**2.1 Fabrication of the chemically wettability patterned surface**

Chemically wettability patterned surface is composed of areas with different wettability. The authors used the method described below to fabricate the chemically wettability patterned surfaces.

A 2 cm × 2 cm prism transparent glass coated with a 100 nm thick Indium tin oxide (ITO) layer is selected as the substrate. ITO layer functions as a resistive heater and its two edges are deposited with 100 nm thick gold electrodes, which are used for wire bonding with a printed circuit board. After the deposition of gold electrodes, the sample is deposited with a 500 nm thick silicon dioxide as a passivation layer. Then a layer of Teflon, which is commonly used as a hydrophobic layer, is spun coated on the top of the silicon dioxide layer, and stabilized following the procedures suggested by DuPont™:


The Teflon layer was patterned to form a chemical wettability patterned surface with the following procedures as shown in **Figure 2**:


**Figure 2.**

*Schematic fabrication procedures of a heterogeneous wetting surface [13].*


After all the fabrication procedures are finished, the wettability patterned surface and a typical recording image during the droplet evaporation on the surface are shown in **Figure 3**. The wettability patterned surface is a hydrophilic surface (silicon dioxide on the prism glass) with square Teflon hydrophobic islands of D = 50 μm and pitch distance of L = 100 μm.

#### **Figure 3.**

*(a) Microscopic image of a wettability patterned surface and (b) a typical recording image during the droplet evaporation on the surface [14].*

*Multiscale Micro/Nanostructured Heat Spreaders for Thermal Management of Power Electronics DOI: http://dx.doi.org/10.5772/intechopen.100852*

The roughness of the sample is measured by a surface profiler (Dektak 150 Veeco). The roughness of the Teflon and the substrate is only 5 nm and 25 nm, respectively. Thus, its effect on evaporation is negligible. Finally, the sample is bonded on a Printed circuit board (PCB) for the experiments of multicomponent droplet evaporation with different sample temperatures.

### **2.2 Experimental setup and procedure of the droplet evaporation**

The experimental setup is presented in **Figure 4(a)**. A Charge-coupled device (CCD) camera (MotionXtra HG-100 K, Redlake Co., Ltd.) with a long-distance zoom lens (Zoom 6000, Navitar Inc.) is adopted for recording the evaporation process to investigate the droplet evaporation characteristics including dynamic contact angle, base diameter, and evaporation duration of a droplet. Because the droplet profile is high symmetric, the focus plane of the camera is suitable to adjust to the cross-section of the droplet, as shown in **Figure 4(b)**. The droplet profile image is analyzed by a snake-based approach, which is shown in **Figure 4(c)**. Besides, the microscopic motion of the contact line is recorded by an inverted microscope (Eclipse TE2000-U, Nikon Instruments Inc.) connected to the CCD camera.

The droplet for the testing is generated by mixing deionized water and ethanol with an ethanol concentration varied from 0 vol. % to 15 vol. %. The droplets for each experiment are freshly generated before the test and the accuracy of the ethanol concentration is ±0.05 vol. %. The sample is heated and controlled at 40°C by a direct current (DC) power supply with a proportional-integral-derivative (PID) controller. The temperature difference between Teflon and the silicon dioxide layer

#### **Figure 4.**

*Experimental setup and contact angle measurement for the droplet evaporation: (a) schematic of the experimental setup for the droplet evaporation; (b) bottom view of the droplet on a wettability patterned surface and corresponding focus plane of the contact angle measurement; and (c) the contact angle measurement result by the snake-based approach [14].*

is negligible as the thickness of Teflon is only around 60 nm. Only if the sample is kept at 40°C for 5 min the test can be started.

The 1 μl ± 0.05 μl multicomponent droplet is produced by a Hamilton microsyringe (Hamilton, 5 μl TLC syringe with a removable needle of gauge 33, 210 μm of outside diameter) and gently put on the heated homogenous or heterogeneous wettability surfaces. The location of the droplet is the same in every test to ensure the reproducibility of the experiments. After the droplet is put on the sample surface, the CCD camera starts to record the profile of the evaporation droplets or the microscopic motion of the contact line with the inverted microscope until the droplet vaporizes totally. To avoid the trace of the vaporized droplet affecting the next test, the sample is cleaned with acetone, ethanol, and deionized water, and dried with compressed air flow followed by a 105°C bake for 10 min in an oven. To ensure reproducibility, the location of the droplet is the same in every test and the whole experimental setup is kept at 23 ± 1°C and 50 ± 3% RH environment without any airflow. Besides, more than five times each experiment is conducted to identify reproducibility.

A hydrophilic surface, which is form by depositing only a layer of silicon dioxide on the sample, is chosen as a reference to investigate the enhancement effect because a homogenous hydrophilic surface always had a higher evaporation rate than that of a homogenous hydrophobic one [15].

### **2.3 Experimental result and discussion on the evaporation enhancement induced by a wettability patterned surface**

First, the wettability of the multicomponent droplets on a hydrophilic (SiO2), hydrophobic (Teflon), and wettability patterned surfaces at 40°C are measured to confirm the wettability, as shown in **Table 1**.

Then, the evaporation duration of the droplets is recorded and shown in **Figure 5**. The evaporation duration of a droplet on a wettability patterned surface is around 10% shorter than that on a hydrophilic surface. Changing the ethanol concentration has an insignificant effect on the evaporation duration. The increase of the ethanol concentration leads to a shorter evaporation duration, which is contributed from the latent heat of ethanol is only 1/3 of water. In summary, the wettability patterned surface enhances the evaporation rate when compared with a hydrophilic surface.

The increase of the contact line length introduced by the wettability patterned surface plays a critical role in the enhancement. First, the mass flux of the evaporating flux ( *j*(*x*)) of a slowly evaporating droplet on a hydrophilic surface can be calculated by [16]:

$$j(\boldsymbol{\omega}) = j\_o \left[ \mathbf{1} - \left( \frac{\boldsymbol{\omega}}{r\_i} \right)^2 \right]^{-\frac{1}{2} \ast \theta / \pi} \tag{1}$$

Where, θ ( 0 / 2) < < θ π is the instant contact angle during the evaporation, *x* is the length from the center of the drop which has a radius *<sup>s</sup> r* . The factor of mass flux vapor ( <sup>0</sup> *j* ) depends on the saturation pressure, vapor diffusivity, and far-field concentration. According to Eq. (1), the distribution of the evaporation flux for a droplet on a hydrophilic surface is non-uniform. The highest evaporation flux occurs at the contact line and it was also confirmed by Hu and Larson [17]. Besides, they derived an expression of the total evaporation rate of a droplet on a hydrophilic surface, which is:

$$m(t) = -\pi RD(\mathbf{1} - H)c\_v \left(0.27\theta^2 + \mathbf{1.30}\right) \tag{2}$$

*Multiscale Micro/Nanostructured Heat Spreaders for Thermal Management of Power Electronics DOI: http://dx.doi.org/10.5772/intechopen.100852*


#### **Table 1.**

*Wettability data of the wettability patterned surface and the reference homogenous wettability surfaces under 40°C sample temperature [14].*

**Figure 5.**

*Evaporation duration of a droplet with a range of ethanol concentration from 0 vol.% to 15 vol.% on homogenous (hydrophilic) and heterogeneous (wettability patterned) surfaces [14].*

Where, *R* is the contact-line radius, *D* is the vapor diffusivity, and (1− *H c*) *<sup>v</sup>* is the vapor concentration difference. From Eq. (2) we can know the total evaporation rate is proportional to the perimeter of the contact line. Thus, the evaporation rate will be enhanced if the contact line is elongated. The wettability patterned surface increases the length of the contact line according to our observation, as shown in **Figure 6**. The spreading of the contact line is obstructed by the hydrophobic islands, leading to an elongation of the contact line along the islands' edge. Thus, although the contact area of a droplet on the wettability patterned surface is decreased, the length of the contact line is prolonged, resulting in faster evaporation of the droplet when compared with a homogenous hydrophilic surface under the same conditions. Moreover, a molecular dynamics simulation study also showed the increase of the total length of the hydrophobic island boundary in a nanoscale hydrophobic-hydrophilic pattern surface leads to an enhancement of the total evaporation rate [12].

Evaporation has been confirmed as the main phase-change mode in the evaporator of a two-phase heat spreader when the heat flux is less than 100 W/cm<sup>2</sup> . Especially, thin-film evaporation which occurs nears the contact line contributes at

## **Figure 6.**

*The contact line profile of a multicomponent droplet (15 vol.% ethanol) on the wettability patterned surface: (a) the schematic of the contact line and (b) microscopy image [14].*

least 50% even more than 80% of the total heat transfer in the evaporator [18–21]. Therefore, if the wettability patterned surface can be integrated into the evaporator of a two-phase heat spreader, the evaporation rate may be enhanced owing to the increase of thin-film evaporation are introduced by the elongated contact line. Then the thermal performance of the two-phase heat spreader can be enhanced. In the following section, an ultrathin vapor chamber with a wettability patterned surface integrated into the evaporator is presented. The effect of the wettability pattern on the thermal performance of the ultrathin vapor chamber will be discussed.
