The effects of surface energy and roughness on the hydrophobicity of woven fabrics

Abstract

The wetting behavior of a hydrophobic rough surface is investigated on a surface fabricated by applying low surface tension materials such as silicone or fluoropolymer to polyester woven fabric consisting of multifilament yarns. The roughness factor of various woven fabrics can be calculated by Wenzel’s and Cassie–Baxter’s equations. For the fabrics treated with silicone or fluoropolymer, the Cassie–Baxter model was applied, showing a level of agreement for the fabric specimens non-textured filament fibers between the predicted contact angles and the measured values. More precisely, the fabrics treated with silicone or fluoropolymer represent the transitional state between the Wenzel type and the Cassie–Baxter type; that is, the fractional contact area between the water and air f₂ is greater than zero, and the sum of the fractional contact areas for solid–water f₁ and air–water f₂ is greater than 1. A surface with lower energy and higher roughness gave f₁ + f₂ close to 1 with smaller f₁ and larger f₂, which resulted in a high contact angle.

Keywords

Hydrophobic lotus effect roughness factor Wenzel model Cassie–Baxter model

Inspired by natural surfaces like the lotus leaf, surfaces with extreme water repellent properties have received considerable interest in the last decade.¹ The studies by Wenzel² and Cassie and Baxter³ showed that the rough and porous structure of a surface combined with a low surface energy can contribute to the hydrophobicity of a surface. The surface of the lotus leaf is chemically made of wax and structurally has two levels of roughness consisting of nano-scale bumps on the surface of micro-scale protrusions that enables the trapping of air underneath water droplets, thereby contributing to a well-designed superhydrophobic surface.⁴ Drops of water deposited on such superhydrophobic surfaces exhibit extremely high contact angles (>150°) and roll off at slight inclinations. Potential applications range from non-wettable, quick-drying surfaces to anti-fouling or self-cleaning surfaces.^4–8 In view of the significant potential of such surfaces for numerous scientific and industrial applications, many strategies to create superhydrophobic surfaces have been published to date.^6–9

As a measure of the hydrophobicity of the fabric surface, the static contact angle is often used; a larger contact angle with a smaller contact angle hysteresis represents higher hydrophobicity. Wenzel² and Cassie and Baxter³ suggested the theoretical models for contact angles of a liquid on a surface with certain geometry.⁹ Different contact angles may result with the same roughness texture depending on how the liquid is configured on the surface. When a liquid completely fills all the spaces in the pores, the Wenzel model is applied to describe the contact angle $θ_{r}^{W}$ as a function of the ratio of the liquid–solid contact area to the projected area

\cos θ_{r}^{W} = r \cos θ_{e}

(1)

where

r (roughness factor) = \frac{liquid - solid actual contact area}{projected area of geometric surface}

and

$θ_{r}^{W}$ : apparent contact angle of liquid on a rough surface in a Wenzel state;

$θ_{e}$ : equilibrium contact angle when the liquid droplet sits on a smooth surface; and

Projected area: the apparent area whose liquid–solid contact surface is projected to a flat surface.

This model predicts the reinforced hydrophilicity or hydrophobicity by the surface roughness. Wenzel² predicted that when $θ_{e} < 90^{\circ},$ a higher roughness ratio r leads to a larger value for $\cos θ_{r}^{W}$ , towards 1, thus giving a smaller value for $θ_{r}^{W}$ , towards $0^{\circ}$ . More recent studies by Bico et al.¹⁰ and Priest et al.¹¹ discussed that $θ_{e}$ as a critical contact angle is not necessarily $90^{\circ}$ but an angle lower than $90^{\circ}$ , at around 75 $^{\circ}$ . In this situation, as roughness factor r gets larger, the apparent contact angle would go towards $0^{\circ}$ driven by the capillary action, effectively spreading or wicking the water drop on a surface. On the other hand, if $θ_{e} > 90^{\circ},$ a higher roughness factor generates a value for $\cos θ_{r}^{W}$ close to -1, giving a value for $θ_{r}^{w}$ close to $180^{\circ}$ , which represents the reinforced hydrophobicity on a rough and low energy surface.

Cassie and Baxter³ extended the Wenzel² model to include the heterogeneous and porous surface in their model to predict the relationship between the contact angle and the fractional contact areas of multiple-composition surfaces as

\cos θ_{r}^{CB} = f_{1} \cos θ_{e} + f_{2} \cos θ_{e^{'}}

(2)

where

$θ_{r}^{CB}$ : apparent contact angle of liquid on a rough surface in a Cassie–Baxter state;

$θ_{e}$ : equilibrium contact angle when the liquid droplet sits on a smooth surface 1;

$θ_{e^{'}}$ : equilibrium contact angle when the liquid droplet sits on a smooth surface 2;

f₁: fraction of surface 1 area in contact with liquid = $\frac{area of surface 1 in contact with liquid}{projected area of surface 1 in contact with liquid}$ ; and

f₂: fraction of surface 2 area in contact with liquid $= \frac{area of surface 2 in contact with liquid}{projected area of surface 2 in contact with liquid}$ .

In this model, if the surface is not completely wet, the water drop makes contact on the heterogeneous surface of the solid and air. When air traps are present on a rough single-component surface, the contact angle of water in air, $θ_{e^{'}} = 180^{\circ}$ , and the following is derived¹²

\cos θ_{r}^{CB} = r_{f} fcos θ_{e} + f - 1

(3)

where

r_f: roughness of wet surface = $\frac{area of solid surface in contact with liquid}{projected area of solid surface in contact with liquid}$ ; and

f: fraction of solid surface area wet by the liquid = $\frac{projected area of solid surface in contact with liquid}{projected total area (air and solid) in contact with liquid}$ .

From equation (3), the increased roughness r_f is explained to further increase the apparent contact angle $θ_{r}^{CB}$ in the Cassie–Baxter state, when the contact angle $θ_{e}$ on an intrinsically hydrophobic surface is larger than $90$ °.

From a model cross-sectional view of a plain woven fabric made from multifilament yarns, the surface area of a multifilament yarn in the unit fabric can be calculated as illustrated in Figure 1. The projected area of a normal fabric can be calculated by measuring the horizontal and vertical lines in the unit area. From Figure 1, the roughness factor r of the untreated fabric can be calculated by the area in contact with the water divided by the projected area, or $\frac{4.19 {NR}_{f}}{R_{y}}$ .⁹ The equation gives a larger roughness factor with a larger number of filaments, a larger filament size, and a smaller yarn size.

Figure 1.

Cross-sectional view of a model multifilament woven fabric.

The roughness and contact angle of non-wetting fabrics can be calculated by the Cassie–Baxter³ model, equation (3). Fabric yarns can be modeled as separated cylinders in parallel by a distance of 2 d, as illustrated in Figure 2.⁹ A liquid drop sits on the cylinders, and the dotted line represents the projected area of the cylinders in contact with the water. The fraction of the surface area in contact with water drop is given as $f = R \sin α / (R + d)$ , and the roughness of the surface in contact with water is defined by $r_{f} = α / sin α$ from the model in Figure 2.

Figure 2.

Liquid drop on cylinders separated by a distance 2 d.

Marmur,¹² later in 2003, reported that the surface free energy of solid–liquid–air goes to a minimum when $α = π - θ_{e}$ , and equation (4) results from substituting f and r_f into equation (3), and substituting $π - θ_{e}$ for α. By the Cassie–Baxter model in equation (4), the apparent contact angle $θ_{r}^{CB}$ can be predicted for a hydrophobic fabric surface

\cos θ_{r}^{CB} = (\frac{R}{R + d}) (π - θ_{e}) cos θ_{e} + (\frac{R}{R + d}) sin (π - θ_{e}) - 1

(4)

Despite the efforts to understand the characteristics of the hydrophobic surface and the frequent reference of the superhydrophobic surface to textile applications, only few reports exist that actually pertain to superhydrophobic textiles.^13–16 Many of these performed only an initial characterization of the wetting properties of the resulting fabrics and lack in providing the engineering guidelines for a desired superhydrophobic fabric surface in relation to the material surface energy and roughness.

The purpose of this study is to provide the fundamental understanding of the characteristics of the hydrophobic surface associated with surface roughness and surface energy and examine the validity of theoretical models by the observations in the textile applications. To this end, a hydrophobic rough surface was designed on polyester woven fabrics treated with low surface tension materials such as silicone or fluoropolymer. The roughness factor of various woven fabrics was calculated using the Wenzel and Cassie–Baxter equations, and the wetting behavior of the treated fabrics was observed in relation to the predicted contact angles by the theoretical models.

Experimental details

Materials

100% polyester woven fabrics having various yarn diameters and yarn types were purchased from Dong Jin Textile Co., Ltd. (Korea). The number given in the specimen code indicates the denier of the yarn, and the following alphabet code D and F is to differentiate between the filament yarns with and without the drawn textured yarn (DTY) finishing. The characteristics of the fabrics are presented in Table 1.

Table 1.

Characteristics of the fabric specimens

Code	Yarn count	Weight (g/m²)	Thickness (mm)	Density (in cm)
PF (film)	–	52.40	0.18	–
20 F	20 denier yarn in 24 filaments	38.12	0.07	94 × 57
50 F	50 denier yarn in 36 filaments	66.12	0.12	76 × 41
50D	50 denier yarn in 72 filament DTY	65.53	0.13	69 × 44
75D	75 denier yarn in 72 filament DTY	83.42	0.16	57 × 38
150D	75 denier yarn (warp) in 72 filaments + 150 denier yarn (weft) in 144 filament DTY	107.99	0.21	57 × 31

All fabrics were used after purification as in the following. Fabric specimens were washed with a solution of 5 g/l anionic surfactant and 10 g/l Na₂CO₃ for 30 minutes at 97 ± 3℃, rinsed, and dried. Dried fabrics were extracted for 8 hours with a mixture of benzene–ethanol (2:1 v/v) in a soxhlet, rinsed with 40℃ water, and dried at 105 ± 2℃ for 20 minutes.

Two different water repellent agents, polydimethylsiloxane (Phobol RSH®) and perfluoroacrylate (Oleophobol®) were purchased from Huntsman (Texas, USA). Phobol XAN®, a crosslinking agent that was used to chemically bond repellent agents to textiles, was purchased from Huntsman (Texas, USA). Acetic acid (99.5%) and isopropyl alcohol (99.5%) were purchased from Daejung Chemicals and Materials Co., Ltd. (Korea).

Water repellent treatment

Water repellent agents in this study, polydimethylsiloxane and perfluoroacrylate agents, were coded as silicone and fluoro respectively, and their chemical structures are given in Figure 3. The formulation of the treatment solution is presented in Table 2. Acetic acid was used to adjust the pH of the solution to 5–7 for both the silicone and fluoro treatments. 10 ml of Phobol XAN® as a crosslinking agent was added for both the silicone and fluoro treatment. Isopropyl alcohol was added to the fluoro treatment to enhance the penetration of the agent to the polyester fabrics. Both the silicone and fluoro agents were used as 10% (v/v) diluted emulsion in deionized water, and the fabrics were treated by a dip–pad–dry procedure. Soaked fabrics were pressured through two rollers at 50 psi, 20 rpm, dried at 120℃ for 2 minutes, then were cured at 160℃ for 5 minutes.

Figure 3.

Chemical structure of (a) silicone and (b) fluoro.

Table 2.

Formulation of water repellent applications

Silicone		Fluoro
Water	889 ml	Water	884 ml
Phobol RSH®	100 ml	Oleophobol®	100 ml
Acetic acid	1 ml	Acetic acid	1 ml
Phobol XAN®	10 ml	Phobol XAN®	10 ml
Isopropyl alcohol	5 ml

Characterization

The morphology and roughness of the specimen surfaces were analyzed by a field emission scanning electron microscope (FESEM) (SUPRA™ 55VP, Carl Zeiss, Germany).

Contact angle measurements were performed on a Theta Lite contact angle meter (Attension, KSV Instruments, Finland) at room temperature. A fabric specimen was attached to a glass cover slip with double-sided adhesive tape, and 3.6 ± 0.2 µl drops of deionized water were placed on five different spots of the surface to be investigated. The contact angle for a water drop was recorded after 0.5 seconds upon dropping, and the average of ten different measurements were used for the analysis.

Results and discussion

The roughness of the fabric surface was estimated by calculations using equations derived from the Wenzel or the Cassie–Baxter models depending on the wetting characteristics of the fabric specimens. Untreated polyester fabrics were completely wet, and the Wenzel equation was used. Polyester fabrics treated with repellent agents were not completely wet, and the surface could be defined as in a transitional state or the Cassie–Baxter state. The roughness factor in this state was estimated by the Cassie–Baxter equation.⁹ The surface wetting states and the model equations applied are illustrated in Figure 4.

Figure 4.

Wetting characteristics with models applied.

Also, the surface morphology of the untreated 50D fabric and the fabric treated with silicone or fluoro agents were observed by FESEM in Figure 5. Compared to untreated 50D, silicone-treated fabric showed a certain level of added roughness, yet it is not very distinct. The fluoro-treated fabric, compared to the untreated, showed drops of chemical deposit from the aggregation of the fluoro agent on the rather smooth surface.

Figure 5.

FESEM images of the (a) pristine, (b) silicone, (c) and fluoro-treated fabrics (x 3000 magnifications).

Roughness factor and wetting properties of hydrophilic fabrics

The roughness factor r of a hydrophilic surface of a non-treated polyester fabric was calculated by the Wenzel model, and the values for N, R_y, R_f, projected area, wet area, and r are presented in Table 3.

Table 3.

r and related factors calculated by the Wenzel model

Samples	Projected area (µm²)	Area in contact with liquid (µm²)	N (count)	R_y (µm)	R_f (µm)	r
PF	100 × 100 = 10,000	100 × 100= 10,000	–	–	–	1
20F	107.5 × 152 = 16,340	2π(24 × 5.1) × 110.88 × 2= 165,264	24	27.7	5.1	10.1
50F	131.5 × 261.5 = 34,387	2π(36 × 5.9) × 150.01 × 2= 400,188	36	37.5	5.9	11.6
50D	165.5 × 230.5 = 37,897	2π(72 × 4.75) × 166.84 × 2= 716,664	72	41.7	4.8	18.9
75D	188 × 265.5 = 49,914	2π(72 × 6.1) × 209.72 × 2= 1,156,889	72	52.4	6.1	23.1
150D	178 × 306 = 54,468	2π(114 × 6.1) × 321.7 + 2π(72 × 6.1) × 209.727= 2,353,054	144(weft), 72(warp)	80.4/52.4	6.1	43.2

By the relation $cos θ_{r}^{W} = rcos θ_{e}, when θ_{e} < 90^{\circ} and θ_{r}^{W}$ goes towards $0^{\circ}$ , the liquid is drawn into contact with the rough surface. In other words, a hydrophilic characteristic of the surface becomes reinforced by the capillarity when roughness r increases.

For most of the materials, London dispersion forces d, permanent dipoles p, and hydrogen bonding h are the major factors determining the surface tension, and $θ_{e}$ can be calculated as follows¹⁷

γ_{L} (1 + cos θ_{e}) = 2 (\sqrt{γ_{S}^{d} \cdot γ_{L}^{d}} + \sqrt{γ_{S}^{p} \cdot γ_{L}^{p}} + \sqrt{γ_{S}^{h} \cdot γ_{L}^{h}})

(5)

where

$γ_{L}$ : surface tension of liquid;

$γ_{S}^{d}$ , $γ_{S}^{p}$ , $γ_{S}^{h}$ : critical surface tension of the solid contributed by the London dispersion force, the permanent dipoles, and the hydrogen bonding, respectively; and

$γ_{L}^{d}$ ., $γ_{L}^{p}$ ., $γ_{L}^{h}$ : surface tension of the liquid contributed by the London dispersion force, the permanent dipoles, and the hydrogen bonding, respectively.

From equation (5), a water droplet $(γ_{L}^{d} = 21.8 dyne / cm, γ_{L}^{p} = 1.4 dyne / cm, and γ_{L}^{h} = 49.6 dyne / cm)$ placed upon a smooth polyester film ( $γ_{S}^{d} = 47.5 dyne / cm, γ_{S}^{h} = 2.2 dyne / cm)$ should have a contact angle of $θ_{e} = 80^{\circ}$ . The measured value of the contact angles on a cleaned surface of smooth polyester film (PF) were observed to be $78^{\circ} \leq θ_{e} \leq 82^{\circ}$ , which agreed with the theoretical value.

Figure 6 shows that the shape of a water droplet on the untreated samples with lapsing time dependent on the roughness factor and the inside structure of the multifilament yarns. The roughness factors of all fabric samples were higher than ten, and the contact angle of all fabric samples with lapsing time went close to $0^{\circ}$ , being completely wet.

Figure 6.

Solid volume fraction and the shape of the water droplet on untreated samples over time.

Michielsen et al.⁹ regarded the situation where arcos(>1) as complete wetting in the study of superhydrophobic surface in a woven structure. The Wenzel model may not be able to strictly apply to the woven fabrics as their structure involves a complex process of wicking, penetration, and spreading of water through the pores and capillaries. However, the rough fabric surface consisting of a homogeneous material of solid filaments was approximated by the Wenzel model to predict the behavior of fabric wetting for the boundary of rough solid surface-pores with air–water droplet.

The solid volume fraction S of a fabric is the ratio of solid parts to the total volume of the material as can be calculated as: $S = \frac{m / ρ}{at}$ , where S represents the solid volume fraction of the fabric; m is the mass of the specimen at standard condition g; ρ is the density of the fiber (g/cm³); $α$ is the area of the specimen (cm²); and t is the thickness of the specimen (cm).¹⁸

The solid volume fraction has shown to be an influential structural parameter that affects the wetting behavior of multifilament woven fabrics by capillary action. Solid volume fractions for the specimens in this study were in a range of 0.37– 0.4 (Figure 6). The bulkier DTY fabrics showed shorter lapsing time than filament fabrics because larger roughness and inter-yarn spaces reinforced the hydrophilicity of fabrics, trapping more liquid in the space more quickly.

Also, for the fabrics with the same S (20 F vs. 50 F, 50D vs. 75D), the fabric with more filaments had shorter lapsing time due to more effective wicking by a larger number of channels for the capillary action. A decrease in thread density or an increase in inter-yarn space would result in storage of more liquid, which would facilitate both the wicking rate and the equilibrium wicking height.^19–22

Roughness factor and wetting properties of hydrophobic fabrics

The roughness of fabrics treated with water repellent agents was calculated by the Cassie–Baxter equation (equation (4)). The equilibrium contact angle on a smooth surface

θ_{e}

was estimated by equation (5). From the surface tension of materials given in Table 4,¹⁷ the water contact angles

θ_{e}

on a flat surface treated with silicone and fluoro were estimated as

112^{\circ}

and

117^{\circ}

respectively.

Table 4.

Surface tension of various materials.^17,23,25

Surface tension (dyne/cm)
London dispersion forces (d)	Permanent dipoles (p)	Hydrogen bonding (h)	Total
Water	21.8	1.4	49.6	72.8
PET	47.5	–	2.2	49.7
Silicone-treated	24.0	–	–	24.0
Fluoro–treated	18.5	–	–	18.5

Fluorocarbon polymer has been reported as an excellent hydrophobic coating material.²³ Hare et al.²⁴ reported that the surface free energy increases when fluorine is replaced by other elements such as H and C, in the order -CF₃ < -CF₂H < -CF₂- < -CH₃ < -CH₂-, and predicted that the hexagonal packing of -CF₃ groups on the surface would give the lowest surface energy of the materials.

Figure 7 shows the projected area, R, and R + d in a fabric. A circle fitted to the curvature of a bump in cross-section of the fabric was drawn, and this circle’s radius R and the repeated local union as R + d were defined from the image (Figure 7(b)).

Figure 7.

Fabric (a) projected area and (b) cross-section view to measure R and R + d.

θ_{e}

, obtained by equation (5), and R/(R + d), estimated from the image projection, were used to obtain f₁, f₂, and

θ_{r}^{CB}

from equation (4). Only the fabrics treated with water repellent agents were fitted to the Cassie–Baxter model, and the predicted values are given in Table 5. For all treated fabrics, f₂ was greater than 0, and f₁ + f₂ was greater than 1, which confirmed the transitional state of the treated fabrics.

Table 5.

Roughness $(f_{1} + f_{2})$ of repellent fabrics estimated by the Cassie–Baxter model

Materials	Sample	R ( $μ m$ )	R + d ( $μ m$ )	$θ^{CB}$ (°)	f ₁	f ₂	$f_{1} + f_{2}$
Silicone $θ_{e} = 112^{\circ}$	20 F	62.5	108.8	136	0.68	0.47	1.15
	50 F	120.0	199.3	135	0.71	0.44	1.16
	50D	102.0	197.0	139	0.61	0.52	1.13
	75D	115.0	227.2	139	0.60	0.53	1.13
	150D	149.5	252.2	136	0.70	0.45	1.15
Fluoro $θ_{e} = 117^{\circ}$	20 F	62.5	108.8	141	0.63	0.49	1.12
	50 F	120.0	199.3	140	0.66	0.46	1.13
	50D	102.0	197.0	143	0.57	0.54	1.11
	75D	115.0	227.2	143	0.56	0.55	1.11
	150D	149.5	252.2	140	0.65	0.47	1.12

The contact angle appeared dependent on the surface energy and the structural characteristics of fabrics. For the fabrics with the same woven structure treated with different repellent agents, fluoro-treated fabrics showed larger f₂ and smaller f₁ than silicone-treated fabrics, and f₁ + f₂ for fluoro-treated fabrics was closer to 1 than for silicone-treated fabrics. This result implies that, in a same surface structure, the surface with lower energy gets closer to the Cassie–Baxter state after the transitional state. Also, the fabrics with f₁ + f₂ close to 1 gave higher contact angles. Among the five different fabric structures, 50D and 75D showed the largest f₂ and the smallest f₁ + f₂ being close to 1, which may be attributed to DTY fabrics’ increased roughness and bulkiness. For the surface with low energy and high roughness, the air traps in the surface act as a cushion and help support the water drops existing between the fabric bumps. The contact angle with time for the fluoro-treated fabrics is presented in Figure 8, and the repellent-treated fabrics appeared to maintain the contact angle with lapsing time until 250 seconds.

Figure 8.

Values of $f_{1} + f_{2}$ and the shape of a water droplet on fabrics treated with the fluoro agent.

The apparent contact angles predicted by the Wenzel or Cassie–Baxter models and the values measured from the experiments are compared in Table 6 and Figure 9. The pristine polyester fabrics represented Wenzel-type behavior with complete wetting; for the smooth surface of non-treated film, the contact angle $θ_{e}$ is lower than 90°. On the other hand, both the silicone-treated fabrics and the fluoropolymer-treated fabrics showed increased contact angles than untreated, with values greater than 130°. Because $θ_{e}$ of the film-treated with water repellent agents was greater than 90°, the contact angles of those woven fabrics were fitted to the Cassie–Baxter equation, and there was relatively better agreement between the predicted values and the measured contact angles for the fabrics consisting of non-DTY yarns such as 20 F and 50 F.

Figure 9.

Predicted and measured contact angles for (a) silicone and (b) fluoro-treated fabrics.

Table 6.

Comparison of predicted and measured contact angles

Sample	Apparent contact angles (°)
	Untreated PET		Silicone-treated PET		Fluoro-treated PET
	Predicted	Measured	Predicted	Measured	Predicted	Measured
PF	$θ = 80$	$80 \leq θ \leq 83$	$θ = 112$	$111 \leq θ \leq 117$	$θ = 117$	$117 \leq θ \leq 124$
20 F	$θ = 0$	$θ = 0$	$θ = 136$	$131 \leq θ \leq 136$	$θ = 141$	$141 \leq θ \leq 143$
50 F	$θ = 0$	$θ = 0$	$θ = 135$	$133 \leq θ \leq 139$	$θ = 140$	$138 \leq θ \leq 145$
50D	$θ = 0$	$θ = 0$	$θ = 139$	$143 \leq θ \leq 147$	$θ = 143$	$149 \leq θ \leq 156$
75D	$θ = 0$	$θ = 0$	$θ = 139$	$145 \leq θ \leq 151$	$θ = 143$	$149 \leq θ \leq 156$
150D	$θ = 0$	$θ = 0$	$θ = 136$	$152 \leq θ \leq 155$	$θ = 140$	$150 \leq θ \leq 155$

However, the measured values of DTY samples gave greater values than the predicted ones. DTY is a partially drawn filament yarn with a soft crimp, a high bulkiness, and a natural fiber-like texture, thus it tends to retain more air space between the filaments with a rougher surface. It was thought that the DTY’s structural characteristics augmented the roughness of fabrics’ surface, whose microstructure was not fully captured in the model. Also, DTY samples showed higher contact angles, which can be explained by the reinforced hydrophobicity resulting from more air traps and a bulkier structure.

The geometry of textile substrates is significantly different from flat or regularly structured surfaces. A textile usually has coarse, complex textured surfaces which may have similar effects as lotus leaves. In order to achieve a superhydrophobic surface, it would be essential to design a low energy surface with microstructures that can effectively “hold” the air in place.

As the Cassie–Baxter model agreed well with the observed wetting behavior, a surface structure defined by R and R + d can be designed to have a certain contact angle, with known surface energy. For example, a superhydrophobic surface with contact angle greater than 150° can be engineered with a material having

θ_{e}

= 117°. Example structural factors that would enable the fabrication of superhydrophobic fabrics having

θ_{e}

> 150° at a given surface energy are presented in Table 7.

Table 7.

Engineering examples of fabric structure having the static contact angle > 150°

Materials	R ( $μ m$ )	R + d ( $μ m$ )	Fabric density count/cm × count/cm)	R/(R + d)	f ₁	f ₂	$f_{1} + f_{2}$
Silicone $θ_{e} = 112^{\circ}$	50 100	175 349	57 × 57 29 × 29	0.28	0.34	0.73	1.07
Fluoro $θ_{e} = 117^{\circ}$	50 100	142 284	70 × 70 35 × 35	0.35	0.38	0.69	1.07

Conclusions

This study is to investigate the effect of roughness of woven fabrics on the hydrophobicity of the woven fabrics, employing the Wenzel and Cassie–Baxter models by examining the predicted values in comparison with the measured values. Fabrics with multifilament yarns were modeled for their structural definition and roughness estimation, and the models were fitted based on the wetting behavior of the various fabric types.

A superhydrophobic surface can be obtained by two criteria: a low surface energy and an appropriate surface roughness which result in water detaching from the surface at a low roll-off angle. As a first step, polyester woven fabrics in varied yarn counts and constructions were treated for surface energy, using silicone or fluoropolymer repellent agents, and were examined for their contact angles. The pristine fabrics untreated with water repellent agents represented Wenzel-type behavior with complete wetting. On the other hand, both the silicone-treated and the fluoropolymer-treated fabrics showed high contact angles from 131° to 156°.

The contacts angles of the woven fabrics treated with silicone and fluoropolymer were predicted using the Cassie–Baxter equation, and the theoretical contact angle values were in better agreement with the measured values of 20 F and 50 F than those for DTY fabrics. An engineering guidance to fabricate a superhydrophobic fabric surface with a given surface energy was suggested by applying the Cassie–Baxter model to fabrics. However, the measured contact angles for DTY samples were slightly greater than the predicted ones, probably due to the limitation of the model to include the small scale roughness from the textured filaments.

A model that is elaborated to better explain the behavior of surfaces with small scale roughness may help predict more accurate wetting behavior of complex structure surfaces. Further study to fabricate the superhydrophobic surface by adding the nano-scale roughness to mimic lotus leaves that have two levels of roughness in nano to micro-scale is also recommended as future work.

Footnotes

Acknowledgments

This research was supported by the Science Research Center/Engineering Research Center Program of Ministry of Science and Technology/Korea Science and Engineering Foundation (R11-2005-065) and National Research Foundation of Korea Grant funded by the Korean Government (2011-0014765).

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