Dependence of Particle Size and Geometry of Copper Powder on the Porosity and Capillary Performance of Sintered Porous Copper Wicks for Heat Pipes

Abstract

Permeability and capillary performance are the most important parameters relating to the thermal performance of heat pipes. These parameters are deeply linked to pore structure, which has been influenced by the starting powder utilized. In this paper, the effect of particle size and geometry of copper powder on the porosity and capillary performance of porous wicks were systematically studied. Sintered porous wicks were made from different-sized spherical (58 μm, 89 μm, 125 μm) and dendritic (59 μm, 86 μm, 130 μm) Cu powders. The results demonstrated that the porosity and capillary performance of both types of copper powder increase with particle size due to an increase in the connectivity between internal pores. In comparison to the spherical powder, the dendritic powder demonstrated superior capillary efficiency as well as greater porosity. Additionally, a model was proposed for the capillary performance and permeability of sintered porous copper. The predicted results were quite comparable to the experimental data, demonstrating the effect of the starting powder. These findings suggest that porosity and capillary performance of porous wicks are strongly related to powder geometry as well as particle size.

1. Introduction

Since the development of the first integrated circuits in the early 1950s, heat dissipation for electronic devices has always been an interesting research topic [1,2,3,4]. Common methods of heat dissipation include the use of bases and fins. Copper is used to construct heaters since aluminum is only effective for low to moderate heat dissipation. As science and technology continue to progress, a microprocessor chip with millions of transistors on a relatively small space gives off a lot of heat when it works. Additionally, in a high-power LED lighting system with a heat output of up to hundreds of watts on a surface area of only a few square centimeters, the design and construction of radiators with high heat dissipation efficiency is essential to ensure the stability and long-term operation of equipment. Because of the above-mentioned practical requirements, scientists have focused their attention in recent decades on research pertaining to the development of heat dissipation systems utilizing heat pipes that contain capillary layers [5,6,7,8,9]. This is one of the most significant breakthroughs in heat dissipation technology because of its high thermal conductivity. It has found use in a variety of industries, including the electronics industry, aviation, automobiles, energy, the environment, and health care, making it one of the most significant achievements in the field [10,11,12]. It can be observed that the effective thermal conductivity of the heat pipe is many times higher when compared with the thermal conductivity of typical heat dissipation materials, such as aluminum (225 W/m.K) and copper (380 W/m.K). Even when compared to a substance with an extremely high thermal conductivity, such as diamond (which has a thermal conductivity of approximately 2000 W/m.K), the effective thermal conductivity of a heat pipe can be several dozens of times higher.

The thermal performance of the heat pipe is directly influenced by the capillary structure because it makes capillary pumping easier and provides a flow path for conducting the working fluid inside the heat pipe [13,14,15]. There has been a significant shift toward using sintered metal powder capillary structures in heat pipes due to the fact that gravity has less of an impact on the performance of the structures. Because the metal powder is so precisely shaped for sintered wicks, the wicks have a higher heat conductivity and narrower holes than other types of wicks. Since the metal powder adheres to the tube wall with a high contact, there is an additional benefit in the form of a reduction in the heat resistance that exists between the wick and the tube. The key features of a capillary structure are its pore radius, porosity, permeability, window size between cells, and thermal conductivity [13,16,17,18,19,20]. When pumping liquid from the condenser to the evaporator, it is necessary to have a small pore radius in order to accommodate either a high capillary pressure differential or a high heat-carrying capacity. Large permeability is required in a capillary system in order to accommodate for even minute drops in liquid pressure. Because it causes fewer temperature changes throughout the capillary structure of the heat pipe, a high thermal conductivity is ideal for this passive heat transfer mechanism. In earlier investigations, it was suggested that the powder shape and the processing parameters would have an effect on the pore features; nevertheless, their implications on the overall performance of the heat pipe were not well-understood [21,22,23,24,25,26]. Because the impacts of surface roughness, porosity, and pore size, which are dictated by the shape of the powder and the processing parameters used, are not yet fully known, it is desirable to conduct a systematic study on these topics.

Thus, the purpose of this study was to investigate the influence of particle size and geometry of copper powder on the porosity and capillary performance of sintered porous copper. Cu powders with different sizes and geometries were considered for systematic investigation.

2. Materials and Methods

2.1. Materials

Two kinds of raw copper powders (purity 99.5%) with different shapes (spherical, dendritic) and particle sizes in the range of 40–150 µm supplied by Xilong Co., Ltd. (Shantou, China), were used in this study as starting materials.

2.2. Fabrication of Porous Copper Wick

The porous copper wicks were prepared by using the loose-powder sintering process (Figure 1). First, each of the copper powders (spherical, dendritic) was classified into three size groups of 40–70 µm, 70–100 µm, and 100–150 µm by sieve method. After that, the raw Cu powders were filled in stainless steel tubes with an inner diameter of 10 mm and the height of about 200 mm using in-house vibration equipment for 10 min (Figure 1a). Before filling Cu powder, the stainless steel tubes were cleaned in turn with acetone, ethanol, and distilled water by an ultrasonication process. Finally, the samples were sintered at 900 °C for 60 min using a tube furnace under a mixture of hydrogen and argon gas flow to protect and hydrothermally reduce residual Cu oxide in the sample. The heating rate was set at 10 °C/min, then kept at sintering temperature for 60 min and finally cooled down to room temperature (Figure 1b). After sintering, the samples were taken out of the stainless steel tubes for characterization (Figure 1c). Ten samples were sintered for each test and the average values were taken.

2.3. Characterization

Microstructure and morphology of the samples were studied using field emission scanning electron microscopy (FESEM, Hitachi S4800, Hitachi Ltd., Hitachi, Japan). The Archimedes method of determining density (porosity) can frequently produce erroneous results when applied to materials that have an open pore structure and a high porosity. Because of this, the porosity of these materials is typically computed by first measuring the geometrical volume and mass of each material. Based on these values, the density and porosity of each material can be calculated. In this study, the total porosity (γ_TP) of the sample is estimated by measuring its density and comparing it to the density of pure copper. The density was determined by measuring the geometrical volume and mass of the sample. The dimensions of the sample size were measured with a caliper and the sample weight (m) was determined by an electronic balance with an accuracy of 0.001 g. The volume of the sample is determined by the formula:

$$V=\frac{h\pi D^2}{4}$$

(1)

where h and D are the height and diameter of the sample. The density of the sample was determined by the following formula:

$$\rho =\frac{m}{V}$$

(2)

Finally, the total porosity (γ_TP) of sample was determined by using the following formula:

$${\gamma }_{TP}=\left(\frac{{\rho }_{Cu}-\rho }{{\rho }_{Cu}}\right)\times 100\%$$

(3)

The open porosity (γ_OP) of the prepared sample was determined by measuring the amount of saturated distilled water in the material when the samples are immersed in water. Before the experiment, the sample was ultrasonically shaken for 30 min in ethanol to clean the dirt in the pores, and then the sample was left to dry naturally for 24 h. Before immersing in water, the sample was weighed by an electronic balance with an accuracy of 0.001 g. A diagram of the water immersion test to determine the open porosity of the sample is shown in Figure 2, in which the samples were placed in a glass jar and then the jar was vacuumed continuously for 1 h to ensure that the air in the pores was sucked out. Next, the valve connected to the vacuum pump was closed and the valve connected to the water tank was opened to allow water to flow into the tank. When the amount of water introduced into the glass jar was above the sample height, the two valves were closed and the samples were immersed in water for 30 min. The water used in the experiment was distilled water, ensuring that all experiments had the same conditions. After soaking, the sample was immediately weighed to determine the sample weight. The difference between the mass before and after the immersion in water is the amount of water that has filled the pores in the sample. The volume of water contained in the sample indicates the porosity. The open porosity is determined by dividing the volume of water filling the pores by the original sample volume.

Additionally, in comparison, ImageJ analysis software (version 1.53t, National Institutes of Health, Bethesda, AR, USA) was also used to assess and identify the total porosity (γ_TP) of prepared samples on the SEM images. In this method, the distribution of pore areas and the fraction of total pore areas of the sample were determined and exported by ImageJ software. The fraction of total pore areas is assumed to be the same as the total porosity (γ_TP) of the samples [27,28]. The image processing and analysis were performed step by step as reported by Mazzoli et al. [29]. First, the original SEM image (Figure 3a) was converted into a binary image (Figure 3b) by proper thresholding for the image processing algorithms. Second, using the precise threshold limits produced the desired binary image; after that, a high-accuracy size measurement was ensured via the image processing method (Figure 3c). The complexity of the measurement of particle sizes and pore areas varies depending on the shape of the particle (pores) and the number of particles (pores) characterized. The number of measurements needs to be sufficient in order to guarantee an acceptable level of uncertainty in the output parameters. In this study, the distributions of the particle sizes and pore areas were acquired by conducting an analysis of more than 20 SEM images for each sample to improve the reliability of measurements.

For the capillary performance in this study, a technique to quantify the capillary characteristics was developed by measuring the water uptake of the samples. Figure 4 shows the apparatus for measuring the capillary characteristics of the samples. The system incorporates an electronic balance, a PC, a sample holder, and a beaker. The sample holder can move the sample up and down with great accuracy, holding it at 90°, 60°, or 30°. The liquid used in this experiment was distilled water. The measurements were conducted at a fixed temperature of 25 °C to ensure consistent tests. An HDMI cable connected the electronic scale to the PC, and a self-developed software program was employed to record the mass of water lost in the beaker over time. The capillary performance of the samples could be determined by the change in the mass of water before and after the test. The mass flow rate (MFR) was calculated by using the following relationship:

$$MFR=\frac{m_j-m_i}{t_j-t_i}=\frac{\mathrm{\Delta }m}{\mathrm{\Delta }t}$$

(4)

where m_i and m_j are the mass of absorbed water at the time of t_i and t_j, respectively.

3. Results

3.1. Microstructure

Figure 5 shows the SEM images of the fracture surface of the sintered porous Cu samples made from Cu powder with different shapes and particles sizes. As can be seen, the average particle sizes of the samples made with spherical Cu powders were determined to be 58 µm, 89 µm, and 125 µm. The samples made from particles with the size of 89 µm and 125 µm were pretty uniform (Figure 5b,c). The fracture surface of the porous copper samples employing dendritic Cu powder with various particle sizes after sintering is shown in Figure 5d–f. The average particle sizes of samples were measured to be 59 µm, 86 µm, and 130 µm.

Figure 6 shows a cross-sectional SEM image of the samples prepared by using different particle sizes of spherical Cu powders after sintering. The total porosity of the samples was calculated by using ImageJ software on the SEM images. The results show that the trend in the total porosity of the sample increases after increasing the particle size of the Cu powder. The distribution of pore area in samples with different particle sizes was calculated by ImageJ software on the SEM images. The samples made using spherical Cu powder have a proportion of pores with an area of 100–200 µm² of about 17%, 12%, and 8%, respectively, with average diameters of 58 µm, 89 µm, and 125 µm, respectively (Figure 6(a2,b2,c2)). The results also indicated that, for the particle sizes of 58 µm and 89 µm, the distribution of pore area is mainly in the range of 500 µm². When increasing the particle size to 125 µm, the pore area distribution increases and is in the range of 1000 µm². This is also consistent with the observed results of the SEM images. When the particle size increases, the pore size also increases. Figure 7 is a cross-sectional SEM image of sintered porous Cu using dendritic powder with different size. Compared with the sample using the spherical copper powder, the distribution of pore area of the sample using dendritic powder is more uniform, mainly in the range of 0–500 µm². When the particle size is small, the pores tend to have a small area as well, which makes them more prevalent.

3.2. Porosity

The total porosity (γ_TP), open porosity (γ_OP), and closed porosity (γ_CP = γ_TP − γ_OP) were determined by the volume-weight method shown in Figure 8. The results show that the total porosity and open porosity of the samples prepared by using spherical powder increased as the particle size of the raw Cu powder increased. The total porosity and open porosity increased, respectively, from 36.3% to 43.3% and from 30.1% to 37.6% when increasing the particle size from 59 µm to 130 µm. This could be attributed to the increase in the driving force for sintering as result of more interactions between the fine particles than between the coarse particles, thus leading to an increase in the densification status with smaller particles [30]. As a result, the porosity is reduced as the particle size decreases. This trend is similar to the previous results of Jabur [31]. This also means that the sealing ability of the pores decreases with an increase in the particle size, leading to a decrease in the close porosity. Here, when increasing the particle size from 59 µm to 130 µm, the closed porosity decreased from 6.2% to 5.7%.

Similar to spherical powder, the sample using the dendritic Cu powder had the total porosity and the open porosity increase with an increase in the particle size of the starting powders. When increasing the particle size from 59 µm to 130 µm, the total porosity increased from 47.1% to 58.4% and the open porosity increased from 40.3% to 53.2%, while the closed porosity tended to decrease from 6.8% to 5.2%. Samples using dendritic powder with a size of 59 µm had total porosity and open porosity (47.1% and 40.3%, respectively) that were higher than those of the samples using spherical powder with an average size of 125 µm (43.3% and 37.6%, respectively). As a result, the open porosity and total porosity of the sample using dendritic powder are much higher than those of the sample using spherical powder. Figure 9 shows the value of total porosity and open porosity of the sample using spherical and dendritic powder with different particle sizes. It can be seen that, in all the particle sizes used, the total porosity and open porosity of the sample using the dendritic powder are always larger than those of the sample using the spherical copper powder.

3.3. Capilary Performance

Figure 10 shows the amount of water absorbed over time in the sample at different angle positions using spherical copper powder with different particle sizes. The results show that the amount of water absorbed into the sample increases with time and reaches the saturation value after about 70 s. As the particle size of copper powder increases, the amount of water absorbed in the sample also increases. Samples using a copper powder size of 89 µm absorbed about 42.7% more water than the sample using a powder size of 58 µm. Samples using the powder with the particle size of 125 µm absorb more water than the sample using 89 µm copper powder at about 67%. The amount of water absorbed decreases when increasing the tilt angle of the sample. At an angle of 30^o, the amount of water absorbed was the largest and decreased gradually when increasing the angle of inclination in all three sizes of copper particles. This is because as the tilt angle increases, the force of gravity will increase, thus increasing the total drag. When the capillary suction force is constant, the total resistance increases, which will decrease the amount of water absorbed by the sample. Similar to the sample using spherical copper powder, when increasing the particle size for the sample using the dendritic powder, the amount of water absorbed also increased (Figure 11). With powder of an average particle size of 59 µm, the amount of water absorbed is the lowest and is much lower than the two other types of copper powder with the sizes of 86 µm and 130 µm. This is consistent with the measured porosity of the samples, and also shows that when the particle size of copper powder is small, the close porosity is also larger, thereby reducing the water absorption capacity of the sample. The obtained results also show that when increasing the working tilt angle, the amount of water absorbed also decreases due to the increased gravity force.

To evaluate the relationship between the porosity and capillary performance, exponential fitting was used. Figure 10c and Figure 11c show the correlation between time and amount of absorbed water for different shape and particle size. The correlations can be summarized as below:

m(t) = A(1 − e^t/B)

(5)

According to Wei et al. [22], A depends on the porosity and B depends on the permeability of samples. As a result, the A value of the samples made from dendritic powders is always higher than that of spherical powder. This means the porosity of samples is higher. This is in good agreement with the porosity of samples as discussed in the previous section. Similarly, the value B related to the permeability with an inverse proportion of samples [22]. The values for B given in Figure 10c and Figure 11c decrease with increasing particle size. The values for B are smaller for dendritic powders (12,5/13,1/16,1) than for spherical powders (19,8/21,6/22,3). This means an improvement in the permeability of the dendritic powder compared to the spherical powder. The Cu powders with larger particle size also retain a smaller B value resulting from the increased permeability.

The mass flow rate (g/s) of water absorption of samples with different shapes and particle sizes and at different sample inclination angles are presented in Figure 12. For all three types of particle sizes used and at different inclination angles, the mass flow rate is highest at the initial time and then gradually decreases. For Cu powder with an average size of 58 µm, the rate drops to zero at about 100 s. However, for the powder with an average size of 89 µm and 125 µm, the suction rate decreases to zero at about 80 s. In the same particle size of raw copper powder, when increasing the angle, the absorption speed also decreases, but the results are not clear, possibly due to the error of the measurement or the delay of the received signal displayed on the computer. If comparing the mass flow rate at the same inclination angle for the three particle sizes, when increasing the particle size from 58 µm to 125 µm, the rate of water absorption also increased at all three different inclination angles. This is because the increase in the particle size led to an increase in the pore size and thus reduces the frictional force of the water with the capillary wall. The amount of water absorbed (water absorption rate) of the samples at different inclination angles for each type of powders was determined. The general trend observed is that when the angle of inclination is smaller than the horizontal, the absorption rate is higher at the beginning due to the weak force of gravity, but then is almost equal at the saturation point. The sample using a larger particle size has a higher water absorption rate due to the large pore size leading to friction with the hole wall, reducing the capillary gap. Comparing the two kinds of powders, using the particle sizes of about 58 µm and 59 µm, there is not much difference in the amount of absorbed water, only the initial time: the water absorption rate of the sample using spherical powder is higher than for the sample using dendritic powder. This can be explained by the fact that, at the small particle size, although the sample using the dendritic powder has total porosity, the open porosity is larger than that of the spherical powder, but due to the small pore size, there is an increase in the friction force between the pore wall and the liquid, thus making the mass flow rate low. When increasing the particle size to 89 µm and 130 µm, the sample using the dendritic powder always had a higher mass flow rate than the sample using the spherical powder. This is also consistent with the microstructure analysis: when the pore size is large enough, the internal friction force is reduced, and the sample with large porosity will give a larger mass flow rate. This trend is only biased when the flow rate is close to saturation, possibly due to measurement errors.

4. Conclusions

We investigated the effect of particle size and geometry of Cu powder on the porosity and capillary performance of porous wicks. Cu powders of varying spherical (58 µm, 89 µm, 125 µm) and dendritic (59 µm, 86 µm, 130 µm) sizes were used to fabricate sintered porous wicks. The findings revealed that the porosity and capillary performance of both forms of copper powder increase with particle size due to an increase in the connection between internal pores. Compared to the spherical powder, the dendritic powder exhibited improved capillary efficiency and greater porosity. In addition, a model was proposed for the capillary performance and permeability of sintered porous copper. The effect of the beginning powder was demonstrated by the consistency of the predicted and experimental results. These results indicate that the porosity and capillary performance of porous wicks are directly associated with the powder shape and particle size.