Effect of Length Scales on the Boiling Enhancement of Structured Copper Surfaces

Boiling heat transfer is widely used in a variety of modern applications, from the production of steam to generate electricity in power plants, to its use in heating, ventilation and air conditioning and thermal management. Due to the latent heat of vaporization and large density change, liquid-to-vapor phase change is an extremely efficient means of heat transfer and has been leveraged in numerous industrial and commercial processes. Boiling is a complex process with heat transferred from the surface to the fluid through evaporation, transient conduction, and convection generated by the ebullition cycle of vapor bubbles near the wall [1]. The efficiency of boiling heat transfer is measured via the HTC, defined as the ratio of surface heat flux to the wall superheat. Here, the superheat is defined as the temperature difference between the solid wall and the saturation temperature of the fluid. The maximum heat flux that can be stably maintained during boiling is given by the CHF. Beyond CHF, the rate of vapor generated at the surface cannot be balanced by the rate of liquid returning to the surface. This instability leads to an uncontrollable increase in wall temperature as the surface is blanketed with a layer of insulating vapor during the dry-out process.

Techniques to enhance CHF and HTC during boiling heat transfer have been employed for decades using a variety of porous materials and mechanically deformed structures on metal substrates [2]. Researchers have also examined the impact of machining microstructures directly into metallic substrates, creating microscale structures and channels [3]. The observed enhancements using these approaches have been generally attributed to the ability of surface structures to promote bubble nucleation and enhance the ebullition cycle. Kandlikar demonstrated the use of three-dimensional contoured structures embossed into copper substrates to promote the formation of discrete liquid and vapor pathways to and from the surface [4]. These millimeter-scale structures were shown to produce extremely large enhancements of CHF (150% increase) and HTC (740% increase) as compared to bare copper. Rahman et al. also demonstrated the use of spatial ordering for boiling enhancement on copper substrates [5]. In that work, in-plane gradients in surface temperature were used to order flow fields leading to an increase in CHF of 100% and an increase in HTC of 400%.

With the recent development of a variety of micro/nanofabrication techniques, numerous researchers have studied the impact of microscale and nanoscale structures on silicon substrates. Surface modification techniques including biotemplating [6,7], etching [8–10], electroplating [8,11], oxide growth [12,13], evaporation [14], and electro-deposition [12], as well as deep reactive ion etching [7,15] have been utilized to enhance pool boiling heat transfer. The surfaces studied in these works typically had structure length scales of less than 10 μm. Enhancements in CHF of up to 220 W/cm² and HTC values of up to 75 kW/m² K have been reported for single length scale nanostructured [6,8,10,14] and microstructured [3,7,15] surfaces. Hierarchical surfaces containing both micro and nanostructures on silicon substrates have been shown to further enhance CHF up to 257 W/cm² while showing no significant change in HTC as compared to single length scale surfaces [7,12].

More recently, a series of studies have been conducted on the combined effect of porous coating layers and open microchannel geometries on metallic substrates. Patil and Kandlikar deposited microporous coating only on fin tops of the copper microchannel and demonstrated a CHF of 325 W/cm² [16]. Jaikumar and Kandlikar performed a series of studies on the effects of sintered porous coating on microchannel surfaces. They selectively deposited porous layers of 5–20 μm pore size on various portions of the channel, and varied channel dimensions to yield a maximum CHF of 420 W/cm² [17,18] They have attributed that the enhanced surface can sustain separate liquid and vapor flow fields at high heat fluxes which results in significant CHF enhancement.

While numerous researchers have studied boiling heat transfer on structured surfaces, continued work is necessary to understand the fundamental mechanisms leading to enhanced performance. In particular, little understanding exists on the role of structure length scales and the interplay between CHF and HTC. This includes their enhancement, and in some cases, their degradation due to the addition of surface structures. This work focuses on a systematic study of the effect of structure length scale from 100's of nanometers to millimeters. Specifically, the impact of using single length scale structures, as well as multiscale structures, for boiling enhancement on copper substrates has been investigated here.

To study the effects of length scale on boiling enhancement, thirty distinctly different surfaces were fabricated with structure dimensions as small as 100's of nanometers and as large as several millimeters. These include single length scale surfaces, as well as multiscale surfaces comprised of multiple structures superimposed onto one another. To create these thirty surfaces on copper substrates, two fabrication methods were used, electrical discharge machining (EDM) and hydrothermal oxidation. Wire EDM was used to machine microchannel geometries and create test samples of uniform thickness from a large copper block. During wire EDM, material is removed via rapid current discharges between a wire (kept in tension) and the copper block immersed in a dielectric fluid. Figures 1(a) and 1(b) show optical images of the resulting microchannel geometries produced using wire EDM on 2 cm × 2 cm substrates. After wire EDM, the samples are diced to 1 cm × 1 cm so that the array of microchannels extends across the entire boiling surface (not shown in Fig. 1). Figure 1(c) lists the details of the five microchannel designs considered in this work including the naming convention and the resulting geometries as measured optically. Microchannel surfaces with two to ten channels per centimeter (named M2 to M10) have been studied, with nearly hemispherical channels of nominally 0.42 mm wide and 0.28 mm deep. The fin widths of the samples (distance between two channels) vary from W_F = 0.78 − 3.28 mm, resulting in area ratios (true surface area to footprint area) of 1.14–1.65. While wire EDM is a convenient tool for rapid production of lab-scale test samples, the resulting geometries could be easily made using other approaches as well. The relatively large feature sizes (from 100's of micrometers to several millimeters) are achievable using a variety of traditional macroscale manufacturing techniques. While these surfaces are referred to in this work as “microchannels” for simplicity, the length scales are sufficiently large and the area ratios sufficiently small that capillarity and surface wicking is not expected to play a role in boiling enhancement from these structures.

Nanoscale surface structures are also studied in this work and have been fabricated via hydrothermal oxidation of the copper surfaces. Figure 2 shows scanning electron microscopy (SEM) images at two magnifications of the four different copper oxide nanostructures considered here, which have been named CuO-1 through CuO-4. To create CuO nanostructures, the copper substrates were first stripped of their native oxides in a bath of 2% hydrochloric acid for 10 min. Afterward, they were quickly rinsed with de-ionized (DI) water, dried with nitrogen, and placed directly into an alkaline bath. The bath temperature is maintained using a hotplate and closely monitored during CuO growth. Figure 2(a) shows CuO-1, which was grown in a bath of NaClO₂, NaOH, and DI water (16:1:100 wt %) for 10 min at 70 °C using the method described by Love and Packman [19]. Figure 2(b) shows CuO-2, which was grown in a phosphate buffer solution consisting of Na₂HPO₄, NaH₂PO₄, and DI water (0.91:0.56:100 wt %) at room temperature (20–22 °C) for a period of 24 h. Figure 2(c) shows CuO-3, which was grown in a bath of NaClO₂, NaOH, Na₃P0₄ 12H₂0, and DI water (3.75:5:10:100 wt %) for 10 min at 96 °C using the method described by Chu et al. [12]. Figure 2(d) shows CuO-4, which was grown in a bath of 65 mM of ammonia (NH₄OH) diluted with DI water at a temperature of 60 °C for 20 h [20].

As can be seen in Figs. 2(a)–2(d), various copper oxide nanostructures have been made with a wide range of morphologies and sizes. Using hydrothermal oxidation under various conditions, structures have been fabricated with representative feature sizes down to ∼100 nm (CuO-1) and up to ∼100 μm (CuO-2). The resulting nanostructures exhibit sharp blade-like morphologies (CuO-1 and CuO-3), broad flower pedal shapes (CuO-2), and 3D hierarchical structures (CuO-4). This has been used to not only create CuO nanostructures on flat copper surfaces (Figs. 2(a)–2(d)) but also to create multiscale surfaces with both microchannel geometries and CuO nanostructures. Figures 2(e) and 2(f) shows SEM images of two multiscale surfaces comprised of CuO nanostructures grown directly onto microchannel surfaces using the exact same fabrication techniques described above. By superimposing each of the four distinct CuO nanostructures (CuO-1 through CuO-4) onto each of the five distinct microchannel geometries (M2 through M10), a total of twenty different multiscale surfaces have been created. Along with bare copper surfaces, this results in thirty distinct boiling surfaces fabricated and tested in this work (one bare, four nanostructured, five microchannel, and 20 multiscale).

Each fabricated surface has been characterized during pool boiling using a custom built experimental apparatus. Complete details of the boiling apparatus, experimental methods, and measurement uncertainties can be found in prior publications [5–7,21]. Briefly, each sample has been characterized up to CHF during pool boiling of saturated water at atmospheric conditions. Each copper sample is soldered to an insulated copper heater block instrumented with an array of thermocouples to measure surface temperature, as well as the surface heat flux. The surfaces are submerged in a bath of degassed de-ionized water held at saturations conditions using auxiliary heater. The surface heat flux is increased incrementally, and after each step, the system is left to reach thermal equilibrium for ∼20 min, after which the surface temperature is recorded. The reported surface temperature is the temperature at the liquid–solid interface and accounts for all of the resistances between the thermocouple embedded in the heater block and the sample surface (solder, substrate, etc.). All results presented in this work use the projected surface area to calculate heat flux. During testing, the heat flux is increased in small discrete steps until CHF is reached. CHF is taken to be the highest stable heat flux after which there is an uncontrollable increase in surface temperature due to dry-out. When CHF is reached, the surface temperature quickly exceeds the solder melting temperature (182 °C), the sample de-solders from the heater block, and the system is shut down. HTC at each point is calculated as the ratio of the heat flux to the wall superheat temperature difference. Based on the previously reported uncertainty analysis [6,7], the experimental uncertainty for heat flux varies from 10.9% to 2.3%, and the heat transfer coefficient varies from 18.7% to 5.7%, for a heat flux range of 50–300 W/cm². Accordingly, the nominal uncertainties for heat flux, heat transfer coefficient, and wall superheat are ±6.7 W/cm², ±17.3 kW/m² K, and ±1.5 K, respectively, for the testing conditions considered in this work.

All thirty of the copper surfaces have been tested up to CHF including surfaces with single length scale structures (nanostructures only and microchannels only), as well as multiscale surfaces comprised of both microchannels and nanostructures. Additionally, a bare copper sample with a sanded flat surface was tested for control purposes. Figure 3 shows all of the boiling curves for the single length scale surfaces tested here. The naming convention for nanostructured copper oxide samples and microchannel surfaces is defined in Figs. 1 and 2, respectively. As can be seen, the bare copper surface reaches a CHF value of 117 W/cm² at a wall superheat of 17 K. This closely matches Zuber's prediction for CHF on flat surfaces and is consistent with results from other researchers [3,4,14,16]. This demonstrates the efficacy of the boiling apparatus and measurement techniques used here.

Boiling curves for the four nanostructured surfaces are shown as closed circles in Fig. 3, exhibiting CHF values from 141 W/cm² to 228 W/cm². This represents increases in CHF from 20% to 95%, as compared to bare copper surfaces. The enhancement of CHF on the CuO surfaces is consistent with prior work and is attributed to the ability of the samples to delay dry-out via surface wicking. Figure 4 shows the measured CHF, plotted against the wicked volume flux for all four CuO surfaces and bare copper. The wicked volume flux is a phenomenological parameter used to characterize the wickability of structured surfaces. The measurement of the wicked volume flux and the development of a wicking-enhanced CHF model for structured superhydrophilic surfaces have been described in previous publications [7,21]. Using this approach, it can be seen that the model developed by Rahman et al. accurately predicts CHF enhancement on the CuO surfaces during pool boiling of saturated water at atmospheric conditions [7]. Examination of the SEM images in Fig. 2 and the results in Fig. 4 show that the size and shape of the nanostructures was not a critical factor dictating CHF. The surfaces with both the smallest (CuO-1) and the largest (CuO-2) structures showed relatively modest enhancements. While the surfaces with moderate scale structures (CuO-3 and CuO-4) showed larger enhancements due to their ability to efficiently wick. This shows that wickability is the key feature dictating CHF enhancement on structured superhydrophilic surfaces. The nanostructured CuO-4 surface shows the highest CHF (228 W/cm²) at the largest wicked volume flux (4.3 mm/s) and exceeds the performance of the various CuO nanostructures tested previously in Rahman et al. [7]. This is attributed to the complex three-dimensional nature of the CuO-4 coating (Fig. 2(c)), which has features that are on the order of 1 μm and smaller features of less than 100 nm. This too is consistent with prior work, where hierarchical surfaces showed the largest wickability and CHF [7].

These increases in CHF are achieved by extending the boiling curves to higher superheats. As seen in Fig. 3(b), this leads to a decrease in HTC as compared to bare copper at an equivalent heat flux for all of the samples tested. Three of the four CuO structures tested here show lower HTC across their entire boiling curve, while CuO-4 exhibits an increase in maximum HTC, but this is only achieved at high heat fluxes. The apparent decrease in HTC (at a common heat flux) is attributed to the suppression of the nucleation process. By conformally coating the surface with CuO nanostructures, the nominal size of available cavities distributed across the copper surface is reduced. This decrease results in a larger superheat required to activate a given cavity, as modeled by Hsu [22], and produces an effective decrease in HTC at a given surface temperature as compared to bare copper. This phenomenon is not seen during boiling on enhanced silicon substrates. This is due to the fact that a bare silicon surface is extremely smooth, and the addition of nanostructures increases the size and number of cavities available for nucleation.

The addition of CuO nanostructures to a bare copper substrate increases CHF but leads to a notable decrease in HTC (at a given heat flux). Alternatively, the microchannel geometries fabricated and tested here show a simultaneous increase in both CHF and HTC across the entire boiling curve. All five of the microchannel surfaces outperform the flat copper with CHF increasing with the number of channels up to 206 W/cm². Similarly, HTC has been increased up to 186 kW/m² K, representing more than a 2.6× enhancement relative to bare copper for the M6 and M8 samples. This provides an interesting comparison between microscale and nanoscale features on surface with a single length scale. As seen here, the simple microchannel surfaces with millimeter scale features essentially outperform the nanostructured coatings. They demonstrate comparable CHF values but with notable higher HTC values.

The feature sizes of the microchannel surfaces are too large for capillarity or surface wicking to be playing a dominant role in boiling enhancement. Similarly, the area ratio is seemingly too small for the enhancements to be associated with roughness, finning, or other surface area related effects. The results for the microchannel surfaces tested here are qualitatively and quantitatively similar to those studied by Cooke and Kandlikar [3]. In that work, the enhancement was attributed to the nature of the nucleation and the ebullition cycle on microchanneled surfaces. Nucleation occurs predominantly within the microchannels and at reduced superheats, while the bubble departure diameter is increased. As the bubbles depart the channels, they direct liquid toward the active nucleation sites within the channel. This increases HTC by enhancing the ebullition cycle and increases CHF by providing a means for the surface to remain wetted at high fluxes. While the maximum heat flux (CHF was not achieved) and maximum HTC values reported by Cooke and Kandlikar were larger than those measured here (244 W/cm² and 269 kW/m² K), these discrepancies could be explained by the differences in the microchannel geometries. Cooke and Kandlikar studied surfaces with high-aspect-ratio fins and microchannels, allowing for a much larger density of channels to be fabricated on a sample of similar size.

Figure 3 demonstrates that copper microchannel surfaces are clearly superior for overall boiling enhancement as compared to nanostructured copper surfaces. They provide high CHF, but more importantly, they demonstrate a consistently high HTC across the entire boiling curve. These results are based on the performance of surfaces that, in general, contain structures with only a single length scale. The CuO structures are sufficiently small to enhance capillarity and surface wicking, while the microchannel surfaces are sufficiently large to enhance nucleation and bubble dynamics. In addition, multiscale surfaces have been tested here to examine the performance of surfaces with these two different types of structures superimposed onto each other. Twenty distinct multiscale surfaces have been fabricated by combining the four different CuO nanostructures with the five different microchannel designs. The boiling performance for all twenty multiscale surfaces are shown in Figs. 5–8, as compared against a bare copper sample.

As can be seen in Figs. 5 and 6, the multiscale surfaces containing the CuO-1 and CuO-2 nanostructures are qualitatively and quantitatively similar to one another, with CHF values of 200–250 W/cm² and a maximum HTC around ∼200 kW/m² K. Comparing the results shown in Figs. 5 and 6 for multiscale structures with the results shown in Fig. 3 for surfaces with just microchannels, the effect of adding nanostructures can be evaluated. The addition of CuO-1 and CuO-2 nanostructures to the microchannel surfaces resulted in modest increases in CHF of 20–25% for all designs. Similarly, the maximum HTC values for the multiscale surfaces remained nominally the same, with some surfaces increasing and some decreasing by up to ∼30%. These results are consistent with what was found when adding these lower-preforming nanostructures (CuO-1 and CuO-2) to bare surfaces.

When adding the two higher-performing nanostructures (CuO-3 and CuO-4) to the microchannel surfaces, notably different behaviors were observed, leading to more definitive and consistent boiling enhancements. As can be seen in Figs. 7 and 8, the multiscale surfaces containing the CuO-3 and CuO-4 nanostructures demonstrate CHF values in the range of 235–313 W/cm², representing an increase of roughly 25–50% as compared to surfaces with only microchannels. A maximum CHF value of 313 W/cm² was observed for the CuO-4 M10 surface. The impact of the addition of CuO-3 and CuO-4 on the HTC of microchannel surfaces showed much larger variations from sample to sample. Again, comparing the results of Figs. 7 and 8 against the performance of the microchannel-only surfaces in Fig. 3 shows that for some samples, maximum HTC did not change significantly, while for most designs, it changed only moderately (25–75%). However, for two of the surfaces tested here, extreme increases in maximum HTC were observed by adding the CuO-3 and CuO-4 nanostructures. The CuO-4 M10 surface and the CuO-3 M4 surface recorded maximum HTC values of 461 kW/m² K and 413 kW/m² K, respectively, representing increases of ∼225% as compared to surfaces with respective microchannels only.

Two interesting behaviors can be seen in the boiling curves for the multiscale surfaces with CuO-3 and CuO-4 nanostructures, particularly in the samples exhibiting the highest CHF and HTC values. First, a discrete change in the slope of the boiling curves is seen as the multiscale surface reaches higher heat fluxes and approaches CHF. This is particularly evident in Fig. 7 (CuO-3 multiscale surfaces) for the higher performing samples and to a lesser extent in some of the data in Fig. 8 (CuO-4 multiscale surfaces). Second, the CuO-4 M10 multiscale surface (Fig. 8) exhibits a distinctly different boiling behavior than the rest of the samples tested. In particular, the wall superheat is shown to decrease as the heat flux increases. This phenomenon is also seen to a lesser extent in the CuO-3 M4 multiscale surface (Fig. 7). These two behaviors were further examined through a series of repeatability tests.

Figure 9 shows repeatability results for the CuO-3 M8 and CuO-3 M10 multiscale surfaces. The boiling curves are compared against bare copper surfaces, as well as the boiling results for each of the independent structures making up the multiscale surface. Each of the multiscale surfaces were tested multiple times, and Fig. 9 shows two representative boiling curves from experiments conducted on the same surface but on two different days. In all cases, the surfaces are tested up to CHF, removed from the heater assembly, and cleaned using solvents between each test. Each of the surfaces shows similar boiling curves for the separate tests conducted on different days, verifying the repeatability and longevity of the experiment and surfaces over the course of the testing period. For both samples, a distinct and repeatable change in the slope of the boiling curve is seen as CHF is approached. This behavior appears to be the product of the two different length scale structures existing on the surface. At relatively low superheats, the microchannel component is promoting the nucleation and removal of vapor bubbles; this is labeled with a “1” in Fig. 9. The multiscale surfaces are behaving similar to the microchannel surfaces both quantitatively and qualitatively. At higher heat fluxes, the nanostructure component delays dry-out leading to an increase in CHF. As can be seen for both samples, the slope of the boiling curve changes and closely matches the slope of the surfaces with only CuO nanostructures, this is labeled with a “2” in Fig. 9. These results suggest that each of the length scales superimposed onto each other in the multiscale surfaces is playing an important and distinct role in boiling enhancement. The microchannel geometry is promoting nucleation and efficient bubble dynamics at low to moderate heat fluxes, while the nanostructured components are delaying dry-out through surface wicking thus increasing CHF. While it cannot be definitively proven by the experimental results collected here, the distinct change in slope of the boiling curves near CHF could represent the beginning of the dry-out process. This change in slope would be consistent with the loss of available surface area associated with the stable dry-out of some fraction of the heater surface. Continued work is required to elucidate the validity of this hypothesis and the nature of this phenomenon.

Figure 10 shows repeatability results for the CuO-4 M10 multiscale surfaces, as compared against bare copper as well as its microchannel (M10) and nanostructure components (CuO-4). While all of the results presented in this work were verified to be repeatable in successive boiling experiments, two separate CuO-4 M10 multiscale surfaces were fabricated and tested. This was done to verify and validate the counterintuitive results shown in Fig. 8, where the wall superheat remains nearly constant (or even decreases) as the heat flux is increased. This behavior leads to the large CHF (303 W/cm²) and maximum HTC (461 kW/m² K) measured for this design. While some discrepancies are observed at low superheats (due to the onset of nucleate boiling), the two separate CuO-4 M10 multiscale surfaces showed very similar performance. These repeatability tests show that this counterintuitive behavior is not a random phenomenon. Additionally, the CuO-3 M4 multiscale surface also exhibits a decrease in wall superheat from ∼7.5 K at 50 W/cm² to ∼5 K at 210 W/cm², producing a similarly large maximum HTC of 403 kW/m² K (Fig. 7).

The overall impact of microchannel geometries, nanostructured coatings, and their combination in multiscale surfaces can be seen in Fig. 11 for all thirty of the distinctly different surfaces tested in this work. The measured CHF and maximum HTC are both plotted against the number of microchannels per unit length, with each CuO nanostructured coating represented as a different curve (closed circles). The microchannel-only surfaces (with no nanostructures) are represented by open triangles, while the nanostructured only samples are represented by all of the data falling on the y-axis (no microchannels). While variations in the data are apparent, several general observations can be made. Figure 11(a) shows that the addition of CuO nanostructures can enhance CHF by up to ∼125 W/cm². This is consistent for bare copper, as well as all of the microchannel geometries considered, and is attributed to delayed dry-out due to wicking. Similarly, the addition of microchannels (up to ten channels per centimeter) shows to consistently increase CHF by approximately 90–110 W/cm² for the bare copper, as well as the surfaces with CuO nanostructures. This is attributed to increased nucleation and enhanced bubble dynamics.

Figure 11(b) shows the maximum HTC measured during boiling as a function of the number of microchannels. With the exceptions of the CuO-3 M4 and CuO-4 M10 multiscale surfaces, the maximum HTC increases relatively consistently with the number of channels on the surface. This is true for the bare copper and all of the CuO nanostructured surfaces considered. Conversely, the addition of CuO nanostructures onto microchannel geometries can lead to moderate increases or moderate decreases in the maximum HTC, which is attributed to two competing effects. Nanostructured coatings suppress the nucleation process by reducing the effective cavity sizes distributed across the surface, but they also allow for operation at higher and higher heat fluxes due to delayed dry-out. As seen in Fig. 11(b), these competing effects produce generally lower maximum HTC for the multiscale surfaces with CuO-1 and CuO-2 (lower wickability) but generally increased maximum HTC for the multiscale surfaces with CuO-3 and CuO-4 (higher wickability).

These observations for HTC are generally consistent for the vast majority of the surfaces tested here. They are not consistent, however, with the HTC results seen for the CuO-3 M4 and CuO-4 M10 multiscale surfaces. For these surfaces, the enhancement of CHF appears to be consistent with the other samples (Fig. 11(a)) and is explained as the combined effects of increased nucleation, bubble dynamics, and surface wicking associated with the microchannel and nanostructure components. The maximum HTC results (Fig. 11(b)) show distinctly higher values for these two multiscale surface designs. Insights into why these two surfaces exhibit such high HTC values can also be found in the open literature. As seen in Fig. 10, the boiling curves for the CuO-4 M10 multiscale surfaces achieve a large HTC by increasing the surface heat flux with essentially no increase (or even a decrease) in the wall superheat. This behavior is extremely similar to the results of Kandlikar, where surfaces with millimeter scale contoured structures were used to promote distinct liquid and vapor flow paths to and from the surface [4]. Figure 10 shows the results of Kandlikar compared against the CuO-4 M10 surfaces, where qualitatively and quantitatively distinct similarities in the boiling curves can be seen. Additionally, a second data set from Kandlikar (not shown here) shows similarities with the boiling curve for the CuO-3 M4 sample (Fig. 7(a)), namely the gradual decrease in superheat from ∼7.5 K at 50 W/cm² to ∼5 K at 250 W/cm². It is not clear why only these two surfaces (out of the thirty surfaces tested here) displayed these behaviors. Interestingly, Rahman et al. have demonstrated boiling enhancement via spatial ordering and found an optimal pitch between flow paths to coincide with the capillary length, λ_C, of the fluid [5]. As seen from the geometric details in Fig. 1, the distances between two microchannels for the M4 and M10 designs are 2.33 mm and 1.2 mm, respectively. This corresponds to a center-to-center pitch of ∼λ_C and ∼λ_C/2, where the capillary length of water at 100 °C is λ_C = 2.4 mm. These similarities suggest the possibility that spatial ordering of the liquid and vapor flow fields may be playing a role in the enhancement of HTC for these two surfaces. It is possible that as heat flux increases, the spatial ordering of flow fields around active nucleation sites results in an increase in the rate at which replenishing liquid is returning to the surface. This pumping effect could increase with heat flux and, therefore, lead to a net decrease in average surface temperature due to the cooler liquid being drawn toward the heater surface more effectively. Jaikumar and Kandlikar also reported a pronounced decrease in superheat with increasing heat flux for their work using multiscale surfaces [18]. This behavior was shown to dramatically increase HTC and to be highly dependent on microchannel geometry. This seems to suggest that this phenomenon may be related to not only spatial ordering but also the existence of surface structures with multiple length scales. While no definitive conclusions can be made regarding spatial ordering and the relation between optimal geometric features and capillary length, the experiments conducted for this work indicate that continued research on the subject is warranted.

The effects of surface structure length scales on the enhancement of pool boiling heat transfer have been experimentally investigated. Copper substrates have been fabricated with multiple types of surface structures including microchannel arrays, nanostructured coatings, and surfaces comprised of both microchannels and nanostructured coatings. Five microchannel geometries were considered with a varying density of microchannels, and four nanostructured coatings were considered using hydrothermal oxidation of the underlying copper substrate. Twenty different multiscale surfaces were fabricated from each permutation of microchannel geometry and CuO nanostructure coating considered, to study the effect of multiple length scales. Along with a bare copper control surface, thirty distinct copper surfaces were fabricated and tested during pool boiling of saturated water at atmospheric conditions. The inclusion of nanostructured coatings were shown to increase CHF due to capillary wicking but decreased HTC due to the suppression of the nucleation process. The maximum CHF achieved using CuO nanostructures was found to be 228 W/cm². Microchannel geometries promoted both CHF and HTC as compared to bare copper, due to increased nucleation at lower superheats and enhanced bubble dynamics. CHF and HTC both generally increase with the number of channels, with maximum values of 206 W/cm² and 186 kW/m² K, respectively. The results for single length scale structures were generally consistent with those found in the open literature.

By adding nanostructures to the microchannel surfaces, the CHF was seen to increase for all twenty multiscale surfaces, where the effect of wicking-enhanced CHF was evident and consistent with the nanostructure only surfaces. The maximum HTC remained nominally unchanged when adding nanostructures to the microchannels, with some surfaces showing up to a ∼30% increase, and others up to a ∼30% decrease. Multiscale surfaces with the two high-wicking CuO nanostructures (CuO-3 and CuO-4) yielded CHF values in the range of 250–300 W/cm² for all designs. Maximum values of CHF and HTC recorded in this work were 313 W/cm² and 461 kW/m² K for the CuO-3 M10 and CuO-4 M10 surfaces, respectively. The multiscale surfaces exhibited distinct behaviors associated with both of their components, as evident in the shape of their boiling curves. Microchannel geometries increased nucleation and bubble dynamics at low fluxes, and nanostructured coatings produced wicking-enhanced CHF and delayed dry-out. Finally, two of the multiscale surfaces tested here exhibited notably larger HTC values than other designs, including a characteristic decrease in superheat temperature with increasing heat flux. This behavior is only seen for multiscale structures and it is speculated here that spatial ordering of liquid and vapor flow paths could be playing a role in the enhancement seen for these two designs.

This work was funded by the National Science Foundation under Award No. 1454407.