Article pubs.acs.org/Langmuir
Physics of Fluid Transport in Hybrid Biporous Capillary Wicking Microstructures Saitej Ravi, Ramanathan Dharmarajan, and Saeed Moghaddam* Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, United States S Supporting Information *
ABSTRACT: The mass transport capacity (i.e., the capillary limit,) of homogeneous wicks is limited by the inverse relation between the capillary pressure and permeability. Hybrid wicks with two or more distinct pore sizes have been proposed as alternative geometries to enhance the capillary limit. In this study, the impact of the two hybridization schemesin-plane and out-of-planeon the capillary transport of hybrid wicks is studied. Experimental data from inplane hybrid wicks in conjunction with a theoretical model show that local changes in the curvature of the liquid−vapor meniscus (i.e., pore size) do not result in a higher mass flow rate than that of a comparable homogeneous wick. Instead, a global change in the curvature of the liquid−vapor meniscus (as occurring in out-ofplane hybrid wicks) is necessary for obtaining mass flow rates greater than that of a homogeneous wick. Therefore, the physics of capillary limit and dryout in out-of-plane hybrid wicks is investigated using a hybrid wick consisting of a 1-μm-thick highly porous mesh suspended over a homogeneous array of micropillars. A study of the dryout process within the structure revealed that the presence of the mesh strongly alters the dryout mechanism. Visualization studies showed that out-of-plane hybrid wicks remain operational only as long as the liquid is constrained within the mesh pores; recession of the meniscus just below the mesh results in instantaneous local dryout. To maintain liquid within the mesh structure, the mesh thickness was increased, and it was determined that the mesh thickness plays the key role in the performance of an out-of-plane hybrid wick.
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It is clear from eq 1 that the mass flow rate can be maximized by designing wicks with a high capillary pressure and permeability. However, in homogeneous (i.e., monoporous) wicks used in the existing heat pipes, these two parameters are inversely related. This inverse relation limits the maximum flow rate that can be generated in homogeneous wicks; those with small pores generate high capillary pressure but have low liquid permeability and vice versa. Therefore, homogeneous wicks are not suitable for applications with high thermal loads. The drawbacks of homogeneous wicks can be overcome by utilizing hybrid wicks with two or more pore sizes, such that the smaller pores generate a high capillary pressure and the larger pores increase wick permeability. In recent years, several hybrid wick designs have been proposed with the goal of enhancing the performance of heat pipes and vapor chambers. These designs can be broadly classified into two different schemes: inplane hybridization, in which the small and large pores are both present along the wick plane (i.e., along the flow direction), and out-of-plane hybridization, in which the size of the pores varies along the direction normal to the wick plane.
INTRODUCTION One of the major hurdles in the development of high-power electronics is substantial parasitic heat generation that must be removed to maintain a safe device operating temperature. The challenges are further exacerbated in high-performance systems where large heat fluxes are accompanied by constrained device spaces, such as those in military applications. Capillary-driven heat carriers/spreaders such as heat pipes and vapor chambers are an attractive means for the thermal management of electronics because of their high effective thermal conductivity and reliability. The most frequently encountered operating limit in these devices is the capillary limit of the wick structure, which occurs when the rate of liquid evaporation from the wick is greater than the maximum rate of liquid transport to the evaporator. This limit is governed by two parameters−the permeability of the wick (K) and the capillary pressure generated in the wick (Pc). The maximum mass flow rate sustained in a wick can be expressed using Darcy’s law (eq 1), where ρ, A, μ, g, and L represent the density of the working fluid, cross-sectional area of the wick, viscosity of the working fluid, acceleration due to gravity, and the wicking length, respectively. ṁ =
ρKA (Pc − ρgL) μL
Received: May 2, 2016 Revised: July 25, 2016
(1) © XXXX American Chemical Society
A
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Figure 1. Schematic illustrations of different hybrid wick structures. (a) An in-plane hybrid wick created through the growth of nanostructures on a homogeneous wick, (b) a biporous in-plane hybrid wick consisting of large and small pores distributed throughout the wick, (c) a segmented inplane hybrid wick with small pores in the evaporator and large pores in the adiabatic section (the arrow indicates the liquid flow direction), and (d) an out-of-plane hybrid wick with small pores at the liquid−vapor interface and large pores adjacent to the wall (the arrow indicates the liquid flow direction). The schematics present a side-on view of micropillar-array-based hybrid wicks.
The third type of in-plane hybrid wick consists of segmented wicks with a change in pore size along the wick length (Figure 1c). These wicks have smaller pores in the evaporator and larger pores in the adiabatic section, causing a local change in meniscus curvature in the evaporator. The primary benefit of this design is the increase in thin film area, which enhances the evaporator effectiveness.8,16 In most segmented wicks, the height of the evaporator section is shorter than the height of the adiabatic section. The larger thin film area and shorter wick lower the evaporator thermal resistance. For example, Weibel et al.4,17,18 designed segmented hybrid wicks with a CNT-based evaporator and a thicker sintered powder or screen mesh adiabatic section to induce nucleate boiling on the wick surface. Some studies have also proposed wicks that combine two or more types of in-plane hybrid wicks to create “capillary-fed boiling wicks”.16,19 A special type of segmented in-plane hybrid wick is a graded wick wherein the pore size of the wick gradually decreases from the condenser to the evaporator.20−22 The out-of-plane hybrid wicks are similar in configuration to the conventional compound wicks, wherein the pore size varies in the direction normal to the wick plane.23−25 These hybrid wicks are formed from a combination of two or more wicks with different pore sizes such that the pore size decreases from the bottom of the wick to the liquid−vapor interface (Figure 1d).26−28 This configuration results in a high capillary pressure due to the small curvature of the liquid−vapor interface and a high permeability for liquid flow at the bottom of the wick. Dai et al.29 fabricated an out-of-plane hybrid wick consisting of an 80-μm-thick copper screen mesh bonded to 250-μm-deep copper microchannels. The authors reported that this hybrid wick exhibited up to an 83% greater dryout threshold than the base microchannel wick. The improvement in performance was attributed to the separation of flow and capillary generation processes. Although this study examined the thermal characteristics of an out-of-plane hybrid wick, the physics of capillary flow through hybrid wick structures was not investigated. Furthermore, the effects of wicking length and wick geometry on the capillary performance of these wick structures were not explored.
Most of the hybridization efforts discussed in the literature are in-plane schemes and can be further categorized into three types. The first type of in-plane hybrid wick involves the implementation of nanostructures on the surface of a homogeneous wick (Figure 1a). The primary function of the nanostructures is to decrease the contact angle subtended by the liquid and increase the capillary pressure (the permeability of this hybrid wick is nearly identical to that of the base homogeneous wick). A secondary advantage of these structures is the increase in thin film area through the wicking effect of the nanostructures, which can increase evaporator efficiency. Because the theoretical limit of the base homogeneous wick is achieved at a contact angle of 0°,1 this type of hybridization only brings the performance of the hybrid wick closer to the theoretical limit of the base homogeneous wick. Examples of this type of wick include a CuO-coated micropillar array wick,2,3 a carbon-nanotube-coated sintered powder wick,4 and nanotextured titania micropillar wicks.5−7 Biporous or bidispersed wicks comprise the second type of in-plane hybrid wick and consist of two or more distinct pore sizes distributed throughout the wick (Figure 1b). These wicks are often designed to facilitate efficient boiling in the wick, with the large pores acting as vapor-venting pathways at high heat fluxes. Therefore, these wicks generally operate at shorter wicking lengths, where boiling is observed before the capillary limit is reached. 8 Several studies have experimentally demonstrated biporous wick designs that exhibit greater dryout thresholds than equivalent homogeneous wicks.9−13 This type of hybrid wick has also been fabricated in a channel-array configuration with carbon nanotubes or micropillars forming the arrays.14,15 In this configuration, the channels supply liquid at low heat inputs and facilitate the removal of vapor at high heat inputs. These channel-array wicks are typically designed to improve the heat-transfer coefficient in the evaporator by increasing the thin film area. Biporous wicks have shown promise at short wicking lengths but may not be suited for the working distances encountered in conventional heat pipe applications. B
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suspended over an array of micropillars. The nitride film was patterned with an array of 4 μm holes spaced 3 μm apart, and the pillar spacing was 48 and 66 μm. (2) Wick D had a 20-μm-thick woven stainless steel mesh bonded on an array of 100-μm-tall micropillars. The mesh had a wire diameter and pore size of 20 μm. The underlying micropillar array in this wick was identical to that of wick A. The mesh utilized in this wick was selected on the basis of analyses of experimental data obtained from wicks C. This mesh was an order of magnitude thicker than the nitride film in wicks C. (3) Wicks E were fabricated through bonding a 180-μm-thick woven mesh on an array of 100-μm-tall micropillars. This mesh had a wire diameter of 50 μm with a pore size of 15 μm. The mesh implemented in this wick was selected on the basis of the data obtained from wick D. This mesh was an order of magnitude thicker than the stainless steel mesh in wick D. The dimensions of the out-of-plane hybrid wicks are summarized in Table 2.
In this study, the effect of in-plane and out-of-plane hybridization schemes on the physics of capillary transport in wick structures is examined. The dryout thresholds of two different segmented wicks are compared to that of a homogeneous micropillar array wick in order to determine the effect of local changes in meniscus curvature on the capillary limit. Out-of-plane hybrid wicks are also fabricated to determine the impact of wick geometry (mesh thickness, pore size, and pillar spacing) on capillary transport and dryout. The insights gained from these studies are implemented to design hybrid wicks with greater capillary limits than a baseline homogeneous wick.
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EXPERIMENTAL METHODS
Three different types of wick structures were fabricated: (1) a homogeneous micropillar array wick; (2) segmented in-plane hybrid wicks composed of distinct micropillar array geometries in the evaporator and adiabatic sections, with the micropillar array in the evaporator having a smaller diameter and spacing than the array in the adiabatic section; and (3) out-of-plane hybrid wicks consisting of a mesh suspended over a homogeneous micropillar array, in which the pores in the mesh are smaller than the spacing between micropillars in the supporting array. Device Design and Fabrication. The basic layout of a device consisted of a micropillar-array-based wick structure on one side and a thin film platinum heater with embedded temperature sensors on the other side.30−32 The heater section was located along one end of the 1cm-wide wick and measured 0.5 cm × 1 cm. The homogeneous wick and the segmented wicks were fabricated by etching micropillars on silicon substrates using the deep reactive ion etching (DRIE) process; a ruler was etched adjacent to the wick to measure the wicking length during tests. The geometry of the homogeneous wick (device A) was identical to the optimized micropillar array wick presented in our earlier study,1 wherein this geometry exhibited the highest dryout threshold among all homogeneous array wicks. In-Plane Hybrid Wicks. The segmented in-plane hybrid wicks were designed to study the effects of (a) a smaller pore size in the evaporator and (b) pillar spacing in the adiabatic section with respect to the capillary limit of micropillar array wicks. Two different segmented wicks were fabricated with identical evaporator geometries, composed of a square array of pillars with 10 μm diameter, spaced 10 μm apart (Figure S1a). The adiabatic sections of both wicks were designed with large pores in order to increase permeability and reduce viscous losses (Figure S1b). The heater and sensor on the back side of the wick evaporator were identical to those on the homogeneous wick. The geometric dimensions of the homogeneous (device A) and segmented wicks (devices B-1 and B-2) are summarized in Table 1.
Table 2. Geometric Dimensions of the Meshes and Micropillar Arrays in the Out-of-Plane Hybrid Wicks micropillar dimensions (μm)
evaporator section (μm)
adiabatic section (μm)
device
spacing, we
height, he
diameter, da
spacing, wa
height, ha
A B-1 B-2
42 10 10
48 10 10
100 100 100
42 42 42
48 58 88
100 100 100
device
diameter/edge, dp
spacing, wp
height, hp
pore size, dm
thickness, tm
C-1 C-2 D-1 E-1 E-2
42 42 42 42 15
48 66 48 48 75
100 100 100 100 100
4 4 20 15 15
1 1 20 180 180
The fabrication of hybrid wicks C (Figure 2a) began with the deposition of the heaters and sensors on one side of the wafer, followed by the deposition of a 1-μm-thick silicon nitride film on the other side. The nitride film was etched to define the open areas (pores) of the mesh and expose the underlying silicon. This pattern consisted of a square array of 4 μm circular holes spaced 3 μm apart. Areas of the nitride film corresponding to the supporting pillars were not etched. The exposed silicon was subsequently etched to create an array of holes. Next, the walls between adjacent holes were etched using an isotropic wet etch solution to create a porous nitride mesh suspended over silicon pillars. Finally, the wick surface was coated with 2000 Å of silicon oxide (plasma-enhanced chemical vapor deposition, PECVD). The oxide coating negated the effect of surface material on the dryout threshold of different structures. Wicks D and E (Figure 2b, c) were fabricated by bonding stainless steel meshes of different thicknesses to the top surface of the micropillars. The lengths of the meshes in wicks D and E were 3.1 and 3.6 cm, respectively. Prior to bonding, the meshes were coated with a thin layer of silicon oxide. The adhesion of the meshes to the array was accomplished by coating the bonding surfaces with a thin film of an adhesive using a recently developed process.33 Test Methods. All wick structures described here were tested using a methodology similar to the one described in our previous studies.30−32 The devices were tested under saturation conditions in a 9 in. stainless steel chamber that incorporated a translatable arm on the top flange to raise or lower test devices within the chamber and thus change the wicking length (Figure S2). The test device was mounted on a polycarbonate holder attached at the lower end of the arm. The chamber was connected to a vacuum pump for 12−14 h, after which deionized water was distilled into the chamber. The test device was lowered into the chamber to a wicking length of 2 cm. The power input to the thin-film heater was raised in small increments (with the system allowed to reach steady state prior to each increase) until the onset of dryout was observed in the evaporator. The power input at this stage was recorded as the dryout threshold of the test device at a wicking length of 2 cm. The device was raised and set to a new wicking length, and the process was repeated to obtain a new value of the dryout threshold. In this manner, the dryout threshold was obtained at different wicking lengths; at least three data points for dryout threshold were collected at each wicking length.
Table 1. Geometric Dimensions of the Homogeneous and Segmented In-Plane Hybrid Wicks diameter, de
mesh dimensions (μm)
Out-of-Plane Hybrid Wicks. The out-of-plane hybrid wicks were composed of a porous mesh suspended over an array of micropillars such that the pores in the mesh were smaller than the spacing between the pillars. The rationale in the design of these out-of-plane hybrid wicks was that the liquid−vapor interface formed in the smaller pores of the mesh would generate a high capillary pressure whereas the underlying pillar array would provide a highly permeable path for bulk liquid transport. Three out-of-plane hybrid wicks were investigated: (1) Wicks C consisted of a 1-μm-thick porous silicon nitride film C
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Figure 2. SEM of the out-of-plane hybrid wicks: (a) hybrid wick C consisting of a 1-μm-thick nitride mesh, (b) hybrid wick D with a 20-μm-thick stainless steel mesh, and (c) hybrid wick E with a 180-μm-thick stainless steel mesh. The stainless steel meshes were coated with silicon oxide prior to bonding.
Figure 3. (a) Comparison of the dryout threshold of the segmented in-plane hybrid wicks with the homogeneous wick. Each data point represents the mean dryout threshold at a given wicking length, and the error bars represent one standard deviation about the mean. (b) Comparison between experimental dryout threshold values from the B-1 segmented hybrid wick and the theoretical dryout threshold predicted for a hypothetical homogeneous micropillar array wick with dimensions identical to those of the adiabatic section of the B-1 wick (i.e., dp = 42 μm, wp = 58 μm, and hp = 100 μm). The theoretical values are calculated using the experimentally validated flow model reported in our previous study.31 Uncertainty Analysis and Error Propagation. The uncertainty in wicking length, based on the dimensions of the etched ruler, was ±0.05 cm. The measurement uncertainties in the voltage (17 mV) and current (2 mA) supplied to the heater were based on specifications of the power supply (Keithley 2200-72-1) used in the experiments. On the basis of these quantities, the uncertainty in the total power supplied to the heater was calculated using eq 3.
Q in = VI dQ in Q in
R th =
(2)
⎛ dV ⎞ ⎛ dI ⎞ ⎜ ⎟ + ⎜ ⎟ ⎝V ⎠ ⎝I ⎠ 2
=
The thermal resistance of the insulating epoxy was calculated using eq 5. The thermal conductivity of the epoxy (ke) was 0.177 W/m2 K (DP 270 black, 3M), and the heated area (Ae) was equal to the area of the evaporator (0.5 cm2). The thickness of the epoxy coating (t) was approximately 3 mm.
Tev − Tres Lc
(5)
On the basis of these values, the thermal resistance was estimated to be 339 K/W. Such a high value of thermal resistance suggests that heat loss through the epoxy layer contributed negligibly to the heat loss. The dryout threshold of a wick geometry was then calculated as
2
(3)
Here, dQin is the power input uncertainty, dV is the voltage uncertainty, and dI is the current uncertainty. The maximum uncertainty in the power supplied to the heater was 49 mW. The two major sources of heat loss during thermal tests were (Figure S3) conduction heat loss through the wick to the pool of water, Qcond, and heat loss through the thermally insulating epoxy, Qepoxy. The conduction heat loss was calculated on the basis of the temperature difference between the evaporator and the pool of water just prior to dryout (eq 4). Here, k is the thermal conductivity of silicon, Asub is the cross-sectional area of the substrate, Tev is the average evaporator temperature prior to dryout (measured using the thin film sensors), Tres is the temperature of the pool of water, and Lc is the distance between the center of the evaporator and the pool of water.
Q cond = kA sub
t keAe
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Q = Q in − Q cond − Q conv
(6)
RESULTS AND DISCUSSION In-Plane Hybrid Wicks. The heat-transfer data for the segmented hybrid wicks (devices B-1 and B-2) and the homogeneous wick (device A) are plotted in Figure 3a. The data are represented as the mean dryout threshold at each wicking length, and the error bars represent one standard deviation about the mean. In each of the segmented wicks, the adiabatic section has greater permeability and the evaporator section has a smaller capillary radius than device A. The dryout threshold of both wicks is lower than that of homogeneous wick A at all wicking lengths. The results suggest that decreasing the capillary radius in the evaporator (and increasing the local capillary pressure) does not enhance the wick capillary limit. Moreover, the performance of a segmented hybrid wick
(4) D
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Langmuir decreases when the spacing between pillars in the adiabatic section is increased (from B-1 to B-2). To understand the data trends in Figure 3a, we consider a hypothetical homogeneous micropillar wick with geometry identical to the geometry of the adiabatic section of the B-1 segmented wick (i.e., dp = 42 μm, wp = 58 μm, and hp = 100 μm). The theoretical dryout threshold values of such a wick can be predicted using the experimentally validated capillary flow model presented in our previous studies.1,31 This flow model was based on Darcy’s law with the permeability determined from the expression proposed by Byon and Kim34 and the capillary pressure calculated from Xiao et al.’s model.35 A comparison of the predicted dryout threshold of the hypothetical homogeneous geometry and experimental data from the B-1 segmented wick (Figure 3b) shows that these two wicks have identical capillary limits at all wicking lengths. This implies that the local capillary pressure increase caused by a smaller pore size in the evaporator of a segmented wick does not result in a higher mass flow rate than the base homogeneous wick. Instead, the mass flow rate of a segmented wick is governed by the liquid pressure gradient in the condenser and adiabatic sections of the wick. The effect of this pressure gradient is seen in Figure 3a, where an increase in the pillar spacing of the adiabatic section (between devices B-1 and B-2) results in a decrease in the dryout threshold. The insights gained on the limitations of segmented wicks can be extended to the operation of other in-plane hybrid wicks. Since the capillary limit of an in-plane hybrid wick is dictated by the pressure gradient in the adiabatic and condenser sections of the wick, it can be deduced that the utilization of a biporous evaporator with homogeneous adiabatic and condenser sections will not result in any significant increase in mass flow rates over those observed for an equivalent homogeneous wick. Furthermore, the effectiveness of a typical biporous wick is limited to only short wicking lengths because the pressure gradient in the large pores limits the maximum mass flow rate of the wick. Graded wicks (wicks with a continuous pore size gradation between the condenser and evaporator) have been proposed as alternate designs to increase the capillary limits of in-plane hybrid wicks.20,22 Out-of-Plane Hybrid Wicks. The out-of-plane hybrid wicks were designed to decouple the inverse relationship between the capillary pressure and permeability observed in homogeneous wicks. This was accomplished by utilizing two distinct structures for enhancing capillary pressure and permeability; the menisci formed in the small pores of the mesh generate a high capillary pressure, and the wide spaces between the pillars facilitate large liquid flow rates. Unlike the in-plane hybrid wicks, the design of these wicks ensured a global change in the liquid−vapor interface and hence the wick capillary radius. The C hybrid wicks were designed on the assumption that a thin mesh layer with small pores assembled on an underlying structure with larger pores would generate a greater capillary limit than homogeneous wick A. However, the dryout threshold data from wicks C-1 and C-2 (Figure 4) do not support this assumption. The higher capillary pressure in these hybrid wicks (due to the small pores in the mesh) does not result in an improvement in performance compared to that of wick A. To understand the role of the mesh on dryout in an out-ofplane hybrid wick, the progression of dryout in wicks A and C-1 was studied using a high-speed camera (Photron SA4, 125 frames per second). The results suggested that the dynamics
Figure 4. Comparison of the dryout thresholds of hybrid wicks C with the homogeneous wick. Each data set is represented as the mean dryout threshold at a given wicking length. The error bars represent one standard deviation about the mean.
and nature of dryout in an out-of-plane hybrid wick are strongly influenced by the presence of the mesh. Figure 5 shows a selected sequence of images captured during dryout on wick A. As seen in the images, the progression of dryout in this wick is accompanied by a gradient in the liquid height at the interface between the wet and dry regions (appearing as a dark band in Figure 5b−e). The width of this interface is between 100 and 120 μm (based on the dimensions of the wick). The presence of this gradient at the interface indicates that the position of the meniscus gradually decreases from the top of the pillars in a completely wet section to the bottom of the pillars in a dry section of the wick. In contrast, no gradient in the liquid height is observed at the interface between the wet and dry regions of the C-1 hybrid wick (Figure 6). This wick appears to support only two states, i.e., wet and dry states, with no intermediate region, suggesting that this wick remains functional only when liquid is in contact with the mesh (wet regions). This behavior can be attributed to differences in the physical nature of dryout in an out-of-plane hybrid wick and a homogeneous wick. In the homogeneous wick, as the evaporation rate increases, the liquid meniscus recedes along the pillar walls into the pores. When the local meniscus recedes to the base of the pillars, dryout is reached. On the other hand, the meniscus in an out-of-plane hybrid wick is stable only when it is constrained within the mesh; recession of the meniscus to below the mesh in a hybrid wick results in spontaneous dryout (Figure S4). As heat input into the wick is increased, the menisci recede into the mesh pores such that the degree of recession increases along the flow direction (Figure S4a). This continues until the menisci at the end of the evaporator are formed at the bottom surface of the mesh. Further increases in the heat input causes the local liquid level to drop just below the mesh, and the local menisci are formed between the supporting pillars. At this stage, the wick is divided into two distinct regions (Figure S4b): In region 1, the local liquid menisci have receded below the mesh and are formed between the pillars supporting the mesh. The capillary radius of a meniscus formed in this region is greater than the radius of a meniscus formed in the mesh pores. In region 2, liquid wets the mesh and the meniscus is formed within the mesh. E
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Figure 5. Sequence of images showing the progression of dryout through homogeneous wick A. The gradient in height of the liquid between the wet and dry regions appears as a dark band in the images.
The dissimilar capillary radii in these two regions generate an adverse capillary pressure gradient (opposing bulk liquid flow) that drives liquid from region 1 to region 2, resulting in spontaneous local dryout in region 1 (Figure S4c). The thin mesh limits the extent of meniscus recession, thus resulting in low values of dryout threshold. The experimental data for hybrid wicks C suggest that decreasing the mesh pore size alone (to increase capillary pressure) does not necessarily translate into improved performance. On the basis of the dryout mechanism described here, it can be postulated that using a thicker mesh will increase the dryout threshold. The thicker mesh would constrain the liquid at greater evaporation rates and delay the recession of the meniscus below the mesh. This hypothesis on the dominant role of mesh thickness on dryout was tested with the D-1 wick, which had a thicker mesh (20 μm) with larger pores (20 μm) than wicks C. The stainless steel mesh, extending up to a wicking length of 3.1 cm on the D-1 wick, was bonded to a micropillar wick with an array geometry identical to that of device A. This hybrid wick exhibits significantly greater dryout thresholds than the B wicks, with a performance comparable to that of wick A between wicking lengths of 2 and 3 cm (Figure 7). In this configuration, liquid flows through the highly permeable pillar array and into the mesh; flow through the mesh does not contribute significantly to the overall mass flow rate because of the lower permeability of the mesh compared to that of the supporting pillars (Supporting Information section 5). At wicking lengths greater than the length of the mesh (i.e., greater than 3.1 cm), the performance of the D-1 wick drops significantly and is almost 50% lower than that of wick A. This is because the wick is no longer in an out-of-plane hybrid configuration at wicking lengths greater than 3.1 cm.
The test results on wicks C and D show that the mesh thickness plays a critical role in determining the performance of the out-of-plane hybrid wicks. This understanding was used to design hybrid wicks E to further enhance the capillary limit of the out-of-plane hybrid wicks. Two E wicks were built with meshes thicker than that of the D-1 wick; the meshes extended up to a length of 3.6 cm. The array in the E-1 wick was identical to the array in wicks A and D-1. The superior dryout threshold of both E wicks compared to those of wicks A and D-1 can be attributed to the combined effects of greater capillary pressure and a thicker mesh (Figure 7). The dryout threshold values of the E-1 wick are between 1.1 and 1.7 times greater than the corresponding values of wick A. At a wicking length of 3 cm, the dryout threshold of this wick is almost equal to that of wick A at 2 cm. The larger pillar spacing of the E-2 wick (75 μm) increases the permeability of the wick and reduces viscous losses in the major flow path (through the pillars), which translates into greater dryout threshold values compared to the E-1 wick at all wicking lengths. It must be noted that increasing the pillar spacing would improve the performance of the hybrid wick until the increased evaporator thermal resistance due to a low pillar density reaches an unacceptable level. The experimental data obtained from the out-of-plane hybrid wicks (C−E) show that the dryout threshold increases with the mesh thickness. However, it must also be noted that increasing the mesh thickness beyond a certain threshold would result in an extremely high thermal resistance between the heated surface and the liquid−vapor interface, thereby lowering the efficacy of the out-of-plane hybrid wick. The effectiveness of hybrid wicks E can be determined from the ratios of the dryout thresholds of these wicks and homogeneous wick A, as presented in Figure 8. The F
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Figure 6. Sequence of images showing the progression of dryout in the C-1 hybrid wick. The interface between the wet and dry regions of the wick is highlighted in blue.
Figure 8. Ratio of the dryout threshold of hybrid wicks E and wick A at different wicking lengths.
Figure 7. Dryout threshold vs wicking length data for hybrid wicks D and E compared to homogeneous wick A.
identical capillary pressures (identical meshes used in both hybrid wicks). At a wicking length of 3 cm, the dryout threshold of the E-2 wick is nearly twice that of the homogeneous wick. Because identical meshes are used in both of these hybrid wicks, it can be surmised that the effectiveness of an out-of-plane hybrid wick at a given wicking length is strongly influenced by the mesh type. Hybrid wicks
performance ratios of both hybrid wicks exhibit similar trends with respect to the wicking length, with the lowest effectiveness observed at a wicking length of 2 cm and the greatest effectiveness observed at 3 cm. The greater effectiveness of the E-2 wick is due to the higher permeability of the array in this wick compared to that in the E-1 wick while generating G
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increase in the permeability of the supporting array for a given mesh type increased the effectiveness of the hybrid wick. The results presented in this study showed that an out-ofplane hybridization scheme must be implemented in order to achieve greater capillary limits than observed for the homogeneous wicks. Although the effects of utilizing small pores in the mesh were evident, the insights gained from this study show that the interactions of this parameter with the thickness of the mesh dictate the capillary limit. These results can be used to optimize the design of out-of-plane hybrid wicks by developing structures (such as a mesh) that generate high capillary pressure while delaying meniscus recession at high heat inputs and designing flow support structures (such as micropillar arrays) that have high permeability with a low thermal resistance penalty.
that are more effective than wicks E at wicking lengths of 2 or 2.5 cm can be designed by hybridizing a homogeneous wick with a suitable mesh. The higher mass flow rates in hybrid wicks D and E resulted in greater dryout thresholds and evaporator temperatures compared to those in wick A. In wicks A and D-1, steady-state evaporator temperatures were observed prior to the dryout (Figure S6), indicating that heat transfer in these wicks was dominated by thin film evaporation at the interface. This implies that dryout occurred in these wicks because the capillary limit was reached. In contrast, oscillating evaporator temperatures were observed for wicks E (Figure S6), suggesting that the primary heat transfer mode prior to dryout in these wicks was nucleate boiling. The higher applied heat resulted in elevated temperatures in the evaporator, which were sufficient to initiate bubble nucleation. Therefore, it can be inferred that the boiling limit rather than the capillary limit was the primary cause of dryout in wicks E.
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ASSOCIATED CONTENT
S Supporting Information *
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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b01611. Scanning electron micrographs of the B-2 segmented inplane hybrid wick. An image of the test chamber. Schematics with the different heat loss components in a typical wick and of the behavior of an evaporating meniscus. The evaporating meniscus recedes below the mesh, resulting in spontaneous dryout. Permeability of the stainless steel meshes in wicks E-1 and E-2 estimated using the rate of rise method, with data and subsequent analyses to obtain an order-of-magnitude estimate of this parameter. Comparison of the evaporator temperatures of wicks A, D-1, and E-2 just prior to dryout. (PDF)
CONCLUSIONS In this study, for the first time, the effect of different hybridization schemes on the capillary limit of wick structures was systematically investigated. A homogeneous wick, identical in geometry to the optimized micropillar array presented in an earlier study,1 was selected as a baseline geometry. Dryout threshold data from segmented in-plane hybrid wicks, with smaller pores in the evaporator and larger pores in the adiabatic section than the homogeneous wick, were lower than the homogeneous wick at all wicking lengths. A capillary flow model introduced in our previous study was used to show that local changes in the pore size (such as those encountered in inplane hybrid wicks) do not increase the capillary limit of the hybrid wick compared to that of an equivalent homogeneous wick. This is because the pressure gradient between the condenser and the adiabatic section of the hybrid wick determines the capillary limit of the wick. The out-of-plane hybrid wicks were composed of a porous mesh with small pores suspended over an array of micropillars. Hybrid wicks C, with an ultrathin silicon nitride mesh (mesh pore size of 4 μm), exhibited much lower dryout thresholds than the baseline homogeneous wick (wick A). Visualization studies of dryout on this wick and the homogeneous wick suggested that the addition of a mesh on the hybrid wick changed the dryout mode of the wick. This type of hybrid wick remained operational as long as the liquid meniscus was formed within the mesh pores, with catastrophic dryout occurring when the receding meniscus detached from the mesh. This mechanism of dryout implied that, unlike homogeneous wicks, the capillary limit of the out-of-plane hybrid wicks was not determined by the mesh pore size and array spacing alone; the thickness of the mesh also had a strong influence on the capillary limit. The mesh thickness established the extent of meniscus recession prior to catastrophic dryout such that a thicker mesh delayed the onset of dryout. On the basis of this understanding, out-of-plane hybrid wicks with thicker meshes were fabricated by bonding stainless steel meshes on micropillar arrays. The experimental data from these wicks validated the role of the mesh thickness in determining dryout, with hybrid wicks E exhibiting significantly greater dryout thresholds than the homogeneous wick. The data from these wicks showed that the effectiveness of an out-of-plane hybrid wick over a homogeneous wick varied with wicking length, with the maximum effectiveness observed at 3 cm for both wicks. An
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AUTHOR INFORMATION
Corresponding Author
*E-mail: saeedmog@ufl.edu. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the support of DARPA and Dr. Bar-Cohen, program manager. Fabrication of the devices was conducted in the Nanoscale Research Facility (NRF) at the University of Florida.
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