Drop impact cooling enhancement on nano-textured surfaces. Part I: Theory and results of the ground (1 g) experiments

International Journal of Heat and Mass Transfer 70 (2014) 1095–1106

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Drop impact cooling enhancement on nano-textured surfaces. Part I: Theory and results of the ground (1 g) experiments Suman Sinha-Ray a, Alexander L. Yarin a,b,⇑ a b

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor St., Chicago, IL 60607-7022, United States College of Engineering, Korea University, Seoul, South Korea

a r t i c l e

i n f o

Article history: Available online 29 November 2013 Keywords: Spray cooling Nano-textured surface Normal gravity

a b s t r a c t The present work consists of two parts. Part I covered in this article is devoted to the experimental setup built as a prototype of the setup for parabolic flights and tested in the earth experiments at 1 g. This part encompasses the sample (nanofiber mat) preparation by electrospinning, sensitization and electroplating, as well as the development of the drop-on-demand device for drop cooling. It also details the methodology of the heat flux measurements, in particular, an in-depth exploration of the non-trivial interplay between the heater operation and drop cooling. The article also contains theoretical foundations developed in the present work for the measurement methods used. The results of the earth experiments in Part I encompass the experiments with a single needle producing drop trains or jets with water or Fluorinert fluid FC-7300. The article also contains the experimental results obtained with two-needle system used for droplet generation, as well as the discussion of all the results obtained. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Drop and spray cooling is one of the most effective methods of cooling compared to many other air- or liquid cooling systems [1– 3]. Direct spray cooling of high-heat flux surfaces in Unmanned Aerial Vehicles (UAVs) carrying high power densities on board is under discussion and testing and is fully realizable [2,4,5]. It was discovered recently that the efficiency of spray cooling can be significantly enhanced if a high-heat flux surface is covered by a nano-textured layer, namely, an electrospun polymer nanofiber mat of the thickness about 100 lm [6–10]. This stems from the fact that liquid delivered by the impacting drops of the size D  0.1 cm easily penetrates under the dynamic conditions into the much smaller inter-fiber pores in the mat which are on the scale d  104–103 cm. Therefore, the texture of the electrospun nanofiber mats facilitates coolant penetration into their pores, as well as anchors the drops on the surface thus eliminating the receding motion of the contact line and the droplet bounce. The hydrodynamic focusing of the liquid into the pores and the accompanying suppression of the receding motion of the drops greatly facilitate drop and spray cooling through porous mats consisting of either polymer or metal-plated nanofibers [6–10].

⇑ Corresponding author at: Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor St., Chicago, IL 60607-7022, United States. Tel.: +1 (312) 996 3472; fax: +1 (312) 413 0447. E-mail address: [email protected] (A.L. Yarin). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.007

Even though spray cooling of high-heat flux surfaces for microelectronic applications is still in its infancy, it has already revealed some significant obstacles, namely formation of fluid excess at the surface due to an imbalance between mass rates of coolant supply and evaporation [11–14]. To enhance heat removal rate, ordered rough surfaces were proposed as heat transfer elements [13,14]. Drop spreading over a high-heat flux surface is accompanied by intensive evaporation and boiling. In such regimes the heat transfer between the surface and drop is very high. On the other hand, if the contact temperature is significantly higher than the liquid saturation temperature, the Leidenfrost effect sets in [15], droplets levitate and heat transfer from the wall is significantly hindered by the intermediate vapor layer. Moreover, the high pressure in the vapor layer leads to the instability of spreading liquid drops accompanied by their shattering and the formation of a cloud of small secondary droplets. A recent comprehensive review [16] shows that the dynamic Leidenfrost temperature, corresponding to the transition to the Leidenfrost regime, is a function of drop impact parameters. Abundant literature devoted to the Leidenfrost effect continues to expand at a steady pace [17,18] even though today a comprehensive theory (for example a reliable prediction of the skittering speed) is still absent. In the regimes with flooding, coolant forms a puddle on the hot surface and the situation resembles pool boiling [11–14]. The importance of pool boiling in cooling of microelectronics for space missions and automation was recognized as early as in 1959 when a study of pool boiling under microgravity conditions was conducted [19]. In that preliminary work it was found that the heat

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transfer rate in nucleate boiling on smooth surfaces under microgravity conditions is comparable to that under the earth gravity at 1 g. In a series of experiments under different gravity conditions it was found that gravity has a negligible effect on the heat removal rate at smooth surfaces subjected to nucleate boiling [20–23]. However, it was also shown that under the earth gravity the heat removal rate was lower than that under supergravity for all superheats studied [24] (in the present work the term supergravity denotes all cases with the gravity acceleration higher than the earth gravity). Comparing the microgravity and supergravity cases of nucleate boiling, it was also shown that the boiling curves were similar at the lower wall superheats but at higher superheats the heat removal rate under supergravity was higher [24]. Overall, there is a plethora of self- contradictory experimental observations reported regarding pool boiling under different gravity conditions. A detailed review of such studies can be found in Ref. [25]. The dramatic reduction of heat removal rate in the film boiling regime (above the Leidenfrost temperature) is one of the main challenges of spray cooling of high temperature surfaces. An attractive way to enhance heat removal rate is associated with textured substrates, in particular, different types of rough, structured or coated surfaces, which affect the outcome of a drop impact onto cold and hot surfaces [25–27]. In particular, the nanofiber mats on the high heat-flux surfaces completely suppress the Leidenfrost effect [8–10]. This work aims at the development of a drop generator and surface modification using copper nanofiber mats to reach heat removal rates of the order of 1 kW/cm2 with water drops as a coolant. In the present work the approach to development of rough heat transfer surfaces based on the electrospun nano-textured and porous surfaces introduced in our previous works [6–10] was tested under the conditions of the earth gravity (1 g; Part I), as well as zero gravity (0 g; Part II) and supergravity (1.8 g; Part II) onboard of an aeroplane during parabolic flights. In addition, a novel drop-on-demand droplet generator was developed, as well as several methodologies of the heat transfer measurements were proposed. 2. Experimental 2.1. Materials Polyacylonitrile (PAN; Mw = 150 kDa) was obtained from Polymer Inc. N-Dimethyl formamide (DMF) anhydrous-99.8%, sulfuric

acid, hydrochloric acid, copper sulfate, formaldehyde were obtained from Sigma–Aldrich. Novec fluid FC-7300 was kindly donated by 3 M. Copper plates of different grades were obtained from McMaster-Carr. They were cut into 100  100 square pieces and used as substrates. Prior to deposition of nanofiber mats, copper plates were roughened using a coarse sand paper. 2.2. Preparation of solutions For electrospinning, 12 wt% PAN solution in DMF was prepared. For electroplating copper on the nanofiber surfaces and bonding them to the substrate, the solutions were prepared similarly to Ref. [8]: sulfuric acid (5 g), hydrochloric acid (0.5 g), copper sulfate (16 g) and formaldehyde (10 g) were mixed with 100 mL of deionized (DI) water. 2.3. Electrospinning, sensitization & electroplating of polymer nanofiber mats 12 wt% PAN solution was electrospun to a mat thickness of about 30–50 lm using a standard electrospining setup [28–30]. Electrospun nanofibers were collected on different grades of copper plates. Then, the polymer nanofiber mats were sensitized by sputter coating of Pt–Pd 15 nm-thick layer using Cressington Sputter Coater. After that, prior to electroplating the sputter-coated samples were soaked in electroplating solution, in distinction from Ref. [8]. Then, polymer nanofibers were electroplated as described in Ref. [8]. 2.4. Drop impact onto hot surfaces covered with copper-plated nanofiber mats using drop/jet-on-demand device The drop impact experiments were done using a drop/jet-ondemand device sketched in Fig. 1. This device was used with water as a working liquid. The device is kindred to the pneumatic single-drop-on-demand device [31]. Droplets were ejected in the frequency range 0.83–10 Hz from 25 G flat head needles fixed on top of a nut connected to the supply line. Between the liquid reservoir and the needle there was another bifurcation connected to high pressure line (40–60 Psi) through a solenoid valve (ASCO-8262H022 12 V DC solenoid valve 2-way NC 1/400 ), as shown in Fig. 1. The frequency range and the control signal duration chosen are associated with the evaporation rate of the individual droplets and the activation time required for the sole-

Fig. 1. Schematic of the setup for drop impact experiment.

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Fig. 2. (a) Jet issued from the needle. (b) Drop issued from the needle.

Fig. 3. (a) Sketch of a drop on the surface. (b) Dimensionless temperature field u.

noid valve. The signal frequency and duration were controlled by a function generator (BNC Model 555 Pulse/Delay Generator). It was found that the best result was obtained at a rectangular function with duration of 7.78 ms, while the voltage was varied between 14.6 and 15.2 V. Between the solenoid valve and the delivery tube there was a release valve for venting air (Fig. 1). The best results were obtained by keeping the vent wide open. When the solenoid valve was opened for a controlled duration, air pressed the liquid through the nozzle. Then, as the solenoid valve was closed, the excess air was issued through the release valve resulting in a negative pressure, which pulled a portion of the pushed liquid inside the supply tube. Based on the actuation voltage, which controlled the opening of the solenoid valve, at a fixed actuation time, either individual drops or jets were issued (Fig. 2). When using water as a working liquid, every impulse produced satellite droplets in addition to the main ones. In the experiments with water issued from a single needle on top of the nut, it was also found that at higher frequencies the droplet size was reduced. This can be attributed to the fact that at higher frequencies a faster reversal from the applied positive pressure to a negative pressure happened, which resulted in formation of smaller droplets. At every frequency the water mass issued by the system per pulse or per unit time was measured. To do that, the target was temporarily removed and water mass issued by the device for 2 min was collected in Petri dish and measured, which provided the calibration of water mass delivered by the system per pulse or per unit time. It was found that changing the water reservoir volume from 0.2 to 2 L affected the droplet size, which was probably associated with water inertia in the supply system. Increasing the needle size also led to an increase in droplet size but could cause dripping. So, to increase the droplet size, the reservoir size was changed instead of changing the needle size, and the frequency range was reduced to below 2.5 Hz.

In addition, the experiments were conducted with water being issued from two 25G needles (each fixed on top of the nut at a distance of 1.5 mm from its center). When using FC-7300 as a working liquid, the drop/jet-on demand device was not used due to the following reasons. FC-7300 possesses a very low surface tension of 15 mN/m in comparison to that of water (72 mN/m). Such a low surface tension results in dripping of FC-7300 even without pressure impulse applied. To avoid the undesirable dripping in the the heat transfer experiments with FC-7300, this liquid was delivered using a syringe pump. The liquid was issued through a 32G needle (ID of 0.108 mm and OD of 0.235 mm) at different flow rates of 10, 20, 30, 40, 50, 60, 70 and 80 mL/h. All the other parts of the device in Fig. 1 were the same as in the experiments with water. 2.5. Heat flux measurement A high density heat flux heater [Watlow ULTRAMIC Advanced Ceramic Heater (25 mm  25 mm  2.5 mm/967 Watts/240 V)], a solid state relay [Watlow DIN-A-MITE series A, single phase, 4.5– 32 VDC control signal] and a PID cascade controller [Watlow PM series, 1/8 DIN Vertical, Integrated PID model, 100–240VAC] were purchased from Watlow. The voltage supply line to the heater was connected in parallel to a transformer, which converted the peak to peak supply voltage signal of +240–240 V to an AC signal of peak to peak voltage of +1.58–1.58 V measured using DATAQ datalogger at 960 Hz. This allowed fast measurement of the voltage signal transferred into the system and thus allowed us to compute the power supply spectrum. The controller read the temperature at every 100 ms. The heater was fixed in a Teflon block, thereby insulating its rear side and edges. Then, the sample was fixed on the heater by threaded mica blocks to avoid any loss caused by the fixture. After that, two thermocouples were fixed on the surface (T1 and T2 as shown in Fig. 1). Both thermocouples were put between

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perature is equal to Td which is lower than Ts (the dimensional coordinates are denoted by asterisk as a superscript), as depicted in Fig. 3a. It is convenient to consider the modified temperature function (the potential) u⁄ = k(T⁄  Ts) where k is the thermal conductivity of the sample material (the dimensional potential and temperature are denoted by asterisk as a superscript). Note, that u 6 0. This function obviously satisfies the planar Laplace equation as well. It is equal to zero everywhere at the sample surface except the section b 6 x 6 b, y⁄ = 0 where it is given as u0 = k(Td  Ts) > 0. The sample domain is assumed to fully occupy the domain y P 0. The solution of the planar Laplace equation for the function u⁄ is given by Poisson’s integral formula for the upper half-plane [32] which reduces to the following expressions for the above-mentioned boundary conditions

u ðx; yÞ ¼ ¼ Fig. 4. The field of the qx component of the heat flux.

the mica blocks and the sample upper surface to measure the surface temperature. To ensure good thermal contact, the end of the thermocouple was coated with silver paste. That ensured that the thermocouples measure the sample surface temperature correctly, not the surrounding air temperature. T1 was connected to the controller, and T2 was connected to a thermometer, which measured the temperature every 1 s. It was observed that when no liquid was on a sample, the values of T1 and T2 were almost identical, however on wetted samples, variation of 5–10 °C in the value of T1 was observed, while the value of T2 was approximately constant. Therefore, only temperature T2 was used for data processing. The controller was monitored by a cascade control so that the surface was set at 120 °C and the maximum allowable heater temperature was set 175 °C. This was done to keep the surface temperature of the sample almost constant and prevent the heater temperature from shooting up too high to protect the heater from burning. All the experiments were recorded using a Phantom V9.1 high speed camera at a frame rate of 1900 fps or 2800 fps. The high speed images allowed measuring the effective wetted area through which heat transfer occurred and the duration of the drop/jet evaporation.

1

Z

p

b

u0 p

u ðX  ; 0Þy

b

Z

2

ðX   x Þ þ y2 b

b

dX

y 

2

ðX  x Þ þ y2



dX



ð1Þ

where X⁄ is the dummy variable. Evaluating the integral in Eq. (1), we obtain

u ðx ; y Þ ¼

 u0 2by arctan 2 p x2 þ y2  b

! ð2Þ

3. Theoretical 3.1. Planar problem Fig. 5. The field of the qy component of the heat flux.

Consider a planar problem on the temperature field in a sample cooled by a drop array impinging onto its surface. For a single droplet impact, it takes about si = 0.07 s to evaporate water on a copper sample surface [8]. If one is interested in the thermal field in a copper layer of thickness h below the surface, the characteristic time of reaching a steady-state thermal field there would be of the order of st = h2/a where a is the thermal conductivity of copper (a = 1.12 cm2/s). Taking for the estimate h = 2 mm, we obtain st = 0.036 s. Since st < si, even for cooling by a single droplet the thermal field in the sample can be assumed being steady. In the case of a multi-droplet cooling, when a liquid puddle at the surface appears, the thermal field in the sample is steady as well. When the temperature field in the sample is steady, it satisfies the planar Laplace equation (a planar two-dimensional case is considered in this subsection). The temperature at the entire surface of the sample is given and equal to Ts everywhere except a section of the surface y⁄ = 0 where the impact takes place, where at b 6 x 6 b the tem-

Fig. 6. Power supplied by the heater. The power supply is on after impact of a new droplet which corresponds to peaks visible in the graph.

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Fig. 7. Drop impact onto copper-plated nanofiber mat. The impact frequencies were: (a) 3.33 Hz, (b) 4 Hz, (c) 5 Hz, (d) 6.67 Hz, and (e) 10 Hz. The droplets at the moment of impact are shown by arrows. In panel (c) it can be seen that sometimes instead of a single droplet, a jet breaking into series of droplets appears (shown by arrows and encircled by the oval line). The wetted spots at later times are traced by dotted lines.

Rendering u⁄ dimensionless with u0, and x⁄ and y⁄ dimensionless with r, we reduce Eq. (2) to the following dimensionless form

uðx; yÞ ¼

1

p

 arctan

2y x2 þ y 2  1

 ð3Þ

where the dimensionless parameters do not have superscripts (asterisk), and, in particular, u ¼ ðT   T s Þ=ðT d  T s Þ P 0. Denote S = x2 + y2  1. It is easy to see that for S < 0, the branches of the arctangent in Eq. (3) should be chosen as follows: for S < 0, p=2 6 arctanðSÞ 6 p, whereas for S > 0, 0 6 arctanðSÞ 6 p=2. The dimensionless heat flux is found from the Fourier law as q = ru (since the minus sign is included in the definition of u). The heat flux is rendered dimensionless by u0/b > 0. Its projections qx and qy found from the differentiation of Eq. (1) read

qx ðx; yÞ ¼ qy ðx; yÞ ¼

2y

Z

p 1

p

1

ðX  xÞ

1

Z

1

1

½ðX  xÞ2 þ y2  1 2

ðX  xÞ þ y2

Evaluating the integrals in these equations, we find

2

dX

dX 

ð4Þ

2y2

p

Z

1

1

1 ½ðX  xÞ2 þ y2 

2

dX

ð5Þ

qx ¼  qy ¼ 

4xy 2

p½ð1  xÞ þ y2 ½ð1 þ xÞ2 þ y2  ð1  xÞ½ð1 þ xÞ2 þ y2  þ ð1 þ xÞ½ð1  xÞ2 þ y2 

p½ð1  xÞ2 þ y2 ½ð1 þ xÞ2 þ y2 

ð6Þ ð7Þ

The dimensionless temperature field u and the fields of the components of the heat flux qx and qy given by Eqs. (3), (6), and (7) are plotted in Figs. 3b–5, respectively. It should be emphasized that at the cooling surface y = 0, a discontinuity of the temperature is imposed at x = ±1. Therefore, in the planar problem the heat flux components have infinite magnitudes at y = 0 and x = ±1, as follows from Eqs. (6) and (7). The values of qx and qy at y = 0 are not included in Figs. 4 and 5. The overall heat removal rate through the surface y = 0 and x = ±1 appears to be infinite in the planar problem, as well. Nevertheless, for the general structure of the fields of interest in the sample domain it is rather immaterial, and Figs. 3– 5 give a clear picture of the sample cooling in the case of interest.

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Fig. 8. Temperature of the mat surface T2 vs. time. Panels (a)–(e) are related to the corresponding panels in Fig. 7.

Table 1 Heat removal rate measured by different methods at different frequencies of water drop/jet impacts. The values, which are not in italic were measured using the smaller reservoir, whereas the values in italic were measured using the larger reservoir. Frequency of water drop/jet impact (Hz)

Mass of water delivered per _ (g/s) unit time-m

Average area of wetted spot, Awet (cm2)

qexperimental (W/cm2)

qccd (W/cm2)

qaxis (W/cm2)

10 6.67 5 4 3.33 2.5 1.667 1.333 1.111 0.833

0.008667 0.004833 0.006 0.005 0.00475 0.0075 0.00696 0.00642 0.00842 0.0075

0.097 0.059 0.035 0.022 0.055 0.089 0.119 0.622 0.244 1.490

403.95 523.1 786.92 907.18 376.07 361.04 279.79 57.93 139.66 40.8

231.2 211.96 443.58 588.09 223.47 218.06 151.34 26.71 89.29 13.02

262.42 286.85 324.31 372.68 223.05 439.31 315.19 86.278 213.37 45.82

3.2. Axisymmetric problem It is of significant interest to consider the axisymmetric thermal problem corresponding to drop cooling. In this case the Laplace equation for the temperature field in the sample reads

  1 @ @T @2T þ 2 ¼0 r r @r @r @z

where r is the radial coordinate, z is the vertical axis, and T is the temperature. It should be emphasized that only the dimensional parameters are used here and hereinafter, and therefore, there is no special notation (superscript asterisk) for them. Here, the origin

Overall heat flux per wet spot Q_ s = qexperimental

_ (J/g)  Awet/m

 Awet (W)

4519.394 6385.87 4590.37 3326.33 4354.49 4284.34 4783.77 5612.52 4047.15 8105.60

39.17 30.86 27.54 16.65 20.69 32.13 33.30 36.03 34.03 60.79

of the coordinate system is fixed at the center of surface of a nanofiber-coated sample, and the positive direction of z is taken into the sample towards the hotplate. The boundary conditions are posed as follows

Tjz¼0 ¼ f ðrÞ ð8Þ

Specific heat flux Q_ s = qexperimental

ð9Þ

Tjr¼0 < 1

ð10Þ

Tj r ! 1 < 1 z!1

ð11Þ

The function f(r) is determined by a given temperature distribution at the sample surface discussed below.

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Using separation of variables, the solution for the temperature field is found as

Tðr; zÞ ¼

Z

1

Z expðczÞJ0 ðcrÞc

0

1

 f ðqÞqJ 0 ðcqÞdq dc

ð12Þ

0

where c represents the continuous spectrum of the present problem, J0 is the Bessel function of the first kind of zero order, and q is a dummy variable. Similarly to the planar problem the temperature distribution at the sample surface is assumed to be discontinuous and taken as

f ðrÞ ¼



T0;

r
T1;

r>a

ð13Þ

where T0 is the temperature of the wetted area, a is the effective radius of the wetted area, and T1 is the effective temperature at the copper-plated sample beyond the effective wetted area. Eqs. (12) and (13) yield the following temperature distribution at the symmetry axis r = 0

  z Tjr¼0 ¼ T 1 þ ðT 0  T 1 Þ 1  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi z2 þ a2

ð14Þ

Using Eq. (14) the heat flux at the sample surface is found as Fig. 9. Drop impact on copper-plated nanofiber-coated surface at the following frequencies: (a) 0.833 Hz, (b) 1.111 Hz, (c) 1.333 Hz, (d) 1.667 Hz, and (e) 2.5 Hz. Here the wetted area is significantly larger than that in Fig. 7. This stems from the fact that in the present frequency range larger drops are formed compared to the range corresponding to that in Fig. 7. The wetted spots are traced by white dashed lines.

   @T  qaxis ¼ k  @z

z¼0

   ¼ k ðT 1  T 0 Þ  a

ð15Þ

where k is the conductivity of the sample [for copper k = 4 W/ (cm K); Ref. [33]].

Fig. 10. Temperature T2 of the sample surface vs. time. Panels (a)–(e) correspond to the panels in Fig. 9. Note that the small central peak in the middle in panel (a) was probably caused by an instantaneous reduction in water supply; it has no special significance.

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Table 2 Heat removal rates measured in the case of two needles. Frequency of water drop/jet impact (Hz)

Mass of water delivered per unit _ (g/s) time-m

Average area of wetted spot, Awet (cm2)

qexperimental (W/cm2)

qccd (W/cm2)

qaxis (W/cm2)

10 1.67 1.33 1.11 0.833

0.00767 0.00583 0.00933 0.00767 0.00767

0.845 0.622 0.103 0.312 0.287

34.77 43.39 268.9 102.14 89.81

23.35 24.14 231.73 63.26 68.59

68.67 111.54 877.81 112.54 281.31

Fig. 11. Drop impact on copper-plated nanofiber-coated surface at the following frequencies: (a) 0.833 Hz, (b) 1.111 Hz, (c) 1.333 Hz, (d) 1.667 Hz, and (e) 10 Hz. The wetted spots are traced by white lines. The arrow in panel (d) points at a satellite droplet, which produced a satellite wetted spot.

_ (J/g)  Awet/m

Overall heat flux per wet spot Q_ s = qexperimental  Awet (W)

3830.59 11900.15 2968.56 4154.85 3360.56

29.38 69.37 27.69 31.87 25.78

Specific heat flux Q_ s = qexperimental

electroplating reaction down the nanofiber mat to the copper substrate. This resulted in a perfect bonding of the electroplated nanofiber mat to the copper substrate. Also, it was found that the choice of the copper substrate was very important to achieve an enhanced bonding. The strongest bonding of the nanofiber mat was achieved on an ultra-conductive copper alloy (received from Mcmaster-Carr under the trade name ‘‘copper alloy 101’’; more details are available at http://www.mcmaster.com/#8964kac/=p4cios) as a substrate, which was roughened using a sand paper. The ultraconductive copper alloy promoted the copper-plating reaction front at the bottom of the overlying nanofiber mat and the substrate surface. Also by roughening the copper substrate the copper-plating reaction was promoted by the electric field strengthening at the roughness crests. As a counter-electrode, the same ultra-conductive copper alloy was used. An additional detrimental process during electroplating was recognized. Namely, at the cathode where the electrons were supplied to cations, not only copper with a positive reduction potential but also hydrogen emerging from the reduction of H+ ion in the plating solution was formed. As a result, during fast plating process the excess by-product hydrogen disjoin nanofiber from the copper substrate. To avoid that, at the initial stage of plating the deposition rate was carefully controlled at a low level until a sufficiently dense coating layer was formed. Then, the current density was increased during the following stage of the plating process to create additional surface features (roughness of the individual nanofibers in the mat) as was shown in Ref. [8]. All the above-mentioned measures helped to optimize the electroplating protocol and achieve samples with the strongest possible mat bonding to the substrate. 4.2. Measurements of the heat flux in experiments with single needle

4. Results and discussion 4.1. Optimization of electroplating procedure In Ref. [8] all drop impact experiments were conducted with a single drop. In the present case multiple drop impacts were studied. It was found that periodic heating/cooling results in significant thermal stresses in the sample. Therefore, in distinction from Ref. [8], these thermal stresses could cause delamination of the nanofiber mat from the substrate, a definitely detrimental effect. To eliminate delamination, special measures described below were taken. In electrospun nanofiber mats fibers are charged and repel each other which results in a certain fluffiness. During sputter coating the sample experiences successive cycles of pressure variation from the atmospheric pressure to vacuum, which enhances fluffiness. As a result, during electroplating the reaction front cannot reach the mat bottom and bond it to the top of the underlying copper substrate. To avoid that, the sputter-coated nanofiber mat was soaked with electroplating solution prior to electroplating. This was beneficial because (i) upon drying the fluffiness of the nanofiber mat diminished, and (ii) nanofibers throughout the entire depth along with the copper substrate were coated with the electroplating solution. This led to an easier access of the front of the

Standard practice of measuring heat flux employs two thermocouples embedded in the sample in the direction normal to its surface. They measure the temperature difference DT at a known distance Dx normal to the surface, and the magnitude of the heat flux is found as kDT/Dx, where k is the thermal conductivity of the sample. However, in the present study the copper substrate used was very thin (with the thickness of 0.65 mm). This precludes using the standard procedure of measurement of the heat flux, since the sample cannot accommodate two thermocouples to be embedded in its depth. It is tempting to attach the sample to a bigger copper block, to connect the latter to a heater, and then follow the standard routine of measuring the heat flux by two thermocouples. However, the expected depth of the wetted spot is about 100 lm and the diameter 2a is about 3–4 mm. As illustrated in Figs. 3–5, the temperature distribution in the copper block will be strongly nonlinear (cf. Eqs. (3) and (14)) and the temperature gradients will not be accurately measurable at depths of the order of a. Given the nonlinear character of the temperature distribution and a relatively small domain in which the temperature drop is felt, the standard method of two embedded thermocouples will not be suitable for the present experiment. Therefore, to measure heat flux the following technique was used. T1 was set at 120 °C.

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Then, drops were delivered onto the surface, and the controller tried to keep the temperature T1 constant, whereas the power delivered by the heater (Wheater) was measured by the measurement system. An example of the power supply by the controller is shown in Fig. 6 where each peak signifies arrival of a new droplet. The power removed by the surrounding air (Wair) is also measured. This was achieved by keeping the system at room temperature with no liquid supply. The measured power supply was then equal to heat removed by natural convection in the surrounding air. It was subtracted from the power supplied by the heater, and the difference of Wheater–Wair was associated with heating up and evaporation of a droplet. It should be emphasized that the controller follows the analogy of a cascade control [34], so that the heater temperature does not increase dramatically high, which may burn the heater up. So, the heater always delivers heat in a conservative (follow-up) manner rather than in an aggressive one. In addition, the controller measures the surface temperature every 100 ms. According to [8], the characteristic time of evaporation is about 50 ms. This shows that the actual heat removal can be even higher than the one measured here. Therefore, the results on the heat flux below underestimate the real heat removal rate, and the exact value could be only measured with a still faster controller, capable of control of such high-heat-flux heater (unavailable at present). The images acquired by the CCD camera allowed measurement of the wetted spot area (Awet). Then, the heat removal rate was calculated as qexperiment = (Wheater–Wair)/Awet. It should be emphasized

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that the frequencies of the drop impacts were chosen that way that liquid has fully evaporated between two successive impacts. The area of the wetted spot was also changing during evaporation. Therefore, the wetted spot area used to calculate the heat flux P was calculated as Awet ¼ Ni¼1 Ai Dt i =t total , where Ai is the area of the wetted spot over the time interval Dt i and ttotal is the time interval between two successive drop impacts. In addition, the heat removal rate was also measured using the optical observations as follows. The mass of coolant droplets delivered by the system per second (M) was measured. As the frequencies were chosen to work in the regime with no sample flooding, the heat flux can be estimated as qccd = M(L + CpDT)/Awet where L is the latent heat of evaporation (L = 2260 kJ/kg for water, 102 kJ/ kg for FC-7300), Cp is the specific heat capacity [Cp = 4.2 kJ/(kg °K) for water and 1.14 kJ/(kg K) for FC-7300] and DT is the temperature difference over which the temperature of the puddle increases from room to the boiling temperature (DT = 78 K for water and 76 K for FC-7300), with the room temperature being 22 °C. When liquid impacts the surface, a puddle is formed. Following Ref. [35], the thickness of the thermal boundary layer in the puddle d is of the order of 0.1 mm for water. It can be seen below that in all our experiments the water puddle thickness dwater  Vdel/Awet  0.1 mm, with Vdel being the volume delivered per pulse and Awet the wetted area. The thermal diffusivity of water awater  103 cm2/s. Then, water puddles reaches the boiling point of 100 °C in 2 about dwater =awater ¼ 100 ms time interval. In the experiments it was found that water puddles evaporate approximately in the

Fig. 12. Temperature T2 of the sample surface vs. time. Panels (a)–(e) correspond to the panels in Fig. 11.

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Ref. [8]. As the time interval between two successive droplet impacts increases, the duration of the existence of the wetted spot decreases, and thus the effective wetted area Awet decreases. The differences between the corresponding values of qaxis, qexperimental and qccd can be explained as follows. The basic assumption involved in the evaluation of qccd was that a fixed constant water flux was delivered throughout the entire heat transfer experiment, which is only an approximation. The evaluation of of qaxis depends on the temperature difference (T1  T0), where T1 is measured as T2. According to the estimate discussed above, in the experiments with water T2 can be taken as the water boiling temperature of 100 °C. Since water droplets arrive at the room temperature of 22 °C and not immediately heat up to the boiling temperature, the effective value of T0 is somewhat lower than 100 °C. Therefore, the values of qccd and qaxis should be considered as the order of magnitude estimates only, and the most reliable is the experimental value qexperimental. Note also that Table 1 shows that the frequency of 4 Hz is the optimal frequency at which water supply is exactly equal to the evaporation rate, with no flooding or dry spots on the surface. Thus, all three methods of the heat flux measurement used show the heat removal maximum at this frequency (Table 1). Aside from the maxima, the inaccuracies characteristic of any of the three methods could result in some localized trend fluctuations when the frequency varies, but the overall trend is the same in all the three sets of data. 4.4. Variation of heat removal rate with drop size

Fig. 13. Drop impact of FC-7300 onto copper-plated nanofiber-coated surface at different flow rates: (a) 10 ml/h, (b) 20 ml/h, (c) 30 ml/h, (d) 40 ml/h, (e) 50 ml/h, (f) 60 ml/h, (g) 70 ml/h, and (h) 80 ml/h. The wetted spots are traced by white lines.

same time range, in 30–60 ms, similar to Ref. [8]. Therefore, the temperature of the puddle in the case of water impact can be taken as the boiling temperature, i.e. as 100 °C. Therefore, to measure the heat flux qaxis using Eq. (15), the value of T1 can be taken as 100 °C. 4.3. Dependence of heat flux on drop impact frequency To study the effect of drop impact frequency of the heat removal rate, experiments with water drop/jet impacts at frequencies of 3.33, 4, 5, 6.67 and 10 Hz were conducted. It can be seen from the images in Fig. 7 that the water droplet did not bounce from the mat surface and the Leidenfrost effect was completely eliminated similarly to our previous works [6–10]. It was also found that the water drops evaporated during about 30–60 ms after the impact. The surface temperature plot (Fig. 8) shows that during the entire process the surface temperature was practically constant, which allows one to use Eq. (15) to calculate the heat flux qaxi. On the other hand, qexperiment was measured as described in the previous subsection. In addition, the heat flux qccd was also evaluated. The results are combined in Table 1. It can be seen that qaxi, qexperiment, and qccd are of the same order for the entire frequency range. The experimental results show that it was possible to remove heat at the rate of 0.4–0.9 kW/cm2 in continuous operation of the present setup when using copper-plated nanofiber mats bonded on the heater surface. It should be emphasized that these values are underestimated, as discussed in the previous subsection. Note, that heat removal rate of about 0.4 kW/cm2 was reported for single drop impact onto copper-plated nanofiber mats in

Drop size was controlled by changing the reservoir size at lower frequency as it was explained in the experimental section. Five different frequencies were chosen in this study 0.833, 1.111, 1.333, 1.667 and 2.5 Hz (cf. Fig. 9). In this frequency range larger drops were produced than in the previously studied range of 3.33– 10 Hz. The evolution of the temperature T2 in time is illustrated in Fig. 10, which shows that T2 is almost constant during the entire experiment. The corresponding measured and evaluated values of the heat flux are presented in Table 1 in italic. Table 1 shows that as the wetted spot area (the effective radius of the wetted spot) increased, the heat flux decreased. This trend is visible in all the different heat flux approximations qaxis, qccd and qexperimental. Eq. (15) shows that for a fixed value of (T1  T0), the heat flux is inversely proportional to the radius of the wetted spot a, as discussed above. Table 1 shows that both qaxis and qexperimental are of the same order. 4.5. Measurement of heat flux in experiments with two needles When two needles are used, flooding at certain frequencies happens due to multiple satellite droplets in distinction from the experiments with a single needle described in the previous section. Only the results of the experiments with two needles where no flooding occurred are listed in Table 2 which contains the values of the heat removal rate. The corresponding images of the wetted spots are shown in Fig. 11 and the nanofiber surface temperature plots are shown in Fig. 12. Table 2 shows that in most of the cases the values of qaxis are overestimating the values of the experimental heat removal rates, either qexperimental or qccd, in distinction from Table 1 for a single needle. This can be attributed to the fact that in the experiments with two needles, as Awet increased in comparison to those corresponding to Table 1, the assumption of an infinite target embedded in Eq. (15) is invalidated and the values of qaxis become inaccurate. The comparison of Tables 1 and 2 shows that the heat removal rate is much higher when water is delivered through a single needle than through the two needles. This is associated with the fact that the puddle thickness is significantly larger in the case of water delivery through two needles as compared

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Fig. 14. Temperature of the mat surface T2 vs. time. Panels (a)–(h) are related to the corresponding panels in Fig. 13.

with a single needle (d = 0.3–0.9 mm vs. d = 0.1 mm, respectively). As a result, the thermal resistance of the water puddle in the case of two needles is higher than in the case of a single needle, and thus the heat flux lower. On the other hand, the wetted area dramatically increases in the case of two needles compared to the case of a single needle, which tends to increase the overall heat flux. Therefore, it is of interest to introduce the specific and overall heat _ and Q_ ¼ qexperimental Awet , respectively. fluxes Q_ s ¼ qexperimental Awet =m Tables 1 and 2 show that in both cases the values of Q_ s and Q_ are of the same order. Therefore, in the case of cooling hot spots, water delivery through a single needle is preferable, while in the case of cooling large areas, multi-needle systems have an obvious benefit. 4.6. Measurement of heat removal rate corresponding to FC-7300 In this case the experiments were done using delivery through a single needle. In the previous sections it was shown that

qexperimental reveals the most accurate evaluation of the removed heat flux. Therefore, in the experiments with FC-7300 only qexperimental was measured. The results are listed in Table 2 for different flow rates. One snapshot for each flow rate is depicted in Fig. 13 and the corresponding surface temperature profile is shown in Fig. 14. In comparison with Figs. 8 and 10 for water, Fig. 14 shows that FC-7300 is incapable of cooling the hot surface as effectively as water because of its low latent heat of evaporation and specific heat. Indeed, the surface temperature variation in the case of FC7300 is not as large as that for water. The low latent heat of FC7300 also transcribes itself in relatively low values of the heat removal rate listed in Table 3, which are in the range 33.92–71.41 W/ cm2. These values are an order of magnitude lower than those of water. It should be emphasized that the thermal diffusivity of FC-7300 is about 104 cm2/s, which is one order of magnitude lower than that of water. Therefore, for the same puddle thickness as for water (0.1 mm), the time required for FC-7300 to reach its boiling point of 98 °C is of the order of 1 s. This is also detrimental for

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Table 3 Heat removal rate for FC-7300. Flow rate of FC-7300 (ml/h)

Average area of wetted spot (Awet) (cm2)

qexperimental (W/cm2)

10 20 30 40 50 60 70 80

0.0408 0.0584 0.1071 0.0774 0.1425 0.2007 0.2052 0.2172

33.92 46.94 36.06 71.41 46.10 38.96 44.23 46.34

reaching higher heat removal rate from the surface. Table 3 shows that there is an optimal flow rate of 40 ml/h, at which the heat removal rate with FC-7300 reaches the maximum. 5. Conclusions A pneumatic drop generator was developed in this work to supply water either as single drops or jets using single or two nozzles. The drop or jet volume was controlled by the actuation frequency or reservoir size. Three different methods of heat flux measurement (one direct and two indirect) were employed in this work, with one of them being based on the one-dimensional heat flux model, the second one- on the two-dimensional (axisymmetric) heat flux model, and the third one- on the three-dimensional heat flux nature. It was found that results obtained by these three different methods were in good agreement with each other. The heat transfer surfaces were covered by metal-plated electrospun nanofiber mats. In the ground experiments it was found that at such surfaces heat removal rate up to 0.9 kW/cm2 could be reached. It was also found that there is an optimal frequency of about 4 Hz at which the heat removal rate is the highest for the present system, since the coolant supply is equal to that of the evaporation rate and no flooding or dry spots appear. Another coolant, Fluorinert FC-7300 was delivered using a syringe pump at a different supply rate. For FC-7300 drops the heat removal rate was 71 W/cm2. It should be emphasized that even though sample flooding was observed at some frequencies of drop supply in the present work, the cooling regimes never resembled those of pool boiling. Therefore, the heat removal rates in our case were significantly higher than those characteristic of pool boiling. Acknowledgments The authors are grateful to NASA for the support of this work through the Grant No. NNX10AR99G. References [1] A.M. Briones, J.S. Ervin, S.A. Putnam, L.W. Byrd, L. Gschwender, Micrometersized water droplet impingement dynamics and evaporation on a flat dry surface, Langmuir 26 (2010) 13272–13286. [2] I. Mudawar, Assessment of high-heat-flux thermal management schemes, IEEE Trans. Compon. Packag. Technol. 24 (2001) 122–141. [3] L.P. Yarin, A. Mosyak, G. Hetsroni, Fluid Flow, Heat Transfer and Boiling in Micro-Channels, Springer, Berlin, 2009. [4] J. Child, FPGA boards and systems boost UAV payload compute density, COTS J. (J. Military Electron. Comput.) 2 (2009) 1–2.

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