![M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 219
1. Introduction
In addition to energy, the issue of water shortage and scarcity is
one of major global concerns, since about one billion people living
in rural areas of African, Asian, and Latin American countries do not
have access to clean water sources [1]. A water shortage has been
a major problem faced by the modern civilization in both arid and
humid environment [2]. In an arid environment with little rainfall
every year, fog may be an important water source to some desert
plants and animals, such as the cactus Opuntia microdasys [3], which
originates from Chihuahua Desert, the Namib dune bushman grass
Stipagrostris sabulicola [4], the species Tillandsia landbecki in coastal
Atacama [5], mesophytic geophytes in Namaqualand and the Lit-
tle Karoo [6], and the Namib tenebrionid beetle Stenocara [7,8]. A
few artificial fog collectors have been recently developed [7,9–24].
Most of them mimic the fog-collection mechanisms of the afore-
mentioned cactus [9–16] and beetle [7,17–21]. On the other hand,
these collectors appear still at the stage of laboratory research, and
have not yet been applied in the field.
For the last two decades, in at least five countries, such as Chile,
the most commonly used large fog collector in the field employs a
Raschel mesh that is vertically oriented between two poles to col-
lect water from fog [25–28]. The Raschel mesh has meter-scaled
lengths and widths, and it also has mm-scaled pores and filaments
(Fig. 1(a)). The pores of a Raschel mesh have approximately trian-
gular shapes, and some filaments are inclined with lengths close to
1 cm (Fig. 1(b)). The filaments are about 20 m thick, while their
joints are 200–400 m thick. Fog is composed of tiny water drops
with diameters in the range of 1–40 m. The fog collection includes
two steps. Tiny drops that are carried in a wind hit and accumulate
on filaments. Under gravity, large drops, which are formed due to
the coalescence of the tiny drops, may drain off from the filaments
to an underneath gutter. Raschel meshes are effective in fog collec-
tion. Their fog collection rates are typically 1–10 L/m2 per day [28].
Also, the presence of light rain with the fog has produced collec-
tion rates as high as 300 L/m2 per day for a wind speed of 10 m/s
[28]. On the other hand, there is a large room to improve their fog-
collection efficiency. According to recent experimental results, only
around 2% of water drops that pass by a typical Raschel mesh have
been collected by this mesh [24]. In contrast, an optimal mesh with
rectangular pores has shown a five-time enhancement in the fog-
collection efficiency of a typical Raschel mesh [24]. Meanwhile, it
has already been demonstrated that Raschel meshes are effective
to harvest water in the field. Therefore, a Raschel mesh should have
its unique advantages in collecting fog.
Using woven polyolefin Raschel meshes (Fig. 1), Schemenauer,
Cereceda, and their co-workers have conducted numerous pilot-
scale studies that demonstrate the feasibility of collecting fog
[28–32]. However, as commented in ref. 24, most studies on
mesh-based fog harvesters have been performed in the field using
uncontrolled natural fog conditions, and systematic studies of these
fog harvesters under laboratory conditions have been rare [27–32].
Under controlled laboratory conditions, Azad et al. have recently
explored the effect of wettability on the fog collection of a double
layered polyolefin Raschel mesh [12]. They found that the amount
of water collected by superhydrophilic mesh was about 5 time that
of a hydrophilic (untreated) mesh, and that a hydrophobic mesh
collected 2.5 times higher amount of water than the hydrophilic
one. Their results indicate that the enhancement of either surface
hydrophilicity or hydrophobicity may increase fog-collection effi-
ciency. The superhydrophilic mesh has been previously shown to
be effective in fog collection [12]. In this work, we consider the
effect of surface hydrophobicity, with particular attention to that
of superhydrophobic coating. We also explore the influence of the
changes in filament dimensions and orientations. Although double
layered Raschel meshes are usually used in the field, our investi-
gation is focused on a single layered one. A good understanding of
its fog-collection behavior may lead to a better application of the
double layered ones.
2. Theoretical background, and comparison tests
2.1. Theoretical background
The collection efficiency, Á, of a mesh depends on aerodynamic
collection efficiency (Áace), capture efficiency (Ácap), and draining
efficiency (Ádra) [27]:
Á= ÁaceÁcapÁdra. (1)
All of these three efficiencies are not larger than 100%. Áace is
the fraction of the unperturbed water flux heading towards a mesh
that would collide with the mesh filaments. Ácap is the fraction of
the collided water drops that actually deposit on filaments from the
fog flow initially headed toward the filaments. Ádra is the fraction of
the deposited water that would drain off from the filament, which
is subsequently collected through a gutter located at the bottom of
the mesh.
Áace is related to shade coefficient (SC), which is the ratio of the
filament area over the total mesh area. Áace does not necessarily
increase with the decrease in the pore area. The expression of Áace
is [27]
Áace =
s
1 + Co
Cd
, (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 is
the 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), Áace is only 9% for a solid plate,
which has no pores. It is 20% for a typical Raschel mesh, whose SC
ranges from 35 to 37%. However, Áace can be easily improved to the
maximum value of 24.5% if SC is 55%, when the filament area of a
typical Raschel mesh is increased relative to the pore area.
Langmuir and Blodgett have previously derived an empirical
expression of Ácap for a circular cylinder [33]. This expression,
together with Eq. (2), was adopted in ref. 24 to optimally design
rectangular meshes, which have circular filaments. Since the fila-
ments of a Raschel mesh have rectangular cross-sections, instead of
circular ones, the empirical expression of Ácap may not be applicable
to the Raschel mesh. In addition, we have not seen any theoretical
models for Ádra. Thus, we would like to have a good understanding
about these two efficiencies through experiments.
2.2. Comparison tests
Fog-collection experiments were performed on different
meshes using an experimental setup shown in Fig. 2. Each test
is 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 mist
to cover a tested sample. A plastic pipe is employed to guide
this mist flow. A fan (model: Breeze color USB Desktop fan, Arc-
tic USA Co.) is used at 800 rounds per minute to increase the
mist flow speed. At the end of the pipe, the mist flow speed is
1.1 m/s, which is measured using a wind speed meter (model:
WM-2 Handheld Weather meter, AmbientWeather USA Co.). The
entire process is conducted in a closed chamber with dimensions of
74 × 31 × 30 cm3 (length × width × height). 100% humidity is main-
tained inside the chamber, and a humidity meter (model: Hydro-](https://image.slidesharecdn.com/51782c99-d6b9-4a89-9e06-ac12c393534a-161023012009/85/Enhancement-of-Fog-collection-Efficiency-of-a-Raschel-Mesh-Using-Short-Roughness-Structures-published-2-320.jpg)
![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.
Fig. 2. (a) Experimental setup for fog collection: vapors are generated by two humidifiers, and a fan is used to drive these vapors towards a hanged mesh through a plastic
pipe (tests are not started yet, and no mesh is hanged at the sample location). (b) Close-up view of the sample location during a test (a mesh was hanged over there, and a
funnel was put at the end of the plastic pipe to ensure that the mist flow covered the whole mesh sample).
Thermometer Humidity Alert with Dew Point- 445815, EXTECH
USA Co.) is used to monitor the humidity throughout a process
cycle. A tested mesh is placed 5 cm away from the exit of the pipe,
and a glass container is put below the mesh to collect water that
drains down.
Two rectangular stainless steel meshes (McMaster-Carr Co.,
USA) and a polyethylene Raschel mesh (Marienberg Co., Chile) were
tested (Fig. 3). The fiber diameter and pore spacing of the first
rectangular mesh are 0.34 and 0.9 mm, respectively. The second
rectangular mesh has thicker fibers and larger pores. Their diame-
ter and spacing are 0.89 and 2.3 mm, separately. The Raschel mesh
has the same dimensions as the ones shown in Fig. 1(b). Its SC is
37%. It is currently being used in a double layer by FogQuest Orga-
nization to collect fog in developing countries.34 All of the three
tested meshes, as well as the other tested meshes of this work, had
the same length of 3.3 cm and width of 2.0 cm.
Receding and advancing contact angles were also measured
on each mesh. In this work, three measurements were taken for
each contact angle with an error of 2◦. Their mean was given in
Table 1. The receding contact angles of the first rectangular, second
rectangular, and Raschel meshes were 45◦, 45◦ and 98◦, respec-
tively. The corresponding advancing contact angles were found to
be 72◦, 56◦, and 113◦. The contact hystereses were 17◦, 11◦, and
15◦, respectively. Since the rectangular meshes had different con-
tact angles from the Raschel mesh, we did not specifically compare
the amounts of water collected by them. Instead, we focused on the
difference in their fog-collection mechanisms.
The two rectangular meshes have a main draining path different
from 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, and
these 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 second
rectangular 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 a
plate without any pores. Thus, Áace actually decreases to the lowest
value of 9% during the collection process. In addition, the drops on
the side surfaces of a fiber are directly exposed in the wind, and they
are lack of strong support of their substrate (Fig. 3(a1)). These may
result in the second problem. That is, although we did not observe
in our tests (the flow speed was 1.1 m/s), such drops may be blown
off by a high-speed wind (e.g., 10 m/s) [24], resulting in the decrease
of Ádra.
In contrast, the Raschel mesh does not have these two prob-
lems. It has rectangular fibers. Initially, tiny drops mainly appeared
on the front surface of a filament, since this surface was directly
exposed 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 surface
of an inclined filament then merged into a small drop (Fig. 3(c1)).
The small drop subsequently moved towards the joint of the fila-](https://image.slidesharecdn.com/51782c99-d6b9-4a89-9e06-ac12c393534a-161023012009/85/Enhancement-of-Fog-collection-Efficiency-of-a-Raschel-Mesh-Using-Short-Roughness-Structures-published-3-320.jpg)
![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 side
surfaces 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 a
Raschel 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 the
mesh 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 1
Contact angles measured on samples before the start of fog tests.
Type Receding contact angle
with an error of 2◦
Advancing contact angle
with 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◦
NeverWet-coated Raschel mesh 154◦
156◦
2◦
Hydrobead-coated Raschel mesh 156◦
158◦
2◦
ZnO nanowires-coated Raschel mesh 112◦
138◦
26◦
ments, coalescing with other drops at this joint to form a large drop
(Fig. 3(c2)). During this process, due to the support of the filament
surfaces and the pinning effect of the filament edges, drops were
difficult to get blown off from a filament by a wind, or to move out of
the filament along the direction perpendicular to this filament. Con-
sequently, in our tests, no water drops were visibly seen to bounce
off from a filament, and they just moved down along the longitu-
dinal direction of an inclined filament. Accordingly, almost all the
water drops that hit the filaments should be captured. The same
applied to the case when the mesh was covered with a superhy-
drophobic coating (the coating and testing results will be detailed
in Section 3). Thus, the Raschel mesh should have a value of Ácap
close to 100%.
Furthermore, the inclined filaments in a Raschel mesh, in com-
parison with vertical fibers in a rectangular mesh, enable drops that
are located on these filaments to merge at their joint (Fig. 3(c2)),
increasing the rate of generating a large drop. When the drop at the
joint became large enough, it overcame the adhesion force over
there and fell down into the underneath water container (Fig. 3(c2)
and (d3)). This drop did not clog much of the pore area. Hence,
in comparison with a rectangular mesh, the Raschel mesh should
have a higher Ádra, and its Áace does not decrease during the fog-
collection process.
The flow speed in our tests was about 1.1 m/s. It is expected
that, at a much higher wind speed (e.g., 10 m/s), water drops may
be bounced off or blown away from the filaments. In addition, it is
noted that, in the case of rectangular meshes [24], the hydrophobic
coating was the most effective in collecting water, while the super-
hydrophobic one was not. They found that the adhesion was not
strong between water drops and superhydrophobic coating, which
may cause a re-entrainment problem to reduce the collection effi-
ciency. However, due to the support of the filament surfaces, the
adhesion is not a major concern in the case of a Raschel mesh, unless
the wind speed is high. To solve the adhesion problem in the case of
high-speed wind, in the near future microchannels may be incorpo-
rated into inclined filaments. The microchannels are oriented along
the longitudinal directions of these filaments. Accordingly, along
the directions perpendicular to the filaments, water drops are fur-
ther pinned by these channels. Meanwhile, these channels do not
affect the movements of the water drops along the longitudinal
directions of such filaments.](https://image.slidesharecdn.com/51782c99-d6b9-4a89-9e06-ac12c393534a-161023012009/85/Enhancement-of-Fog-collection-Efficiency-of-a-Raschel-Mesh-Using-Short-Roughness-Structures-published-4-320.jpg)
![222 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229
As discussed above, Ácap of the typical Raschel mesh may be
considered to be approximately 100% unless the flow speed is high.
Hence, in this work, we focus on increasing Ádra and Áace of a Raschel
mesh.
3. Effects of surface coatings
3.1. Experimental methods and results
To increase Ádra, it is important to make the deposited water
drain off from the mesh filaments. A coating may change wet-
ting properties of a surface such that even a small drop may move
down from the corresponding surface [35,36]. In this work, Raschel
meshes were, respectively, coated with Teflon, ZnO nanowires,
NeverWet, and hydrobead to examine the effects of these coat-
ings on Ádra. The corresponding meshes were, respectively, referred
to as “Teflon mesh,” “nanowire mesh,” “NeverWet mesh,” and
“hydrobead.” These four meshes, together with as-received Raschel
meshes, were tested. Both NeverWet (Rust-Oleum Co., IL, USA)
and hydrobead (Hydrobead Co., CA, USA) are commercially avail-
able. They are often applied to enhance surface hydrophobicity.
NeverWet includes two aerosols, which are called “base coat” and
“top coat”, respectively. The base and top coats were successively
sprayed onto a Raschel mesh. The solid ingredients of the base
and top coats are, respectively, aliphatic hydrocarbon and silicone
derived proprietary ingredient [37,38]. Hydrobead is an aerosol as
well. It was also sprayed onto a Raschel mesh. Its solid ingredients
are aliphatic petroleum distillates and proprietary additives [39].
Teflon films were deposited on the meshes through a dip-coating
process, while ZnO nanowires were grown on these meshes using
a hydrothermal approach [40].
Fig. 4 shows surface structures on the coated meshes. The cor-
responding images were taken using a Hitachi S-3000N Scanning
Electron Microscope (SEM). The dimensions of the surface struc-
tures were also measured using this SEM. The ZnO nanowires have
hexagonal cross-sections with an average length of 2.1 m and
diameter of 0.36 m (Fig. 4a). They have different orientations with
their tips close to each other. The maximum distance of a wire
tip with its neighboring ones is about 5 m. Both NeverWet and
hydrobead have cracks in their coatings. The NeverWet coating has
a thickness of 2.2 m. The cracks are linked with each other, and
most of them have widths ranging from 5 to 10 m (Fig. 4b). The
distance between two neighboring cracks is usually above 100 m.
The hydrobead coating is about 1.8 m thick. The widths of the
cracks range from 1 to 40 m, and their lengths vary from 10 to
180 m (Fig. 4c). Most of the cracks have widths and lengths of
around 15 and 100 m, respectively. The distances between the
cracks range from 20 to 200 m. On the other hand, we did not
observe such cracks on the surface of an as-received Raschel mesh
(Fig. 4d).
Two different samples were prepared for each coating, and three
fog-collection tests were also done for each sample. That is, for
each coating, there were six collected results in total, which also
applies to the tests that will be presented in Section 5. After 1-
h durations, on average Teflon, NeverWet, hydrobead and ZnO
nanowires meshes collected 14, 16, 17 and 13 mL of water, respec-
tively, whereas the as-received Raschel mesh collected only 11 mL.
Hence, the hydrobead has shown the highest collection efficiency,
which is about 1.55 times that of the as-received Raschel mesh.
The receding and advancing contact angles were measured
before fog tests by slightly decreasing and increasing the vol-
ume of a millimeter-scale water drop on a coated mesh (Table 1).
The receding contact angles of Teflon, NeverWet, Hydrobead and
nanowire meshes were 120◦, 154◦, 156◦ and 112◦, respectively. The
corresponding advancing contact angles were found to be 125◦,
156◦, 158◦, 138◦. The contact hystereses were 5◦, 2◦, 2◦, and 26◦,
respectively. After a 1-h fog test, equilibrium contact angles of
water drops that still remained on a vertically-oriented mesh were
also 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 drops
were 121◦, 146◦, 144◦, and 116◦, respectively. In the cases of Nev-
erWet and Hydrobead meshes, these angles were lower than the
receding contact angles obtained before the fog tests, indicating
that contact angles were decreased during the fog tests. Mean-
while, no large reduction in contact angles was found for Teflon
and nanowire meshes, since the average contact angles measured
after fog tests were still slightly higher than the receding ones
determined before the fog tests.
3.2. Simple model
A simple model is developed to explain the fog-collection results
on different coatings. Due to gravity, large drops that are condensed
on a mesh may move down from the mesh. However, tiny drops
may get stuck on the filaments and thus are not harvested. Hence,
to enhance collection efficiency, it is important to harvest as many
tiny drops as possible. A simple model is developed for this purpose.
Let  denote apparent contact angle of a drop. A drop on a substrate
that is inclined by an angle of  suffers a gravitational force G and
a threshold adhesive force F. The two forces, respectively, have the
following expressions:
G = gVsinˇ, (4)
F = FoA(Â, 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 per
unit area of the drop base. In Eq. (5), A(Â, V) denotes the area of the
drop base. It is a function of  and V. By geometric analysis, when V
is fixed, A(Â, V) decreases with the increase in Â. If
G ≥ F, (6)
then the drop moves down from the substrate. For a drop with
a fixed V, by Eq. (4), its G is also fixed. According to Eq. (5), to have
a small F, should be as large as possible to reduce A, while Fo
should be as small as possible. Thus, for the purpose of reducing
F, we desire to make  as high as possible by enhancing surface
hydrophobicity.
On a smooth surface, Â is normally less than 120◦, even if this
surface is coated with highly water-repellent materials [41], such
as Teflon [42]. Hence, to make the corresponding contact angle well
above 120◦, roughness structures are normally incorporated on a
surface.
When a liquid drop is placed on a rough surface, there are
two possible wetting states: Wenzel [43] or Cassie-Baxter [44].
In the Wenzel state (Fig. 5(a)), the drop completely fills grooves
between roughness structures (e.g., pillars and channels), while in
the Cassie-Baxter state, air is trapped between these structures and
the 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 the
hydrophobicity [43,44].
Due to small sizes of roughness structures on NeverWet,
hydrobead and ZnO nanowire meshes, it is difficult to directly
determine whether water fills the gaps of these roughness struc-
tures through an optical microscope. Hence, their wetting state is
judged through theoretical analysis [45–47] (see Supplementary
material for detail). According to this analysis, on these meshes,
the wetting is considered to be in Cassie-Baxter state during our](https://image.slidesharecdn.com/51782c99-d6b9-4a89-9e06-ac12c393534a-161023012009/85/Enhancement-of-Fog-collection-Efficiency-of-a-Raschel-Mesh-Using-Short-Roughness-Structures-published-5-320.jpg)
![224 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229
a
b
b
Cell
a
Liquid drop
Pillar
Solid
substrate
(a)
(b)
Fig. 5. (a) Schematic side view of Wenzel state, and (b) schematic top view of an
array of square micropillars.
process of measuring contact angles before fog tests, while it is in
that of Wenzel during the fog tests.
In the Cassie-Baxter state, due to small contact area between a
drop and the substrate, the drop is easy to roll off from the substrate.
In the Wenzel state, although  may still be large, the roughness
structures may pin the drop, making it difficult to move off from
the surface. Since during the fog tests the wetting may be in the
state of Wenzel, our focus now is on reducing the pinning effect in
this state to reduce Fo.
Let Â0 denote intrinsic contact angle. The equation for Wenzel
state is [43]:
cos  = r cos Â0. (7)
In this equation, r denotes the roughness ratio. It is the ratio of the
actual surface area of the rough surface, Aa, to the projected surface
area, Ap, and is given by
r =
Aa
Ap
. (8)
It is observed from this equation that
r ≥ 1. (9)
When r is 1, it implies that the surface is smooth. As observed from
Relations (7) and (9), to make  larger than Â0, Â0 should be larger
than 90◦, indicating that the surface coating should be hydrophobic.
To have a good understanding about r for choosing it properly,
consider an array of square micropillars with a pillar size of a × a,
spacing of b, and height of h. It is a type of simple structures. Consid-
ering a representative cell around a micropillar (Fig. 5(b)), we have
Ap = (a + b)
2
and Aa = 4ah + (a + b)
2
, where Aa actually equals the
addition of Ap with the four pillar sidewall areas. By Eq. (8), the
corresponding r is
r = 1 +
4ah
(a + b)
2
. (10)
It can be seen from this equation that, for given a, r increases
with the increase in h and decrease in b.
Next, let’s consider two cases. In the first case, we assume that
b a. Accordingly, we get
r ≈ 1 +
4h
a
. (11)
Subsequently, given that Â0 = 100◦, by Eqs. (7) and (11), to make
 equal 150◦, we should have h = a. In the second case, we assume
that b = a. Given that Â0 = 100◦, by Eq. (11), we should have h = 5a to
get  = 150◦. The surface structures in the two cases are illustrated
in Fig. 6. Two points can be observed. First, there are narrow gaps
between 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 ratios
of the structures in these two cases are 1 and 5, respectively. These
two differences indicate that, although the structures in the two
surfaces produce the same r, which actually resulted in the same A,
the values of Fo are different. In Case II, the pillars penetrate a water
drop, and the sidewalls of these structures block the movement of
the drop. In contrast, in Case I, the water in narrow gaps can be con-
sidered stationary, and it becomes part of the substrate surface. The
portion of the drop located above the substrate moves on this com-
posite substrate surface (Fig. 6(a)). Accordingly, the drop in Case
I should suffer a smaller Fo than that in Case II. Furthermore, the
drop volume is in the order of the third power of its radius. Since
b a, it is readily shown the total gap sizes are much smaller than
the drop radius. This result indicates that, as far as the volume is
concerned, the amount of water inside the gaps can be neglected
in comparison with the part of the drop that moves down on the
substrate.
Consider a third case, in which the substrate is flat and it is not
incorporated with any roughness structures (Fig. 6(c)). In Case I,
part of the solid surface in Case III is actually replaced with the
surface of water that fills the narrow gaps. Accordingly,Fo in Case
I is smaller than its counterpart in Case III, because the adhesion
between water and solid should be larger than that between the
same liquid. Furthermore, for a given drop, Case I has a smaller A
than Case III due to the increase in the contact angle. Thus, F in Case
I is smaller than that in Case III, making the corresponding drop
easier to move down on the corresponding substrate. Case II also
has a smaller A than Case III. However, it is not clear whether Fo also
has a smaller value in Case II. Thus, it is uncertain whether Case II
has a smaller F. In summary, there are two possible results after
incorporation of roughness structures. First, if the roughness struc-
tures are closer to those of Case I, then the drop is easier to move
down than in Case III. Second, when these structures are closer to
those of Case II, it is not clear whether the drop is easier to move
down.
Let Âr and Âa, respectively, denote receding and advancing con-
tact angles of the drop. Â ranges between Âr and Âa. The threshold
adhesive force F is often expressed as
F = W (cos Âr − cos Âa), (12)
where W is the diameter of the drop base. On the other hand, there
is a problem of applying this expression to determine F. In Cases I
and II, r has the same value. The same applies to Âo. Accordingly, the
resulting W should be the same in the two cases. Also, by Eq. (7),
(cosÂr-cosÂa) should also be the same as well. Therefore, F should be
the same in both cases. However, as justified above, the two cases
should lead to different values of F. Hence, (cosÂr-cosÂa) may not
always 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 adhesive
force.
In our tests, the NeverWet and hydrobead belong to the first
case, and ZnO nanowires the second case. According to the data](https://image.slidesharecdn.com/51782c99-d6b9-4a89-9e06-ac12c393534a-161023012009/85/Enhancement-of-Fog-collection-Efficiency-of-a-Raschel-Mesh-Using-Short-Roughness-Structures-published-7-320.jpg)
![226 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229
Fig. 7. Two-step process to fabricate the proposed mesh (cross-sectional schematics): (a) a polymer sheet is placed on the bottom mold, and (b) at room temperature, the
top mold is inserted into the polymer sheet to cut undesired portion of the sheet. Fabricated (c1) top and (c2) bottom molds, and (c3) Type II PMMA mesh (optical images).
given in Sub-section 3.1, the ratio of b with a for the NeverWet
coating is above 10, while it is about 13 for the hydrobead. Hence,
for either coating, the assumption that b a is met. Consequently,
both coatings belong to the first case, resulting in the high collection
efficiency. Meanwhile, ZnO nanowires belong to the second case,
and they are not as efficient as the NeverWet and hydrobead.
4. Effects of local geometric changes
4.1. Fabrication of the meshes
Áace of a typical Raschel mesh may be improved to the maxi-
mum value of 24.5% if SC is increased from around 35% to 55%. The
existing meshes are mainly fabricated by weaving fibers together,
such as a typical Raschel mesh shown in Fig. 1(a). When the same
approach is used to create meshes with different SCs, there may be
no polymer fibers that exactly meet the corresponding size require-
ments. To generate a mesh with SC of 55%, what is normally done
is to stack two typical Raschel meshes together to form a double
layered one [24,34]. In this work, we develop a new manufactur-
ing method, which is capable of directly fabricating meshes with
different SCs and shapes.
To manufacture a mesh, pores have to be fabricated in a poly-
mer sheet. Polymer or metal sheets are usually patterned after they
are softened at a raised temperature using a hot-embossing pro-
cess or injection molding [48]. However, it is observed that, even at
room temperature, an office punch can punch holes in paper, which
avoids the needs of heating and cooling a material to be patterned.
Under the motivation of this observation, it should also be feasible
to punch hollow patterns in a polymer sheet at room temperature.
The new method used to fabricate the desired mesh is essentially
a 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)). These
blocks have sharp edges, and are employed to cut off the polymer
for generating pores. The bottom mold also includes mm-scaled
holes. These holes are used to assist in the cutting and removal of
the cut-off polymer.
Two steps are applied in the punching process to fabricate the
new mesh. First, a polymer sheet is placed on the bottom mold
(Fig. 7(a)). Second, at room temperature, the top mold is inserted
into the polymer sheet (Fig. 7(b)). During this step, due to the stress
concentration at the sharp edge of a mm-scaled block of the top
mold, the part of the polymer directly underneath this block is first
cut off from the neighboring polymer, and then pushed into the
corresponding hole inside the bottom mold.
The top and bottom molds in this work were fabricated using
an Epilog laser (Fig. 7(c)). With the aid of these molds, the desire
meshes were generated in a poly-methyl methacrylate (PMMA)
sheet using the two-step punching process. PMMA is a commonly
used material in hot-embossing processes [49]. The used PMMA
sheet is 30 m thick. It is thicker than a Raschel mesh, which
has a thickness of 20 m. Three different types of PMMA meshes
have been fabricated, which are called Types I, II and III meshes,
respectively. Fig. 7(c3) gives a representative Type II mesh that was
fabricated. If needed, the molds can be applied to punch a PMMA
sheet multiple times to fabricate a larger mesh.](https://image.slidesharecdn.com/51782c99-d6b9-4a89-9e06-ac12c393534a-161023012009/85/Enhancement-of-Fog-collection-Efficiency-of-a-Raschel-Mesh-Using-Short-Roughness-Structures-published-9-320.jpg)
![M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 229
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Enhancement of Fog-collection Efficiency of a Raschel Mesh Using Short Roughness Structures published
- 1. Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 Contents lists available at ScienceDirect Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa Enhancement of fog-collection efficiency of a Raschel mesh using surface coatings and local geometric changes Mithun Rajaram, Xin Heng, Manasvikumar Oza, Cheng Luo∗ Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, 500 West First Street, Woolf Hall 226, Arlington, TX 76019, United States h i g h l i g h t s • In this work, we explored the pos- sibility of enhancing fog-collection efficiency of typical Raschel meshes, which have been widely used to col- lect fog in a few countries, such as Chile. • We found that a superhydropho- bic coating resulted in about 50% enhancement in the collection effi- ciency, and developed a simple model to explain the reason behind this enhancement. • We also observed that the reduc- tion of pore size, together with the increase of the distance between two inclined filaments, yielded another 50% enhancement, and found that different pathways of drops resulted in this enhancement. • After the surface modification and local geometric changes, the result- ing mesh has collected water about 2 times that of a typical Raschel mesh. • In addition, we also developed a new punching 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 a r t i c l e i n f o Article history: Received 2 June 2016 Received in revised form 18 August 2016 Accepted 20 August 2016 Available online 22 August 2016 Keywords: Fog collection Raschel mesh Superhydrophobic coating Shade coefficient Punching Wenzel state 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, we explored the possibility of enhancing fog-collection efficiency of typical Raschel meshes. We found that a superhydrophobic coating resulted in about 50% enhancement in the collection efficiency, and that the reduction of pore size, together with the increase of the distance between two inclined filaments, yielded another 50% enhancement. After the surface modification and local geometric changes, the resulting mesh has collected water about 2 times that of a typical Raschel mesh. © 2016 Elsevier B.V. All rights reserved. ∗ Corresponding author. E-mail address: chengluo@uta.edu (C. Luo). http://dx.doi.org/10.1016/j.colsurfa.2016.08.034 0927-7757/© 2016 Elsevier B.V. All rights reserved.
- 2. M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 219 1. Introduction In addition to energy, the issue of water shortage and scarcity is one of major global concerns, since about one billion people living in rural areas of African, Asian, and Latin American countries do not have access to clean water sources [1]. A water shortage has been a major problem faced by the modern civilization in both arid and humid environment [2]. In an arid environment with little rainfall every year, fog may be an important water source to some desert plants and animals, such as the cactus Opuntia microdasys [3], which originates from Chihuahua Desert, the Namib dune bushman grass Stipagrostris sabulicola [4], the species Tillandsia landbecki in coastal Atacama [5], mesophytic geophytes in Namaqualand and the Lit- tle Karoo [6], and the Namib tenebrionid beetle Stenocara [7,8]. A few artificial fog collectors have been recently developed [7,9–24]. Most of them mimic the fog-collection mechanisms of the afore- mentioned cactus [9–16] and beetle [7,17–21]. On the other hand, these collectors appear still at the stage of laboratory research, and have not yet been applied in the field. For the last two decades, in at least five countries, such as Chile, the most commonly used large fog collector in the field employs a Raschel mesh that is vertically oriented between two poles to col- lect water from fog [25–28]. The Raschel mesh has meter-scaled lengths and widths, and it also has mm-scaled pores and filaments (Fig. 1(a)). The pores of a Raschel mesh have approximately trian- gular shapes, and some filaments are inclined with lengths close to 1 cm (Fig. 1(b)). The filaments are about 20 m thick, while their joints are 200–400 m thick. Fog is composed of tiny water drops with diameters in the range of 1–40 m. The fog collection includes two steps. Tiny drops that are carried in a wind hit and accumulate on filaments. Under gravity, large drops, which are formed due to the coalescence of the tiny drops, may drain off from the filaments to an underneath gutter. Raschel meshes are effective in fog collec- tion. Their fog collection rates are typically 1–10 L/m2 per day [28]. Also, the presence of light rain with the fog has produced collec- tion rates as high as 300 L/m2 per day for a wind speed of 10 m/s [28]. On the other hand, there is a large room to improve their fog- collection efficiency. According to recent experimental results, only around 2% of water drops that pass by a typical Raschel mesh have been collected by this mesh [24]. In contrast, an optimal mesh with rectangular pores has shown a five-time enhancement in the fog- collection efficiency of a typical Raschel mesh [24]. Meanwhile, it has already been demonstrated that Raschel meshes are effective to harvest water in the field. Therefore, a Raschel mesh should have its unique advantages in collecting fog. Using woven polyolefin Raschel meshes (Fig. 1), Schemenauer, Cereceda, and their co-workers have conducted numerous pilot- scale studies that demonstrate the feasibility of collecting fog [28–32]. However, as commented in ref. 24, most studies on mesh-based fog harvesters have been performed in the field using uncontrolled natural fog conditions, and systematic studies of these fog harvesters under laboratory conditions have been rare [27–32]. Under controlled laboratory conditions, Azad et al. have recently explored the effect of wettability on the fog collection of a double layered polyolefin Raschel mesh [12]. They found that the amount of water collected by superhydrophilic mesh was about 5 time that of a hydrophilic (untreated) mesh, and that a hydrophobic mesh collected 2.5 times higher amount of water than the hydrophilic one. Their results indicate that the enhancement of either surface hydrophilicity or hydrophobicity may increase fog-collection effi- ciency. The superhydrophilic mesh has been previously shown to be effective in fog collection [12]. In this work, we consider the effect of surface hydrophobicity, with particular attention to that of superhydrophobic coating. We also explore the influence of the changes in filament dimensions and orientations. Although double layered Raschel meshes are usually used in the field, our investi- gation is focused on a single layered one. A good understanding of its fog-collection behavior may lead to a better application of the double layered ones. 2. Theoretical background, and comparison tests 2.1. Theoretical background The collection efficiency, Á, of a mesh depends on aerodynamic collection efficiency (Áace), capture efficiency (Ácap), and draining efficiency (Ádra) [27]: Á= ÁaceÁcapÁdra. (1) All of these three efficiencies are not larger than 100%. Áace is the fraction of the unperturbed water flux heading towards a mesh that would collide with the mesh filaments. Ácap is the fraction of the collided water drops that actually deposit on filaments from the fog flow initially headed toward the filaments. Ádra is the fraction of the deposited water that would drain off from the filament, which is subsequently collected through a gutter located at the bottom of the mesh. Áace is related to shade coefficient (SC), which is the ratio of the filament area over the total mesh area. Áace does not necessarily increase with the decrease in the pore area. The expression of Áace is [27] Áace = s 1 + Co Cd , (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 is the 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), Áace is only 9% for a solid plate, which has no pores. It is 20% for a typical Raschel mesh, whose SC ranges from 35 to 37%. However, Áace can be easily improved to the maximum value of 24.5% if SC is 55%, when the filament area of a typical Raschel mesh is increased relative to the pore area. Langmuir and Blodgett have previously derived an empirical expression of Ácap for a circular cylinder [33]. This expression, together with Eq. (2), was adopted in ref. 24 to optimally design rectangular meshes, which have circular filaments. Since the fila- ments of a Raschel mesh have rectangular cross-sections, instead of circular ones, the empirical expression of Ácap may not be applicable to the Raschel mesh. In addition, we have not seen any theoretical models for Ádra. Thus, we would like to have a good understanding about these two efficiencies through experiments. 2.2. Comparison tests Fog-collection experiments were performed on different meshes using an experimental setup shown in Fig. 2. Each test is 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 mist to cover a tested sample. A plastic pipe is employed to guide this mist flow. A fan (model: Breeze color USB Desktop fan, Arc- tic USA Co.) is used at 800 rounds per minute to increase the mist flow speed. At the end of the pipe, the mist flow speed is 1.1 m/s, which is measured using a wind speed meter (model: WM-2 Handheld Weather meter, AmbientWeather USA Co.). The entire process is conducted in a closed chamber with dimensions of 74 × 31 × 30 cm3 (length × width × height). 100% humidity is main- tained inside the chamber, and a humidity meter (model: Hydro-
- 3. 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. Fig. 2. (a) Experimental setup for fog collection: vapors are generated by two humidifiers, and a fan is used to drive these vapors towards a hanged mesh through a plastic pipe (tests are not started yet, and no mesh is hanged at the sample location). (b) Close-up view of the sample location during a test (a mesh was hanged over there, and a funnel was put at the end of the plastic pipe to ensure that the mist flow covered the whole mesh sample). Thermometer Humidity Alert with Dew Point- 445815, EXTECH USA Co.) is used to monitor the humidity throughout a process cycle. A tested mesh is placed 5 cm away from the exit of the pipe, and a glass container is put below the mesh to collect water that drains down. Two rectangular stainless steel meshes (McMaster-Carr Co., USA) and a polyethylene Raschel mesh (Marienberg Co., Chile) were tested (Fig. 3). The fiber diameter and pore spacing of the first rectangular mesh are 0.34 and 0.9 mm, respectively. The second rectangular mesh has thicker fibers and larger pores. Their diame- ter and spacing are 0.89 and 2.3 mm, separately. The Raschel mesh has the same dimensions as the ones shown in Fig. 1(b). Its SC is 37%. It is currently being used in a double layer by FogQuest Orga- nization to collect fog in developing countries.34 All of the three tested meshes, as well as the other tested meshes of this work, had the same length of 3.3 cm and width of 2.0 cm. Receding and advancing contact angles were also measured on each mesh. In this work, three measurements were taken for each contact angle with an error of 2◦. Their mean was given in Table 1. The receding contact angles of the first rectangular, second rectangular, and Raschel meshes were 45◦, 45◦ and 98◦, respec- tively. The corresponding advancing contact angles were found to be 72◦, 56◦, and 113◦. The contact hystereses were 17◦, 11◦, and 15◦, respectively. Since the rectangular meshes had different con- tact angles from the Raschel mesh, we did not specifically compare the amounts of water collected by them. Instead, we focused on the difference in their fog-collection mechanisms. The two rectangular meshes have a main draining path different from 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, and these 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 second rectangular 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 a plate without any pores. Thus, Áace actually decreases to the lowest value of 9% during the collection process. In addition, the drops on the side surfaces of a fiber are directly exposed in the wind, and they are lack of strong support of their substrate (Fig. 3(a1)). These may result in the second problem. That is, although we did not observe in our tests (the flow speed was 1.1 m/s), such drops may be blown off by a high-speed wind (e.g., 10 m/s) [24], resulting in the decrease of Ádra. In contrast, the Raschel mesh does not have these two prob- lems. It has rectangular fibers. Initially, tiny drops mainly appeared on the front surface of a filament, since this surface was directly exposed 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 surface of an inclined filament then merged into a small drop (Fig. 3(c1)). The small drop subsequently moved towards the joint of the fila-
- 4. 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 side surfaces 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 a Raschel 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 the mesh 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 1 Contact angles measured on samples before the start of fog tests. Type Receding contact angle with an error of 2◦ Advancing contact angle with 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◦ NeverWet-coated Raschel mesh 154◦ 156◦ 2◦ Hydrobead-coated Raschel mesh 156◦ 158◦ 2◦ ZnO nanowires-coated Raschel mesh 112◦ 138◦ 26◦ ments, coalescing with other drops at this joint to form a large drop (Fig. 3(c2)). During this process, due to the support of the filament surfaces and the pinning effect of the filament edges, drops were difficult to get blown off from a filament by a wind, or to move out of the filament along the direction perpendicular to this filament. Con- sequently, in our tests, no water drops were visibly seen to bounce off from a filament, and they just moved down along the longitu- dinal direction of an inclined filament. Accordingly, almost all the water drops that hit the filaments should be captured. The same applied to the case when the mesh was covered with a superhy- drophobic coating (the coating and testing results will be detailed in Section 3). Thus, the Raschel mesh should have a value of Ácap close to 100%. Furthermore, the inclined filaments in a Raschel mesh, in com- parison with vertical fibers in a rectangular mesh, enable drops that are located on these filaments to merge at their joint (Fig. 3(c2)), increasing the rate of generating a large drop. When the drop at the joint became large enough, it overcame the adhesion force over there and fell down into the underneath water container (Fig. 3(c2) and (d3)). This drop did not clog much of the pore area. Hence, in comparison with a rectangular mesh, the Raschel mesh should have a higher Ádra, and its Áace does not decrease during the fog- collection process. The flow speed in our tests was about 1.1 m/s. It is expected that, at a much higher wind speed (e.g., 10 m/s), water drops may be bounced off or blown away from the filaments. In addition, it is noted that, in the case of rectangular meshes [24], the hydrophobic coating was the most effective in collecting water, while the super- hydrophobic one was not. They found that the adhesion was not strong between water drops and superhydrophobic coating, which may cause a re-entrainment problem to reduce the collection effi- ciency. However, due to the support of the filament surfaces, the adhesion is not a major concern in the case of a Raschel mesh, unless the wind speed is high. To solve the adhesion problem in the case of high-speed wind, in the near future microchannels may be incorpo- rated into inclined filaments. The microchannels are oriented along the longitudinal directions of these filaments. Accordingly, along the directions perpendicular to the filaments, water drops are fur- ther pinned by these channels. Meanwhile, these channels do not affect the movements of the water drops along the longitudinal directions of such filaments.
- 5. 222 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 As discussed above, Ácap of the typical Raschel mesh may be considered to be approximately 100% unless the flow speed is high. Hence, in this work, we focus on increasing Ádra and Áace of a Raschel mesh. 3. Effects of surface coatings 3.1. Experimental methods and results To increase Ádra, it is important to make the deposited water drain off from the mesh filaments. A coating may change wet- ting properties of a surface such that even a small drop may move down from the corresponding surface [35,36]. In this work, Raschel meshes were, respectively, coated with Teflon, ZnO nanowires, NeverWet, and hydrobead to examine the effects of these coat- ings on Ádra. The corresponding meshes were, respectively, referred to as “Teflon mesh,” “nanowire mesh,” “NeverWet mesh,” and “hydrobead.” These four meshes, together with as-received Raschel meshes, were tested. Both NeverWet (Rust-Oleum Co., IL, USA) and hydrobead (Hydrobead Co., CA, USA) are commercially avail- able. They are often applied to enhance surface hydrophobicity. NeverWet includes two aerosols, which are called “base coat” and “top coat”, respectively. The base and top coats were successively sprayed onto a Raschel mesh. The solid ingredients of the base and top coats are, respectively, aliphatic hydrocarbon and silicone derived proprietary ingredient [37,38]. Hydrobead is an aerosol as well. It was also sprayed onto a Raschel mesh. Its solid ingredients are aliphatic petroleum distillates and proprietary additives [39]. Teflon films were deposited on the meshes through a dip-coating process, while ZnO nanowires were grown on these meshes using a hydrothermal approach [40]. Fig. 4 shows surface structures on the coated meshes. The cor- responding images were taken using a Hitachi S-3000N Scanning Electron Microscope (SEM). The dimensions of the surface struc- tures were also measured using this SEM. The ZnO nanowires have hexagonal cross-sections with an average length of 2.1 m and diameter of 0.36 m (Fig. 4a). They have different orientations with their tips close to each other. The maximum distance of a wire tip with its neighboring ones is about 5 m. Both NeverWet and hydrobead have cracks in their coatings. The NeverWet coating has a thickness of 2.2 m. The cracks are linked with each other, and most of them have widths ranging from 5 to 10 m (Fig. 4b). The distance between two neighboring cracks is usually above 100 m. The hydrobead coating is about 1.8 m thick. The widths of the cracks range from 1 to 40 m, and their lengths vary from 10 to 180 m (Fig. 4c). Most of the cracks have widths and lengths of around 15 and 100 m, respectively. The distances between the cracks range from 20 to 200 m. On the other hand, we did not observe such cracks on the surface of an as-received Raschel mesh (Fig. 4d). Two different samples were prepared for each coating, and three fog-collection tests were also done for each sample. That is, for each coating, there were six collected results in total, which also applies to the tests that will be presented in Section 5. After 1- h durations, on average Teflon, NeverWet, hydrobead and ZnO nanowires meshes collected 14, 16, 17 and 13 mL of water, respec- tively, whereas the as-received Raschel mesh collected only 11 mL. Hence, the hydrobead has shown the highest collection efficiency, which is about 1.55 times that of the as-received Raschel mesh. The receding and advancing contact angles were measured before fog tests by slightly decreasing and increasing the vol- ume of a millimeter-scale water drop on a coated mesh (Table 1). The receding contact angles of Teflon, NeverWet, Hydrobead and nanowire meshes were 120◦, 154◦, 156◦ and 112◦, respectively. The corresponding advancing contact angles were found to be 125◦, 156◦, 158◦, 138◦. The contact hystereses were 5◦, 2◦, 2◦, and 26◦, respectively. After a 1-h fog test, equilibrium contact angles of water drops that still remained on a vertically-oriented mesh were also 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 drops were 121◦, 146◦, 144◦, and 116◦, respectively. In the cases of Nev- erWet and Hydrobead meshes, these angles were lower than the receding contact angles obtained before the fog tests, indicating that contact angles were decreased during the fog tests. Mean- while, no large reduction in contact angles was found for Teflon and nanowire meshes, since the average contact angles measured after fog tests were still slightly higher than the receding ones determined before the fog tests. 3.2. Simple model A simple model is developed to explain the fog-collection results on different coatings. Due to gravity, large drops that are condensed on a mesh may move down from the mesh. However, tiny drops may get stuck on the filaments and thus are not harvested. Hence, to enhance collection efficiency, it is important to harvest as many tiny drops as possible. A simple model is developed for this purpose. Let  denote apparent contact angle of a drop. A drop on a substrate that is inclined by an angle of  suffers a gravitational force G and a threshold adhesive force F. The two forces, respectively, have the following expressions: G = gVsinˇ, (4) F = FoA(Â, 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 per unit area of the drop base. In Eq. (5), A(Â, V) denotes the area of the drop base. It is a function of  and V. By geometric analysis, when V is fixed, A(Â, V) decreases with the increase in Â. If G ≥ F, (6) then the drop moves down from the substrate. For a drop with a fixed V, by Eq. (4), its G is also fixed. According to Eq. (5), to have a small F, should be as large as possible to reduce A, while Fo should be as small as possible. Thus, for the purpose of reducing F, we desire to make  as high as possible by enhancing surface hydrophobicity. On a smooth surface,  is normally less than 120◦, even if this surface is coated with highly water-repellent materials [41], such as Teflon [42]. Hence, to make the corresponding contact angle well above 120◦, roughness structures are normally incorporated on a surface. When a liquid drop is placed on a rough surface, there are two possible wetting states: Wenzel [43] or Cassie-Baxter [44]. In the Wenzel state (Fig. 5(a)), the drop completely fills grooves between roughness structures (e.g., pillars and channels), while in the Cassie-Baxter state, air is trapped between these structures and the 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 the hydrophobicity [43,44]. Due to small sizes of roughness structures on NeverWet, hydrobead and ZnO nanowire meshes, it is difficult to directly determine whether water fills the gaps of these roughness struc- tures through an optical microscope. Hence, their wetting state is judged through theoretical analysis [45–47] (see Supplementary material for detail). According to this analysis, on these meshes, the wetting is considered to be in Cassie-Baxter state during our
- 6. 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. Arrows in (b2) and (c2) indicate locations of represented narrow gaps.
- 7. 224 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 a b b Cell a Liquid drop Pillar Solid substrate (a) (b) Fig. 5. (a) Schematic side view of Wenzel state, and (b) schematic top view of an array of square micropillars. process of measuring contact angles before fog tests, while it is in that of Wenzel during the fog tests. In the Cassie-Baxter state, due to small contact area between a drop and the substrate, the drop is easy to roll off from the substrate. In the Wenzel state, although  may still be large, the roughness structures may pin the drop, making it difficult to move off from the surface. Since during the fog tests the wetting may be in the state of Wenzel, our focus now is on reducing the pinning effect in this state to reduce Fo. Let Â0 denote intrinsic contact angle. The equation for Wenzel state is [43]: cos  = r cos Â0. (7) In this equation, r denotes the roughness ratio. It is the ratio of the actual surface area of the rough surface, Aa, to the projected surface area, Ap, and is given by r = Aa Ap . (8) It is observed from this equation that r ≥ 1. (9) When r is 1, it implies that the surface is smooth. As observed from Relations (7) and (9), to make  larger than Â0, Â0 should be larger than 90◦, indicating that the surface coating should be hydrophobic. To have a good understanding about r for choosing it properly, consider an array of square micropillars with a pillar size of a × a, spacing of b, and height of h. It is a type of simple structures. Consid- ering a representative cell around a micropillar (Fig. 5(b)), we have Ap = (a + b) 2 and Aa = 4ah + (a + b) 2 , where Aa actually equals the addition of Ap with the four pillar sidewall areas. By Eq. (8), the corresponding r is r = 1 + 4ah (a + b) 2 . (10) It can be seen from this equation that, for given a, r increases with the increase in h and decrease in b. Next, let’s consider two cases. In the first case, we assume that b a. Accordingly, we get r ≈ 1 + 4h a . (11) Subsequently, given that Â0 = 100◦, by Eqs. (7) and (11), to make  equal 150◦, we should have h = a. In the second case, we assume that b = a. Given that Â0 = 100◦, by Eq. (11), we should have h = 5a to get  = 150◦. The surface structures in the two cases are illustrated in Fig. 6. Two points can be observed. First, there are narrow gaps between 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 ratios of the structures in these two cases are 1 and 5, respectively. These two differences indicate that, although the structures in the two surfaces produce the same r, which actually resulted in the same A, the values of Fo are different. In Case II, the pillars penetrate a water drop, and the sidewalls of these structures block the movement of the drop. In contrast, in Case I, the water in narrow gaps can be con- sidered stationary, and it becomes part of the substrate surface. The portion of the drop located above the substrate moves on this com- posite substrate surface (Fig. 6(a)). Accordingly, the drop in Case I should suffer a smaller Fo than that in Case II. Furthermore, the drop volume is in the order of the third power of its radius. Since b a, it is readily shown the total gap sizes are much smaller than the drop radius. This result indicates that, as far as the volume is concerned, the amount of water inside the gaps can be neglected in comparison with the part of the drop that moves down on the substrate. Consider a third case, in which the substrate is flat and it is not incorporated with any roughness structures (Fig. 6(c)). In Case I, part of the solid surface in Case III is actually replaced with the surface of water that fills the narrow gaps. Accordingly,Fo in Case I is smaller than its counterpart in Case III, because the adhesion between water and solid should be larger than that between the same liquid. Furthermore, for a given drop, Case I has a smaller A than Case III due to the increase in the contact angle. Thus, F in Case I is smaller than that in Case III, making the corresponding drop easier to move down on the corresponding substrate. Case II also has a smaller A than Case III. However, it is not clear whether Fo also has a smaller value in Case II. Thus, it is uncertain whether Case II has a smaller F. In summary, there are two possible results after incorporation of roughness structures. First, if the roughness struc- tures are closer to those of Case I, then the drop is easier to move down than in Case III. Second, when these structures are closer to those of Case II, it is not clear whether the drop is easier to move down. Let Âr and Âa, respectively, denote receding and advancing con- tact angles of the drop.  ranges between Âr and Âa. The threshold adhesive force F is often expressed as F = W (cos Âr − cos Âa), (12) where W is the diameter of the drop base. On the other hand, there is a problem of applying this expression to determine F. In Cases I and II, r has the same value. The same applies to Âo. Accordingly, the resulting W should be the same in the two cases. Also, by Eq. (7), (cosÂr-cosÂa) should also be the same as well. Therefore, F should be the same in both cases. However, as justified above, the two cases should lead to different values of F. Hence, (cosÂr-cosÂa) may not always 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 adhesive force. In our tests, the NeverWet and hydrobead belong to the first case, and ZnO nanowires the second case. According to the data
- 8. 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 situations are in Wenzel wetting state.
- 9. 226 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 Fig. 7. Two-step process to fabricate the proposed mesh (cross-sectional schematics): (a) a polymer sheet is placed on the bottom mold, and (b) at room temperature, the top mold is inserted into the polymer sheet to cut undesired portion of the sheet. Fabricated (c1) top and (c2) bottom molds, and (c3) Type II PMMA mesh (optical images). given in Sub-section 3.1, the ratio of b with a for the NeverWet coating is above 10, while it is about 13 for the hydrobead. Hence, for either coating, the assumption that b a is met. Consequently, both coatings belong to the first case, resulting in the high collection efficiency. Meanwhile, ZnO nanowires belong to the second case, and they are not as efficient as the NeverWet and hydrobead. 4. Effects of local geometric changes 4.1. Fabrication of the meshes Áace of a typical Raschel mesh may be improved to the maxi- mum value of 24.5% if SC is increased from around 35% to 55%. The existing meshes are mainly fabricated by weaving fibers together, such as a typical Raschel mesh shown in Fig. 1(a). When the same approach is used to create meshes with different SCs, there may be no polymer fibers that exactly meet the corresponding size require- ments. To generate a mesh with SC of 55%, what is normally done is to stack two typical Raschel meshes together to form a double layered one [24,34]. In this work, we develop a new manufactur- ing method, which is capable of directly fabricating meshes with different SCs and shapes. To manufacture a mesh, pores have to be fabricated in a poly- mer sheet. Polymer or metal sheets are usually patterned after they are softened at a raised temperature using a hot-embossing pro- cess or injection molding [48]. However, it is observed that, even at room temperature, an office punch can punch holes in paper, which avoids the needs of heating and cooling a material to be patterned. Under the motivation of this observation, it should also be feasible to punch hollow patterns in a polymer sheet at room temperature. The new method used to fabricate the desired mesh is essentially a 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)). These blocks have sharp edges, and are employed to cut off the polymer for generating pores. The bottom mold also includes mm-scaled holes. These holes are used to assist in the cutting and removal of the cut-off polymer. Two steps are applied in the punching process to fabricate the new mesh. First, a polymer sheet is placed on the bottom mold (Fig. 7(a)). Second, at room temperature, the top mold is inserted into the polymer sheet (Fig. 7(b)). During this step, due to the stress concentration at the sharp edge of a mm-scaled block of the top mold, the part of the polymer directly underneath this block is first cut off from the neighboring polymer, and then pushed into the corresponding hole inside the bottom mold. The top and bottom molds in this work were fabricated using an Epilog laser (Fig. 7(c)). With the aid of these molds, the desire meshes were generated in a poly-methyl methacrylate (PMMA) sheet using the two-step punching process. PMMA is a commonly used material in hot-embossing processes [49]. The used PMMA sheet is 30 m thick. It is thicker than a Raschel mesh, which has a thickness of 20 m. Three different types of PMMA meshes have been fabricated, which are called Types I, II and III meshes, respectively. Fig. 7(c3) gives a representative Type II mesh that was fabricated. If needed, the molds can be applied to punch a PMMA sheet multiple times to fabricate a larger mesh.
- 10. 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 and detailed in the text, the moving paths on Type I and Type III meshes are similar, while the one on Type II is different.
- 11. 228 M. Rajaram et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 508 (2016) 218–229 Table 2 Total amounts of water collected for 1-h durations on different types of meshes with various coatings. Types I, II and III refer to different types of PMMA meshes. Type Coating Mean of collected water (mL) Standard deviation (mL) I ZnO nanowires 13 1.3 I Teflon 15 1.6 I Hydrobead 18 1.4 II ZnO nanowires 16 1.4 II Teflon 18 1.0 II Hydrobead 23 0.9 III ZnO nanowires 15 1.2 III Teflon 17 1.4 III Hydrobead 21 1.6 As-received Raschel mesh Untreated 11 1.1 The shape of the PMMA meshes is similar to that of the as- received Raschel mesh. On the other hand, these PMMA meshes differ from as-received Raschel mesh in the filament sizes or dis- tances. To examine the effect of SCs on the fog collection, Type I has about the same SC of 37% as the as-received Raschel mesh, while the SCs of Types II and III meshes are both 51%. Consequently, the values of Áace for Raschel and Type I meshes are approximately 21.6%, and they are 23.3% for Types II and III meshes. The inclined filaments of Raschel, Type II and Type III meshes have the same widths of 1.8 mm, whereas they are 1.0 mm wide in the case of Type I mesh (Fig. 8). In addition, along the vertical direction, the distance between two horizontal filaments that are next to each other is 7.0 mm for both Raschel and Type I meshes, while it is 5.4 mm for the other two types of meshes. Accordingly, Types II and III meshes have smaller pores than both Raschel and Type I, and thus they have larger SCs. Moreover, at the joint area, two inclined filaments are separated by 1.8 mm in the cases of both Raschel and Type II meshes, while the separation is 1.0 mm for Types I and III. This variation in the separation allows us to examine its effect on the coalescence of drops. The fabricated PMMA meshes are subsequently coated with ZnO nanowires, Teflon, and hydrobead, respectively. The base coat of NeverWet etches PMMA. Therefore, although the NeverWet has previously shown a high collection efficiency, it is not used on the PMMA meshes. Contact angles on a surface are affected by the roughness and coating of this surface. Since both PMMA and Raschel meshes have relatively smooth surfaces, the contact angles on their surfaces depend on the corresponding coatings. As expected, con- tact angles of water on a coated PMMA mesh are measured to be about the same as those on a Raschel mesh that has the same coat- ing. 4.2. Fog-collection results and discussions Table 2 gives the amounts of water collected by the PMMA meshes. Four points are observed from this table. First, as in the previous tests, the hydrobead coating still has the highest col- lection efficiency among the three tested coatings in each type of PMMA meshes. Second, when Type I and as-received Raschel meshes were coated with the same material, they collected about the same amount of water. For example, Type I mesh with the hydrobead coating collected 18 mL water, while hydrobead-coated Raschel mesh harvested 17 mL. These two meshes have the same geometry. This point indicates that, when they have the same sur- face coating, the PMMA mesh does not have distinctive advantage over as-received Raschel mesh in water collection. Third, Types II mesh with the hydrobead coating has shown the highest collection efficiency among all the tested mesh. It has collected 23 mL water during a 1-h period, which is 34.9 L/mm2. This point indicates that, with the further modification of mesh geometry, the collec- tion efficiency has been improved from 1.55 to 2.09 times that of the as-received Raschel mesh. Fourth and finally, the ratio of standard deviation to the mean is less than 0.11, indicating that the varia- tion of the six fog-collection measurements is small on each type of meshes. Contact angles were measured on a dry sample before and after all the tests, and there was no much difference in the cor- responding values. Also, after the tests, no damage was observed on 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 flow patterns, 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 Áace. To explore why Type II mesh was more effective in collecting fog than Type III, we explored the moving paths of condensed water drops on the meshes. As observed from Fig. 8, there are some differences in these moving paths, which influence the drop draining efficiency. The moving paths on Type I and Type III meshes are similar as that on a Raschel mesh (Fig. 3(c)). Once a large drop gets to the joint of two inclined filaments, due to the small separation between these filaments, the drop may be pinned over there. Its growth relies on both the adsorption of the incoming water drops and addition of new drops from the two inclined filaments. However, in Type II, because of the relatively larger separation, a large drop may not be pinned at the joint area. Instead, it may move all the way down till it is large enough to fall down from the mesh. During this process, it receives additional supply of water, which comes from the tiny drops present on its draining path. Although, as in the case of Type II, two inclined filaments of a Raschel mesh are also separated by 1.8 mm at their joint area, there is a critical difference in the way that the inclined filaments are connected with the horizontal one. In the case of the Raschel mesh, the inclined filaments are wrapped around the horizontal filament at the joint area, forming knots over there. These knots pin water drops. However, in Type II mesh, the inclined filaments are smoothly connected to the horizontal one, which reduces the pinning effect such that a drop located at the joint area may further move down. 5. Summary and conclusions In this work, we explore the possibility of improving fog- collection efficiency of Raschel mesh through surface modification and local geometric changes. We considered five different coat- ings on the mesh surfaces. Through experimental and theoretical investigations, we demonstrated that it was possible to improve the fog-collection efficiency using coatings with narrow gaps. The basic idea is to increase the contact angle, while in the meanwhile to reduce the pinning effect. NeverWet and Hydrobead both satisfy these two requirements. As a result, their coatings have increase the collection efficiency of the Raschel mesh by about 50%, and are the most efficient two among the five coatings that were tested. A new punching process was further developed to fabricate three different types of PMMA meshes. Due to the differences in SC and drain- ing paths of condensed water drops, Type II meshes have shown another 50% enhancement in fog-collection efficiency. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.colsurfa.2016.08. 034.
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