. To solve the adhesion problem in the case ofhigh-speed wind, in the near future microchannels may be incorpo-rated into inclined filaments. The microchannels are oriented alongthe longitudinal directions of these filaments. Accordingly, alongthe directions perpendicular to the filaments, water drops are fur-

ther pinned by these channels. Meanwhile, these channels do notaffect the movements of the water drops along the longitudinaldirections of such filaments.

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22 M. Rajaram et al. / Colloids and Surfaces A:

As discussed above, �cap of the typical Raschel mesh may beonsidered to be approximately 100% unless the flow speed is high.ence, in this work, we focus on increasing �dra and �ace of a Raschelesh.

. Effects of surface coatings

.1. Experimental methods and results

To increase �dra, it is important to make the deposited waterrain off from the mesh filaments. A coating may change wet-ing properties of a surface such that even a small drop may moveown from the corresponding surface [35,36]. In this work, Rascheleshes were, respectively, coated with Teflon, ZnO nanowires,everWet, and hydrobead to examine the effects of these coat-

ngs on �dra. The corresponding meshes were, respectively, referredo as “Teflon mesh,” “nanowire mesh,” “NeverWet mesh,” andhydrobead.” These four meshes, together with as-received Rascheleshes, were tested. Both NeverWet (Rust-Oleum Co., IL, USA)

nd hydrobead (Hydrobead Co., CA, USA) are commercially avail-ble. They are often applied to enhance surface hydrophobicity.everWet includes two aerosols, which are called “base coat” and

top coat”, respectively. The base and top coats were successivelyprayed onto a Raschel mesh. The solid ingredients of the basend top coats are, respectively, aliphatic hydrocarbon and siliconeerived proprietary ingredient [37,38]. Hydrobead is an aerosol asell. It was also sprayed onto a Raschel mesh. Its solid ingredients

re aliphatic petroleum distillates and proprietary additives [39].eflon films were deposited on the meshes through a dip-coatingrocess, while ZnO nanowires were grown on these meshes using

hydrothermal approach [40].Fig. 4 shows surface structures on the coated meshes. The cor-

esponding images were taken using a Hitachi S-3000N Scanninglectron Microscope (SEM). The dimensions of the surface struc-ures were also measured using this SEM. The ZnO nanowires haveexagonal cross-sections with an average length of 2.1 �m andiameter of 0.36 �m (Fig. 4a). They have different orientations withheir tips close to each other. The maximum distance of a wireip with its neighboring ones is about 5 �m. Both NeverWet andydrobead have cracks in their coatings. The NeverWet coating has

thickness of 2.2 �m. The cracks are linked with each other, andost of them have widths ranging from 5 to 10 �m (Fig. 4b). The

istance between two neighboring cracks is usually above 100 �m.he hydrobead coating is about 1.8 �m thick. The widths of theracks range from 1 to 40 �m, and their lengths vary from 10 to80 �m (Fig. 4c). Most of the cracks have widths and lengths ofround 15 and 100 �m, respectively. The distances between theracks range from 20 to 200 �m. On the other hand, we did notbserve such cracks on the surface of an as-received Raschel meshFig. 4d).

Two different samples were prepared for each coating, and threeog-collection tests were also done for each sample. That is, forach coating, there were six collected results in total, which alsopplies to the tests that will be presented in Section 5. After 1-

durations, on average Teflon, NeverWet, hydrobead and ZnOanowires meshes collected 14, 16, 17 and 13 mL of water, respec-ively, whereas the as-received Raschel mesh collected only 11 mL.ence, the hydrobead has shown the highest collection efficiency,hich is about 1.55 times that of the as-received Raschel mesh.

The receding and advancing contact angles were measuredefore fog tests by slightly decreasing and increasing the vol-

me of a millimeter-scale water drop on a coated mesh (Table 1).he receding contact angles of Teflon, NeverWet, Hydrobead andanowire meshes were 120◦, 154◦, 156◦ and 112◦, respectively. Theorresponding advancing contact angles were found to be 125◦,

cochem. Eng. Aspects 508 (2016) 218–229

156◦, 158◦, 138◦. The contact hystereses were 5◦, 2◦, 2◦, and 26◦,respectively. After a 1-h fog test, equilibrium contact angles ofwater drops that still remained on a vertically-oriented mesh werealso measured through an optical microscope to gain some under-standing about the change in the contact angles after the fog tests.For Teflon, NeverWet, Hydrobead and nanowire meshes, the aver-age contact angles that were measured on at least three water dropswere 121◦, 146◦, 144◦, and 116◦, respectively. In the cases of Nev-erWet and Hydrobead meshes, these angles were lower than thereceding contact angles obtained before the fog tests, indicatingthat contact angles were decreased during the fog tests. Mean-while, no large reduction in contact angles was found for Teflonand nanowire meshes, since the average contact angles measuredafter fog tests were still slightly higher than the receding onesdetermined before the fog tests.

3.2. Simple model

A simple model is developed to explain the fog-collection resultson different coatings. Due to gravity, large drops that are condensedon a mesh may move down from the mesh. However, tiny dropsmay get stuck on the filaments and thus are not harvested. Hence,to enhance collection efficiency, it is important to harvest as manytiny drops as possible. A simple model is developed for this purpose.Let � denote apparent contact angle of a drop. A drop on a substratethat is inclined by an angle of � suffers a gravitational force G anda threshold adhesive force F. The two forces, respectively, have thefollowing expressions:

G = �gVsinˇ, (4)

F = FoA(�, V), (5)

where � denotes mass density of the liquid, g is gravitational accel-eration, V is the volume of the drop, and Fo is the adhesive force perunit area of the drop base. In Eq. (5), A(�, V) denotes the area of thedrop base. It is a function of � and V. By geometric analysis, when Vis fixed, A(�, V) decreases with the increase in �. If

G ≥ F, (6)

then the drop moves down from the substrate. For a drop witha fixed V, by Eq. (4), its G is also fixed. According to Eq. (5), to havea small F, � should be as large as possible to reduce A, while Foshould be as small as possible. Thus, for the purpose of reducingF, we desire to make � as high as possible by enhancing surfacehydrophobicity.

On a smooth surface, � is normally less than 120◦, even if thissurface is coated with highly water-repellent materials [41], suchas Teflon [42]. Hence, to make the corresponding contact angle wellabove 120◦, roughness structures are normally incorporated on asurface.

When a liquid drop is placed on a rough surface, there aretwo possible wetting states: Wenzel [43] or Cassie-Baxter [44].In the Wenzel state (Fig. 5(a)), the drop completely fills groovesbetween roughness structures (e.g., pillars and channels), while inthe Cassie-Baxter state, air is trapped between these structures andthe drop stays on top of the roughness structures and trapped air.In either state, when the surface material is hydrophobic, the cre-ation of roughness structures on the surface further enhances thehydrophobicity [43,44].

Due to small sizes of roughness structures on NeverWet,hydrobead and ZnO nanowire meshes, it is difficult to directlydetermine whether water fills the gaps of these roughness struc-

tures through an optical microscope. Hence, their wetting state isjudged through theoretical analysis [45–47] (see Supplementarymaterial for detail). According to this analysis, on these meshes,the wetting is considered to be in Cassie-Baxter state during our

M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 223

Fig. 4. Top (SEM) views of the coatings: (a1) and (a2) ZnO nanowires, (b1) and (b2) NeverWet, and (c1) and (c2) hydrobead. (d1) and (d2) Uncoated Raschel Mesh. Arrowsin (b2) and (c2) indicate locations of represented narrow gaps.

224 M. Rajaram et al. / Colloids and Surfaces A: Physi

ab

b

Cell

a

Liquid drop

Pillar

Solid sub strate

(a)

(b)

Fa

pt

dIstst

s

c

Iaa

r

r

WRt

cseAac

r

ig. 5. (a) Schematic side view of Wenzel state, and (b) schematic top view of anrray of square micropillars.

rocess of measuring contact angles before fog tests, while it is inhat of Wenzel during the fog tests.

In the Cassie-Baxter state, due to small contact area between arop and the substrate, the drop is easy to roll off from the substrate.

n the Wenzel state, although � may still be large, the roughnesstructures may pin the drop, making it difficult to move off fromhe surface. Since during the fog tests the wetting may be in thetate of Wenzel, our focus now is on reducing the pinning effect inhis state to reduce Fo.

Let �0 denote intrinsic contact angle. The equation for Wenzeltate is [43]:

os � = r cos �0. (7)

n this equation, r denotes the roughness ratio. It is the ratio of thectual surface area of the rough surface, Aa, to the projected surfacerea, Ap, and is given by

= AaAp. (8)

It is observed from this equation that

≥ 1. (9)

hen r is 1, it implies that the surface is smooth. As observed fromelations (7) and (9), to make � larger than �0, �0 should be largerhan 90◦, indicating that the surface coating should be hydrophobic.

To have a good understanding about r for choosing it properly,onsider an array of square micropillars with a pillar size of a × a,pacing of b, and height of h. It is a type of simple structures. Consid-ring a representative cell around a micropillar (Fig. 5(b)), we havep = (a + b)2 and Aa = 4ah + (a + b)2, where Aa actually equals theddition of Ap with the four pillar sidewall areas. By Eq. (8), the

orresponding r is

= 1 + 4ah

(a + b)2. (10)

cochem. Eng. Aspects 508 (2016) 218–229

It can be seen from this equation that, for given a, r increaseswith the increase in h and decrease in b.

Next, let’s consider two cases. In the first case, we assume thatb � a. Accordingly, we get

r ≈ 1 + 4ha. (11)

Subsequently, given that �0 = 100◦, by Eqs. (7) and (11), to make� equal 150◦, we should have h = a. In the second case, we assumethat b = a. Given that �0 = 100◦, by Eq. (11), we should have h = 5a toget � = 150◦. The surface structures in the two cases are illustratedin Fig. 6. Two points can be observed. First, there are narrow gapsbetween the structures in Case I (Fig. 6(a)), while such gaps are rel-atively wide in Case II (Fig. 6(b)). Second, the height/width ratiosof the structures in these two cases are 1 and 5, respectively. Thesetwo differences indicate that, although the structures in the twosurfaces produce the same r, which actually resulted in the same A,the values of Fo are different. In Case II, the pillars penetrate a waterdrop, and the sidewalls of these structures block the movement ofthe drop. In contrast, in Case I, the water in narrow gaps can be con-sidered stationary, and it becomes part of the substrate surface. Theportion of the drop located above the substrate moves on this com-posite substrate surface (Fig. 6(a)). Accordingly, the drop in CaseI should suffer a smaller Fo than that in Case II. Furthermore, thedrop volume is in the order of the third power of its radius. Sinceb � a, it is readily shown the total gap sizes are much smaller thanthe drop radius. This result indicates that, as far as the volume isconcerned, the amount of water inside the gaps can be neglectedin comparison with the part of the drop that moves down on thesubstrate.

Consider a third case, in which the substrate is flat and it is notincorporated with any roughness structures (Fig. 6(c)). In Case I,part of the solid surface in Case III is actually replaced with thesurface of water that fills the narrow gaps. Accordingly,Fo in CaseI is smaller than its counterpart in Case III, because the adhesionbetween water and solid should be larger than that between thesame liquid. Furthermore, for a given drop, Case I has a smaller Athan Case III due to the increase in the contact angle. Thus, F in CaseI is smaller than that in Case III, making the corresponding dropeasier to move down on the corresponding substrate. Case II alsohas a smaller A than Case III. However, it is not clear whether Fo alsohas a smaller value in Case II. Thus, it is uncertain whether Case IIhas a smaller F. In summary, there are two possible results afterincorporation of roughness structures. First, if the roughness struc-tures are closer to those of Case I, then the drop is easier to movedown than in Case III. Second, when these structures are closer tothose of Case II, it is not clear whether the drop is easier to movedown.

Let �r and �a, respectively, denote receding and advancing con-tact angles of the drop. � ranges between �r and �a. The thresholdadhesive force F is often expressed as

F = W�(cos �r − cos �a), (12)

where W is the diameter of the drop base. On the other hand, thereis a problem of applying this expression to determine F. In Cases Iand II, r has the same value. The same applies to �o. Accordingly, theresulting W should be the same in the two cases. Also, by Eq. (7),(cos�r-cos�a) should also be the same as well. Therefore, F should bethe same in both cases. However, as justified above, the two casesshould lead to different values of F. Hence, �(cos�r-cos�a) may notalways represent the adhesive force per unit surface area particu-larly when the drop is pinned by roughness structures. Accordingly,

in this work, we employ Eq. (5) instead to estimate the adhesiveforce.

In our tests, the NeverWet and hydrobead belong to the firstcase, and ZnO nanowires the second case. According to the data

M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 225

(a)

(b)

(c)

Fig. 6. Wetting situations on: (a) low aspect-ratio structures with narrow gaps, (b) high aspect-ratio structures with wide gaps, and (c) a flat surface. The first two situationsare in Wenzel wetting state.

226 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229

F cs): (at abrica

gcfbea

4

4

mesanmilid

macra

ig. 7. Two-step process to fabricate the proposed mesh (cross-sectional schematiop mold is inserted into the polymer sheet to cut undesired portion of the sheet. F

iven in Sub-section 3.1, the ratio of b with a for the NeverWetoating is above 10, while it is about 13 for the hydrobead. Hence,or either coating, the assumption that b � a is met. Consequently,oth coatings belong to the first case, resulting in the high collectionfficiency. Meanwhile, ZnO nanowires belong to the second case,nd they are not as efficient as the NeverWet and hydrobead.

. Effects of local geometric changes

.1. Fabrication of the meshes

�ace of a typical Raschel mesh may be improved to the maxi-um value of 24.5% if SC is increased from around 35% to 55%. The

xisting meshes are mainly fabricated by weaving fibers together,uch as a typical Raschel mesh shown in Fig. 1(a). When the samepproach is used to create meshes with different SCs, there may beo polymer fibers that exactly meet the corresponding size require-ents. To generate a mesh with SC of 55%, what is normally done

s to stack two typical Raschel meshes together to form a doubleayered one [24,34]. In this work, we develop a new manufactur-ng method, which is capable of directly fabricating meshes withifferent SCs and shapes.

To manufacture a mesh, pores have to be fabricated in a poly-er sheet. Polymer or metal sheets are usually patterned after they

re softened at a raised temperature using a hot-embossing pro-ess or injection molding [48]. However, it is observed that, even atoom temperature, an office punch can punch holes in paper, whichvoids the needs of heating and cooling a material to be patterned.

) a polymer sheet is placed on the bottom mold, and (b) at room temperature, theted (c1) top and (c2) bottom molds, and (c3) Type II PMMA mesh (optical images).

Under the motivation of this observation, it should also be feasibleto punch hollow patterns in a polymer sheet at room temperature.

The new method used to fabricate the desired mesh is essentiallya punching process. It uses two different rigid molds, which are,respectively, referred to as “top mold” and “bottom mold” there-after. The top mold includes mm-scaled blocks (Fig. 7(a)). Theseblocks have sharp edges, and are employed to cut off the polymerfor generating pores. The bottom mold also includes mm-scaledholes. These holes are used to assist in the cutting and removal ofthe cut-off polymer.

Two steps are applied in the punching process to fabricate thenew mesh. First, a polymer sheet is placed on the bottom mold(Fig. 7(a)). Second, at room temperature, the top mold is insertedinto the polymer sheet (Fig. 7(b)). During this step, due to the stressconcentration at the sharp edge of a mm-scaled block of the topmold, the part of the polymer directly underneath this block is firstcut off from the neighboring polymer, and then pushed into thecorresponding hole inside the bottom mold.

The top and bottom molds in this work were fabricated usingan Epilog laser (Fig. 7(c)). With the aid of these molds, the desiremeshes were generated in a poly-methyl methacrylate (PMMA)sheet using the two-step punching process. PMMA is a commonlyused material in hot-embossing processes [49]. The used PMMAsheet is 30 �m thick. It is thicker than a Raschel mesh, whichhas a thickness of 20 �m. Three different types of PMMA mesheshave been fabricated, which are called Types I, II and III meshes,

respectively. Fig. 7(c3) gives a representative Type II mesh that wasfabricated. If needed, the molds can be applied to punch a PMMAsheet multiple times to fabricate a larger mesh.

M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 227

Fig. 8. Moving paths of condensed water drops on Types (a) I, (b) II, and (c) III PMMA meshes, which are all coated with hydrobead (unit: mm). As illustrated above anddetailed in the text, the moving paths on Type I and Type III meshes are similar, while the one on Type II is different.

228 M. Rajaram et al. / Colloids and Surfaces A: Physi

Table 2Total amounts of water collected for 1-h durations on different types of meshes withvarious coatings. Types I, II and III refer to different types of PMMA meshes.

Type Coating Mean of collectedwater (mL)

Standard deviation(mL)

I ZnO nanowires 13 1.3I Teflon 15 1.6I Hydrobead 18 1.4II ZnO nanowires 16 1.4II Teflon 18 1.0II Hydrobead 23 0.9III ZnO nanowires 15 1.2III Teflon 17 1.4III Hydrobead 21 1.6

rdtatv2fiwIb7thl

btsd

nNptrmstai

4

mplomthRgfomed

As-receivedRaschel mesh

Untreated 11 1.1

The shape of the PMMA meshes is similar to that of the as-eceived Raschel mesh. On the other hand, these PMMA meshesiffer from as-received Raschel mesh in the filament sizes or dis-ances. To examine the effect of SCs on the fog collection, Type I hasbout the same SC of 37% as the as-received Raschel mesh, whilehe SCs of Types II and III meshes are both 51%. Consequently, thealues of �ace for Raschel and Type I meshes are approximately1.6%, and they are 23.3% for Types II and III meshes. The inclinedlaments of Raschel, Type II and Type III meshes have the sameidths of 1.8 mm, whereas they are 1.0 mm wide in the case of Type

mesh (Fig. 8). In addition, along the vertical direction, the distanceetween two horizontal filaments that are next to each other is.0 mm for both Raschel and Type I meshes, while it is 5.4 mm forhe other two types of meshes. Accordingly, Types II and III meshesave smaller pores than both Raschel and Type I, and thus they have

arger SCs.Moreover, at the joint area, two inclined filaments are separated

y 1.8 mm in the cases of both Raschel and Type II meshes, whilehe separation is 1.0 mm for Types I and III. This variation in theeparation allows us to examine its effect on the coalescence ofrops.

The fabricated PMMA meshes are subsequently coated with ZnOanowires, Teflon, and hydrobead, respectively. The base coat ofeverWet etches PMMA. Therefore, although the NeverWet hasreviously shown a high collection efficiency, it is not used onhe PMMA meshes. Contact angles on a surface are affected by theoughness and coating of this surface. Since both PMMA and Raschel

eshes have relatively smooth surfaces, the contact angles on theirurfaces depend on the corresponding coatings. As expected, con-act angles of water on a coated PMMA mesh are measured to bebout the same as those on a Raschel mesh that has the same coat-ng.

.2. Fog-collection results and discussions

Table 2 gives the amounts of water collected by the PMMAeshes. Four points are observed from this table. First, as in the

revious tests, the hydrobead coating still has the highest col-ection efficiency among the three tested coatings in each typef PMMA meshes. Second, when Type I and as-received Rascheleshes were coated with the same material, they collected about

he same amount of water. For example, Type I mesh with theydrobead coating collected 18 mL water, while hydrobead-coatedaschel mesh harvested 17 mL. These two meshes have the sameeometry. This point indicates that, when they have the same sur-ace coating, the PMMA mesh does not have distinctive advantage

ver as-received Raschel mesh in water collection. Third, Types IIesh with the hydrobead coating has shown the highest collection

fficiency among all the tested mesh. It has collected 23 mL wateruring a 1-h period, which is 34.9 �L/mm2. This point indicates

cochem. Eng. Aspects 508 (2016) 218–229

that, with the further modification of mesh geometry, the collec-tion efficiency has been improved from 1.55 to 2.09 times that of theas-received Raschel mesh. Fourth and finally, the ratio of standarddeviation to the mean is less than 0.11, indicating that the varia-tion of the six fog-collection measurements is small on each typeof meshes. Contact angles were measured on a dry sample beforeand after all the tests, and there was no much difference in the cor-responding values. Also, after the tests, no damage was observedon surface coatings through an optical microscope. Accordingly,the surface coatings were stable during the tests. Hence, the afore-mentioned variation might be mainly caused by fluctuations in flowpatterns, which could not be identical in all the tests.

Both Types II and III meshes should have higher collection effi-ciencies than Type I, since the former two types have higher �ace. Toexplore why Type II mesh was more effective in collecting fog thanType III, we explored the moving paths of condensed water dropson the meshes. As observed from Fig. 8, there are some differencesin these moving paths, which influence the drop draining efficiency.The moving paths on Type I and Type III meshes are similar as thaton a Raschel mesh (Fig. 3(c)). Once a large drop gets to the joint oftwo inclined filaments, due to the small separation between thesefilaments, the drop may be pinned over there. Its growth relies onboth the adsorption of the incoming water drops and addition ofnew drops from the two inclined filaments. However, in Type II,because of the relatively larger separation, a large drop may not bepinned at the joint area. Instead, it may move all the way down tillit is large enough to fall down from the mesh. During this process,it receives additional supply of water, which comes from the tinydrops present on its draining path.

Although, as in the case of Type II, two inclined filaments ofa Raschel mesh are also separated by 1.8 mm at their joint area,there is a critical difference in the way that the inclined filamentsare connected with the horizontal one. In the case of the Raschelmesh, the inclined filaments are wrapped around the horizontalfilament at the joint area, forming knots over there. These knotspin water drops. However, in Type II mesh, the inclined filamentsare smoothly connected to the horizontal one, which reduces thepinning effect such that a drop located at the joint area may furthermove down.

5. Summary and conclusions

In this work, we explore the possibility of improving fog-collection efficiency of Raschel mesh through surface modificationand local geometric changes. We considered five different coat-ings on the mesh surfaces. Through experimental and theoreticalinvestigations, we demonstrated that it was possible to improvethe fog-collection efficiency using coatings with narrow gaps. Thebasic idea is to increase the contact angle, while in the meanwhileto reduce the pinning effect. NeverWet and Hydrobead both satisfythese two requirements. As a result, their coatings have increase thecollection efficiency of the Raschel mesh by about 50%, and are themost efficient two among the five coatings that were tested. A newpunching process was further developed to fabricate three differenttypes of PMMA meshes. Due to the differences in SC and drain-ing paths of condensed water drops, Type II meshes have shownanother 50% enhancement in fog-collection efficiency.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.colsurfa.2016.08.034.

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