Optimization of bioinspired triangular patterns for water condensation and transport

Abstract

Water condenses on a surface in ambient environment if the surface temperature is below the dew point. For water collection, droplets should be transported to storage before the condensed water evaporates. In this study, Laplace pressure gradient inspired by conical spines of cactus plants is used to facilitate the transport of water condensed in a triangular pattern to the storage. Droplet condensation, transportation and water collection rate within the bioinspired hydrophilic triangular patterns with various lengths and included angles, surrounded by superhydrophobic regions, were explored. The effect of relative humidity was also explored. This bioinspired technique can be used to develop efficient water collection systems.

This article is part of the theme issue ‘Bioinspired materials and surfaces for green science and technology (part 2)’.

1. Introduction

Water shortage is a global issue due to climate change and population growth. Water security requires supplemental water sources [1]. Inspired by insects and plants which can survive in arid deserts, bioinspired water collection approaches from fog have been investigated [2]. Beetles in the Namib desert use their back, which consists of an array of hydrophilic bumps surrounded by a hydrophobic background to harvest water from fog [3]. The fog droplets deposit on the hydrophilic spots. Once they reach a critical size, they slide along the hydrophobic paths to its mouth. The conical spines in a cactus facilitate droplet movement along the cone [4]. The curvature gradient along the cones produces Laplace pressure gradient responsible for the movement of droplets. Several investigations have been carried out to mimic the conical spines in order to increase the water collection rate from fog [5–7].

Another approach to harvest water from ambient air is the direct condensation of water vapour by cooling a surface below the dew point [8]. Water condensation has been investigated in heat transfer applications [9]. To enhance the condensation rate, one needs to increase the degree of subcooling or relative humidity (RH). Another method is to modify the surface wettability so that it can promote the condensation of water as well as transport the condensed droplets. Nucleation of water prefers a hydrophilic surface to a hydrophobic one [10,11]. However, the hydrophilicity increases adhesion of water droplets causing the difficulty of water removal and heat transfer. Because the heat transfer properties of water are poorer than those of many solid substrates, including glass, the water that is adhering to the surface will lower the heat transfer rate between the cold surface and ambient air, and hence lower the condensation rate.

To transport water on a surface, commonly used techniques rely on external forces, such as gravity and shear flow, which are dependent on droplet size and external input of energy [12,13]. To transport liquids in microfluidics, various geometries have been used to transport water droplets [14,15].

As mentioned earlier, for water transport, cactus spines take advantage of the conical geometry to drive water droplets by Laplace pressure gradient to collect water from fog. This bioinspired approach, for the first time, was used by Song & Bhushan [16] to transport condensed water in a triangular pattern, facilitated by Laplace pressure gradient in the longitudinal direction. The wettability of the triangular pattern affects the water condensation process and the hydrophilic pattern has been shown to be better for water transport compared to the superhydrophilic and hydrophobic patterns [16]. In the case of hydrophobic pattern, droplets are more spherical and do not spread and touch the pattern boundaries readily, necessary for droplet movement. In the case of superhydrophilic and hydrophilic patterns, droplets spread and touch the pattern boundaries to facilitate droplet movement. However, in the case of superhydrophilic patterns, condensed water spreads in the form of a thin film which then evaporates; this is not desirable. Furthermore, adhesion of the droplet is high and impedes droplet movement.

The effect of included angle and length of the triangular pattern, as well as the humidity on the condensation process and water collection rate, needs to be investigated. In this study, bioinspired triangular patterns with various included angles and length and the effect of RH were studied to develop optimum structures for high water collection rates.

2. Experimental details

In this section, the water condensation system, fabrication method for samples with triangular patterns and water collection measurements are described. The water transport phenomenon along the triangular pattern was investigated using a single triangular pattern. The water collection rate was studied using a reservoir with multiple triangular patterns in order to increase the amount of water collected.

(a). Experimental set-up

Figure 1a shows a schematic of the water condensation system. The bioinspired samples were placed on top of an aluminium block which was cooled by a Peltier cooler down to 5 ± 1°C. The samples were housed in an acrylic chamber (1 m × 0.5 m × 0.8 m). The air temperature in the chamber was 23 ± 1°C. RH was controlled by injection of humid air. The humid air was produced by an air stream that passed through a tank of hot water. By changing the temperature of the hot water and the flow rate of the air stream, RH in the chamber was able to be controlled between 30% and 95%. A digital microscope CCD camera (Koolertron, 5MP 20-300X) was used to capture the condensation process.

Figure 1.

Schematic diagram of (a) the water condensation system, (b) sample with a single triangular pattern and (c) a reservoir with an array of triangular patterns.

Experiments were conducted at a RH of 85%, except those performed to study the effect of RH. When the sample was cooled down to 5°C at RH greater than 50%, which is lower than the dew point of the ambient air, water vapour continuously condensed on the triangular region [17].

(b). Fabrication method of the bioinspired triangular patterns

The bioinspired triangular patterns were fabricated on a hydrophilic glass slide. The triangular patterns, A, were hydrophilic, surrounded by a rim of superhydrophobic region, B, as shown in figure 1b. The superhydrophobic rim was produced to serve as a dam to the condensed liquid in the triangular pattern. To fabricate the patterned sample, the boundaries of the desired pattern B were printed on a paper that was placed under the glass slide and a piece of adhesive tape was put on top of the glass slide. Next, region B was cut onto the adhesive tape, guided by the pattern on the paper underneath, so that region B was exposed to air and region A was protected by the tape. Then a superhydrophobic coating was spray-coated on the glass slide followed by removal of the adhesive tape that covered region A. The superhydrophobic coating consisted of 10 nm hydrophobic SiO₂ nanoparticles (Aerosil RX300) and a binder of methylphenyl silicone resin (SR355S, Momentive Performance Materials), both of which were pre-mixed in acetone before spraying [18]. Region B after coating became superhydrophobic and region A remained hydrophilic.

The wettability properties of the hydrophilic and superhydrophobic regions are shown in figure 2. It shows optical images of droplets and static contact angles and contact angle hysteresis values.

Figure 2.

Optical images of water droplets on the hydrophilic glass and the superhydrophobic coating and the static contact angles (θ) and contact angle hysteresis (θ_hys). Reproducibility was ±2°.

Two types of samples were fabricated. One type of sample contained a single triangular pattern, which was used to investigate the details of the condensed droplet transport (figure 1b). The single triangular pattern with a 20 mm length was surrounded by a superhydrophobic rim (0.5 mm wide). Three included angles (α = 5°, 9° and 17°) were selected to investigate the effect of α on the droplet condensation and transport process. The other type of sample contained an array of triangular patterns that were located on both sides of a rectangular reservoir, to increase the amount of the collected water for higher accuracy (figure 1c). An array with an included angle of 9° and length of 10 mm was used. To study the effect of included angle, arrays with four included angles of 9°, 17°, 22° and 30°, with a length of 10 mm were used. To study the effect of length, arrays with four length of 5, 10, 20 and 30 mm with an included angle of 9° were used.

(c). Water collection measurements

To measure the mass of the collected water for both types of samples, a piece of paper tissue was used to absorb the water in the reservoir and was weighed by a microbalance (Denver Instrument Company No. B044038) after the condensation tests. Microbalance could measure a minimum weight of 1 mg.

3. Results and discussion

To understand the droplet transport mechanism, droplets of different volumes were deposited on the triangular pattern at room temperature, and the droplet movements were observed. Then the triangular patterns were placed in the condensation system and the effect of included angle, length and RH on the water condensation and transport, as well as the water collection rates were studied.

(a). Droplet transport on the hydrophilic triangular patterns

Droplet transport experiments were conducted by depositing a droplet using a pipette at the tip inside the triangular pattern with varying volume (from 10 to 100 µl) with increments of 5 µl ranging between 10 µl and 50 µl and increments of 10 µl ranging between 50 µl and 100 µl. After deposition, the droplet moved along the pattern due to Laplace pressure gradient, and stopped after travelling some distance. Figure 3a shows the locations of the stopped droplets of different volumes for a triangular pattern with an included angle of 17°. A droplet with larger volume travelled further.

Figure 3.

Transport of the deposited droplet along the triangular pattern. (a) Selected photographs of the transported droplets with different volumes when they stop. (b) Droplet volume and its length as a function of the travel distance. (c) Droplet volume as a function of its length. The droplet was deposited at the tip of the triangular pattern and transported by the triangular pattern to the wider side. The data in (b) and (c) were measured when the droplet stopped.

To understand the role of Laplace pressure gradient on the droplet movement and the distance travelled, we studied a droplet placed on the hydrophilic triangular area, as shown in figure 4. In this example, w(x) is the local width of the triangle at a distance x from the tip of the triangle. The droplet was constrained by the superhydrophobic region and became wedge-shaped. The local radius of the curvature of the droplet along the triangle can be written as $R(x)\sim w(x)/(2\sin \theta (x))$, where θ(x) is the contact angle at the boundaries. The Laplace pressure generated by the local curvature can be simplified as $\delta P\sim \gamma /R(x)\sim 2\gamma \sin \theta (x)/w(x)$, where γ is the surface tension of water in the air [19]. For the constrained droplet, w(x) increases from the narrower side to the wider side, and hence the Laplace pressure at the narrower side is larger than that at the wider side. As a result, a driving force is generated to transport the droplet with the direction pointing to the wider side. The driving force of the Laplace pressure exists as long as the droplet is large enough to contact both boundaries of the triangular pattern. When the droplet moved further in the triangular pattern, the magnitude of the driving force decreased because of the decrease in the curvature gradient. The droplet stopped when the driving force was smaller than the adhesion force.

Figure 4.

Photograph and schematic of a droplet constrained within the triangular pattern.

Figure 3b shows the relationship between the droplet volume and the distance measured from the tip of the triangle to the right-hand edge of the droplet (x_r) at various included angles. The distance was measured when the droplet stopped. A droplet with a larger volume travelled further. A droplet with a fixed volume was transported farther by a triangle with a smaller included angle. For example, to move a droplet 20 mm to the right, the droplet volume had to reach 82, 29 and 20 µl on the triangular pattern with the included angle α = 17, 9 and 5°, respectively.

Figure 3b also shows the relationship between the length of the stopped droplet (l) and x_r. The data showed that l increased linearly with x_r and the included angle had little effect. It was observed that the droplets were elongated along their travel direction due to the adhesion force, which was directly related to the contact angle hysteresis (difference between advancing and receding contact angles) on the triangular area.

Finally, the droplet volume is plotted as a function of the droplet length for various included angles in figure 3c. These data can be used to determine the volume (or mass) of a droplet condensed on a surface by simply measuring the droplet length.

(b). Water condensation and transport on the triangular pattern

(i). Effect of included angle

Figure 5 shows the water condensation on triangular patterns with different included angles. In the beginning of condensation, the condensed droplets were relatively small, as shown in the first column of figure 5a. As the condensation continued, the growing droplets started to coalesce into bigger droplets. Eventually, they were big enough to touch the superhydrophobic borders, which triggered the transport motion driven by the Laplace pressure gradient, as shown in the second and third column of the figure. For example, at a time of 45 min after the start of condensation on the triangular pattern with α = 9°, there were 5 mm sized droplets (numbered 1–5) that touched the borders. At 76 min, droplets 1 and 2 coalesced into one big droplet (1 + 2) and droplets 3 and 4 coalesced into another (3 + 4). After the coalescence of droplets 1 and 2, the droplet volume increased and the Laplace pressure gradient was able to drive the droplet. Owing to adhesion, the droplet (1 + 2) was elongated and stopped after moving a step of 1.4 mm based on the calculation of the centre of the droplet area. It is further noted that the position of the centre of droplets 3 and 4 did not change after their coalescence. This is because the size of the coalesced droplet (3 + 4) was too small and the Laplace pressure gradient along the coalesced droplet could not overcome the adhesion.

Figure 5.

Droplet condensation and transport on a single triangular pattern with different included angles. (a) Selected photographs of the condensation at different times. Arrows shown below some droplets are based on droplet movement observed in videos. (b) Length of the coalesced droplet as a function of the travel distance, x_r, when it stops. (c) Effect of included angle on the mass of the first droplet on the reservoir and the time taken for the droplet travelling through the pattern.

The length of the droplet as a function of travel distance x_r when it stops is shown in figure 5b. Similar to figure 3b, the length of the elongated droplet increases linearly with its position x_r, and the included angle has little effect on the length.

To study condensation rate, one needs to know the size (mass or volume) of the droplet and time taken to reach the reservoir. Figure 5c shows the droplet mass and time needed for the droplet to reach the reservoir through the whole triangular pattern with different included angles. As α increases, it takes more time for the droplet to be transported to the reservoir. However, for a triangular pattern with larger α, the size of a coalesced droplet which starts to move is larger as shown in the figure.

The transport efficiency of the condensed droplet across the triangular pattern needs further investigation. It was carried out using an array of triangular patterns and will be presented in the following section.

(ii). Effect of relative humidity

The effect of RH on condensation and transport was investigated. Figure 6a shows the condensed droplets at two RH on a triangular pattern with included angle 9°.

Figure 6.

Droplet condensation and transport on a single triangular pattern under different relative humidity. (a) Selected photographs of the condensation at different times. Arrows shown below some droplets are based on the droplet movements observed in videos. (b) Effect of relative humidity on the mass of the first droplet on the reservoir and the time taken for the droplet travelling through the pattern.

The droplets coalesced and started to move. The coalesced droplets eventually moved to the reservoir and the sizes of the droplets were weighed with the help of a slice of paper tissue. Figure 6b shows the mass of the final droplet right before reaching the reservoir. RH did not affect the mass of the final droplet before reaching the reservoir. Figure 6b also shows the time it takes for the droplet to reach the reservoir under different values of RH. The travel time through the reservoir decreased with RH.

To understand the role of humidity on the time it takes for a droplet to reach the reservoir, we developed a relationship between condensation rate and humidity. In a humid environment, the condensation rate per unit area on a cold surface is [20,21]

$$w=\frac{D(p_{\mathrm{a}}-p_{\mathrm{s}})}{{\delta }_{0}R{T}_{\mathrm{abs}}},$$ 3.1

where D is the diffusion constant of water in the air, R is the gas constant of water vapour, T_abs is the absolute temperature, p_a is the partial pressure of the vapour in the ambient, p_s is the saturation vapour pressure at the cold surface and δ₀ is the thickness of the depletion layer which is dependent on the external flow.

The saturation vapour pressure is dependent on the local temperature, T in °C [22],

$$p_{\mathrm{s}}(T)=0.611\exp \left(\frac{17.6T}{243+T}\right)\mathrm{kPa}.$$ 3.2

The partial pressure of the water vapour in the ambient air with temperature T_a can be calculated through the RH,

$$p_{\mathrm{a}}=p_{\mathrm{s}}(T_{\mathrm{a}})\mathrm{RH}.$$ 3.3

Combining equations (3.1) to (3.3), the condensation rate per unit area changes to

$$w=\frac{D{p}_{\mathrm{s}}(T_{\mathrm{a}})(\mathrm{RH}-p_{\mathrm{s}}(T_0)/p_{\mathrm{s}}(T_{\mathrm{a}}))}{{\delta }_{0}R{T}_{\mathrm{abs}}}.$$ 3.4

In the current condensation experiments, T_a = 23°C, T₀ = 5°C. Even though the thickness of the depletion layer, δ₀, is not known in the current experiments, equation (3.4) shows that the condensation rate on a cold surface is linear to the RH. It also shows that for the condensation of water, w, to be positive (w > 0), the RH must be larger than RH > p_s(T₀)/p_s(T_a). By using equations (3.2) and (3.3), the value can be calculated as 31%.

Because the condensation rate is proportional to RH, the time needed for the droplet to reach the reservoir is inversely proportional to w, given by equation (3.4),

$$t\sim M_0/w=\frac{{\delta }_{0}R{T}_{\mathrm{abs}}}{D_0{p}_{\mathrm{s}}(T_{\mathrm{a}})}\frac{M_0}{(\mathrm{RH}-p_{\mathrm{s}}(T_0)/p_{\mathrm{s}}(T_{\mathrm{a}}))},$$ 3.5

where M₀ is the mass of the final droplet before reaching the reservoir and L = 20 mm. As shown in figure 6b, the trend of the relationship between the travel time and RH agrees well with equation (3.5).

(c). Water condensation and transport on array of triangular patterns

Figure 7a shows the water condensation on the sample containing an array of triangular patterns surrounding a rectangular reservoir. The condensed water on the triangular area was transported to the reservoir whose weight was measured via a paper tissue. To evaluate the additional mass of water condensed at the reservoir area, a rectangular hydrophilic area was placed beside the array and the mass of the condensed water was measured as well. When calculating the condensation rate on the triangular patterns, the mass of the water on the rectangular region was deducted from the mass of the water on the reservoir with array.

Figure 7.

Effect of relative humidity and included angle and length of the triangular patterns on the water condensation rate. (a) Photograph of the collected water in the reservoir by an array of triangular patterns. (b) Water condensation rate as a function of relative humidity. (c) Water condensation rate as a function of included angle and length of the triangular patterns.

The effect of the RH on the condensation rate is shown in figure 7b. The condensation rate increased linearly with RH in the range of 50%–85%. The trend agrees with equation (3.4).

Next, the effect of the included angle, α, and the length of the triangular patterns, L_a, were studied. As shown in figure 7c, the included angle did not affect the condensation rate. Even though the droplet transported slowly on a triangle with a larger included angle, the size of the droplet was larger which may provide the similar condensation rates. Figure 7c also shows the condensation rate as a function of the length of the triangular patterns. The condensation rate decreases when the length increases. Since a shorter distance requires less time to transport the condensed droplets and the droplets being removed are small, the removal rate increases the condensation rate.

4. Conclusion and outlook

The water condensation and transport ability of the bioinspired triangular patterns were investigated systematically. The hydrophilic triangular patterns were surrounded by superhydrophobic regions. It was found that when the droplets were constrained within the triangular patterns, they started to move once they reached a critical size and touched both sides. As a result, the triangular pattern with a larger included angle needed more time to transport the condensed droplet when the volume of the transported droplet was larger. A water collection reservoir was fabricated with multiple triangular patterns to measure the condensation rate. The RH increased the condensation rate. The included angle did not affect the condensation rate. As the length of the triangle increased, the condensation rate decreased.

To design a condensation water collection tower, a hydrophilic pattern surrounded by a superhydrophobic region should be used. Since the included angle had no effect on condensation rate and a shorter length promoted condensation, triangular patterns with shorter lengths were used to obtain a larger condensation rate. Although RH of the ambient air increased the condensation rate, it could not be controlled.

Data accessibility

This article has no additional data.

Authors' contributions

D.S. performed the experiments and analysed the data. D.S. and B.B. wrote the main text and D.S. and B.B. participated equally in planning, execution and review of the manuscript.

Competing interests

We declare we have no competing interests.

Funding

Financial support for this research was provided by a seed grant GOGCAP from the Center for Applied Plant Sciences (CAPS) of The Ohio State University.