Supplementary materials
Can Multiple Flow Boiling Regimes Be Reduced into a Single One in
Microchannels?
Fanghao Yang1, Xianming Dai1, Yoav Peles2, Ping Cheng3 and Chen Li1,*
1
Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208 USA
2
Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, 110
8th St, Troy, NY 12180, USA
3
School of Mechanical and Power Engineering, Shanghai Jiaotong University, 800 Dong Chuan Rd,
Shanghai, 200240, China
Design of boiling surfaces
Cavity Diameter (μm)
10
Optimized
Nucleation
1
q = 1°
0.1
0.01
q = 0.1°
1
2
3
Super Heat ΔT (K)
4
5
Figure S1. The sizes of optimal nucleation cavity on superheated surface.
The classical theory may not accurately predict the optimal cavity size on nano-engineered surfaces
but, it can still provide a good guidance to determine the optimal range. As shown in Fig. S1, the
optimal size of nucleation cavity on superhydrophilic surface (i.e. contact angles assumed between
0.1˚ and 1˚) range from approximately 100 to 2000 nm as functions of the superheat, ΔT. ΔT is
defined by the temperature difference between wall and saturation temperature, Twall – Tsat, where,
1
Twall is wall temperature and Tsat is saturated temperature. The range of active cavity opening
diameter, Dc, was estimated from Eq. 1.1
Dc max,min 
8 f (T  Tsub )Tsat (1  cos q ) 
 
 t sin q 
T

 (1)
  1  1 
2(1  cos q )  T  Tsub  
v h fg t T 2

, where hfg, ΔTsub, θ, f, v and  denote latent heat, subcooling degree, contact angle, surface
tension, vapor density, and boundary layer thickness, respectively. The surface tension at 100 °C is
58.85 mN/m. The vapor density is 0.598 kg/m2. The boundary layer thickness in microchannel is
equals to the half width of the microchannel, which is 100 μm.
In this study, the measured wall superheat is between 0 – 5 K when nucleation boiling dominate the
heat transfer at the early stage of flow boiling. Later, the evaporation heat transfer involves the whole
flow boiling process with increasing heat fluxes and superheats so that current model may not apply
for this situation.
Micro/Nanofabrication processes
The two-phase microfluidic devices were integrated with thin-film heaters on the backside. The
fabrication of microfluidic chips started with 100-mm-diameter <100> heavily doped P-type silicon
wafers. The thickness of wafer is ~500 m (Figure S2a). Thermal oxidation induced 500 nm dense
oxide layers onto both sides of silicon wafer as an isolation layer (Figure S2b). DC sputtering tool
deposited 10-nm-thickness titanium and 200-nm-thickness aluminum as metal connection pads. Then
thin-film
heaters
were
fabricated
by
photolithography
and
wet-etching.
Consequently,
photolithography and aluminum wet-etching processes created aluminum metal connections for
electrical power as shown in Figure S2c. After that, 500 nm silicon oxide layers and thick photoresist
(SPR 220-7.0) was deposited and spin-coated to protect backside layer device (Figure S2d). At front
2
side, high aspect-ratio microchannels (10 mm L x 200 m W x 250 m D) arrays on the front side of
wafer (Figure S2e) were etched by Deep Reactive Ion Etching (DRIE) on the silicon substrate.
Nanowires were directly etched on inner surfaces of the microchannels using the improved
techniques developed by Zhang et al2. 4.5 M hydrofluoric acid and 0.005M silver nitrite solution
were prepared for deposition of catalyst. The wafer was then carefully placed into this solution to
coat a thin film of AgNPs layer by slowly stirring in the solution (Figure S2f). These AgNPs attached
onto smooth silicon surface as etching catalysts inside microchannels with the rest area coated with
oxide or nitride to prevent bonding during catalyst coating process. The finished wafer was washed
in DI wafer to remove the residual Ag+ and was etched in 4.8 M hydrofluoric acid and 0.15 M
hydrogen peroxide solution. The etching time was about 15 min to achieve 5 micron length of silicon
nanostructures as shown in Figure S2g. through holes will be created by DRIE for pressure
measuring and liquid inlet/outlet as shown in Figure S2h. A Pyrex glass wafer was anodically bonded
on the silicon substrate as windows of optical visualizations as shown in Figure S2i.
(a)
(b)
Oxide
Silicon Wafer
(f)
(c)
Heater
(e)
Ag. NPs
(g)
(d)
Thick P.R.
Microchannels By DRIE
(i)
(h)
Si NWs
Vias
Glass Cover
Figure S2. A flow chart of microfabrication processes.
The top views of the MEMS testing chip are shown in Figure S3. As shown in Figure S3a, There are
3
two pressure measuring ports to facilitate pressure measurement in the inlet and outlet. A flow
stabilizer is used to stabilize inlet flow. There are two thermal isolation gaps by the two sides of
microchannel arrays to minimize the heat loss. The thin-film heater is located on the backside of
heating area in this two-phase microfluidic system. Working fluid is heated in microchannel arrays.
In this study, nanobubbles are generated on nanoengineered surfaces during flow boiling.
Figure S3. Detailed structure and features on a testing chip. (a) and (b) are drawings of the front side
and back side of a test chip, respectively. The light blue bars in (a) denote the bonding interface
between a silicon wafer and a Pyrex glass wafer. The green area in (b) illustrates an aluminum
thin-film heater.
Test Platform
4
Figure S4. The two-phase microfluidic testing platform. (a) The picture of overall testing platform.
(b) An exploded 3D CAD model of package module. (c) A real image of the package module.
Two-phase transport in microchannels with nano-engineered coatings has been experimentally
investigated in a two-phase testing platform as shown in Fig. S4a. As shown in Fig. S4b and S4c, a
customized package was designed and fabricated to house testing chip, to supply power, and to
connect to a data acquisition system. Spring-loaded Pogo pins were used to achieve great electric
contacts. Degassed DI water was stored in a water reservoir and pumped through the microchanenls
by pressurized nitrogen gas. The fluid mass flow rate was controlled by a needle valve and measured
by an Omega digital flowmeter. All testing data, including readings of two pressure transducers, one
flowmeter and voltage/current of a thin film heater, were collected through a multi-channel data
acquisition system. A customized NI LabView program was developed to realize automatic data
acquisition. Fast two-phase flow transport phenomena were visualized by a customized visualization
system comprised of an Olympus microscope (BX-51) with 400 X amplifications and a Vision
Research high speed camera (Phantom V 7.3) with 256 x 256 pixels at approximate 40,000 fps
(frames per second).
5
Data Reduction
Experiments were performed in the two-phase microfluidics chip by applying electrical heating on
the backside of microchannels. When flow boiling occurs inside microchannel, two pressure
transducers measure the transient inlet and outlet pressures. The flow rate is measured by a digital
flowmeter. The average temperatures of heater could be calculated after measuring resistance of
aluminum heater. All measurements are carried out after calibrations under 1 atm and room
temperatures (~22℃).
Once the temperature of the microsystem became steady, the temperatures between the chip and
ambient were collected under corresponding power by an Agilent data acquisition system. The
temperature of the heater, Theater , could be calculated as a linear function (correlation coefficient >
0.9999) of its resistance Rheater ,
Theater  k ( Rheater  Rambient )  Tambient
(S2)
where slope k, Tambient and Rambient in ambient environment has been pre-calibrated. Then average
wall temperature could be calculated as,


T  Theater  P  Qloss t w / k s Ae
(S3)
where t w is the thickness of wall, ks is the thermal conductivity of silicon and the effective
heating area Ae is equals to 20 mm2. The heat loss Qloss is the natural convection heat transfer
between testing system and the ambient environment. The heat loss is a function of Theater as shown
in Figure S5.
6
5.5
4.5
Heat loss (W)
Qloss = 0.0411Theater - 0.7752
3.5
2.5
1.5
0.5
-0.5
10
35
60
85
Temperature (℃)
110
135
Figure S5. Heat loss is a linear function of the temperature of the heater. Correlation coefficient is
larger than 0.99.
 , is
The electrical power, P, is the voltage current product, P  V  I . The effective heat flux, qeff
   P  Qloss  / Ae . The dimensions of microchannel unit are labeled in
defined in our study as qeff
Figure S5.
Wunit
Wwall/2
W
Wwall/2
H
t
q”eff
tw
Figure S6. A cross-section map of a microchannel unit. Wwall is the width of wall between each
channel and t is the thickness of the silicon wafer.
7
Table S1 tells dimensions in Figure S5.
Wwall (μm)
200
W (μm)
200
H (μm)
250
tw (μm)
250
t (μm)
500
Iteration algorithm gives the converged heat transfer coefficients.
Averaged vapor quality of two-phase flow was estimated from   P / (h fg mAc ) , where h fg , m ,
and Ac denote the latent heat of fluid, the mass flux and the cross-section area of a microchannel,
respectively.
Statistical methods were employed to analyze two-phase flow instabilities. When the system reached
steady state at a given mass and heat flux, the data acquisition system would automatically record a
set of data every 2 seconds for 120 sets of data. Pressure drop,  p , was estimated from the absolute
pressure readings from inlet and outlet. Standard deviations (SD) of pressure drop data for a given
mass flow rate and heat flux was employed to evaluate the two-phase flow instabilities in terms of
pressure drop of the overall microchannel system. A smaller SD in the pressure drop implies less
instabilities of mass transfer for a given constant pump power and mass flow rate,
Sp 
1 N
(pi  p)2
i
N 1
(4)
,where, p is the mean value of all pressure drop data. The magnitudes of flow oscillation in Δp-G
figure of smooth microchannels3 are compared in Figure 4 in this article. Generally, the SD of
pressure drop for each measurement was significantly reduced.
The Weber number of vapor flow is calculated as,
We 
vuv 2 Dh

(5)
And the Weber number of liquid flow is calculated as,
l ul 2 Dc
We 

(6)
8
The Reynolds number of vapor flow is calculated as,
Rev 
v uv Dh
v
(7)
The Reynolds number of liquid flow is calculated as,
Rel 
l ul Dh
l
(8)
where  v and  l are the density of vapor and liquid. v and  l
are viscosity of vapor and
liquid. And uv and ul are average flow velocity of vapor and liquid, where uv 
P
h fg v Ac
and ul
is measured by optical microscope. Dh and Dc are hydraulic diameter of microchannel and
cavities. σ is the surface tension of water.
Uncertainty analysis
Two pressure transducers measured the inlet and outlet pressures, respectively. Pressure drop data
was collected by Omega PX01-C1 pressure transducers with ± 0.05% linearity and repeatability. All
zero points of transducer output were calibrated under 1 atmosphere before measurements. Mass
fluxes were measured by a Sensiron ASL1600 flowmeter with 0.03 kg/cm²·s resolution. Bubble sizes
were measured by digital images. Since eaach pixel in digital image was 250 nm, the bubble size
error was ± 125 nm. The local flow velocities and rewetting frequencies were measured by high
speed video (3000 frames/second), so the uncertainty of time is equal to or less than 1/3000 second.
The uncertainties of measured values could be derived by uncertainty theory. According to the
datasheet of measuring and control equipments in our testing system, measurement uncertainties are
listed in Table S2. The uncertainty of other parameters could be calculated by applying the method in
Kline and McClintock’s article4.
9
Table S2: Uncertainties of major parameters (estimated at 389 kg/m2·s and 400 W/cm2).
Name of Variables
Flow rate, Q
Voltage on the heater, V
Current on the heater, I
Ambient Temperature, Tambient
Electrical power on the heater, P
Electrical resistance, R
Average temperature, T
Errors
0.05%
0.10%
0.10%
0.5 ˚C
0.20%
0.20%
0.8 ˚C
Single periodic annular flow under Various Conditions
To further examine the two-phase flow pattern in the nano-engineered microchannels without
convective boiling, bubbles were generated at the inlet manifold of the microchannel array.
Figure S7. (a) to (f) Visualization study of the continously tranportion of periodic annular flow
within saturated water through a nano-engineered microchannel array. The inlet NB flow is
magnified. Velocity profiles of vapor NB flow are sketched by arrows. The interface between NB
flow and the liquid layer are highlighted by white curves. The average mass flux of this observation
is 449 kg/m2·s. The average inlet velocity of NB flow is 0.445 m/s.
Figure S7 indicates there is no bubble slugs formed in microchanel arrays because the bubble
dynamic of single periodic annular flow is totally different from single bubble slugs even it is
10
difficult to identify single NB under current microscopy system limited by the resolution of optical
microscope. The NB flow would be divided into several branch flows thru microchannel arrays other
than large bubble slugs. The absence of NB coalescence also indicated great sustainability during the
transferring process of NB flow. The major difference in the two-phase flow pattern observed in the
nano-engineered microchannels with and without convective boiling was the thickness of the liquid
lubrication layer. It was observed the liquid lubrication layer without convective boiling is
approximately 70 μm thick, much thicker than the approximately 10 μm thick layers, which is
periodically rebuilted with convective boiling.
Moreover, the bubble size under different conditions is investigated in this study as a part of
supplementary materials. The bubble size would decrease with increasing input heat flux and mass
flux (Fig. S8). We suppose the higher mass flux may induce larger drag force and higher heat flux
may lead to faster growth rate of bubble and higher vapor mass acceleration. Combining these
factors, the bubble shall be released at smaller diameters. However, as we stated in the article,
evaporation dominated the phase-change with the heat flux exceeding 225 W/cm². Therefore, the
vapor flow looked misty.
Figure S8. (a), (c), and (e) are images of vapor bubble size and density in nano-engineered
11
microchannels at heat fluxes of 25, 100, 225 W/cm2, with corresponding mass fluxes of 50, 248 and
404 kg/m2·s, respectively. (b), (d), and (f) are magnified images of (a), (c) and (e) to estimate vapor
bubble size and density. Arrows indicate flow directions.
We also studied flow patterns under different exit vapor qualities (0.1 – 0.4) and characterized the
flow pattern. As shown in Fig. S9, the single periodic annular flow pattern has been well observed to
be unified under various working conditions. This unified flow pattern was described in at inlet,
middle and outlet of a 10-mm-long microchannel with different rewetting frequencies. Compared to
Figure 3, all characters of this flow pattern are shown to be identical.
Figure S9. Unified single periodic annular flow pattern in inlet (Window A, a1 - a6), middle
(Window B, b1 - b7) and outlet (Window C, c1-c6) in a microchannel under various working
conditions. The white/gray areas are NB foam flow and the black/dark areas are liquid. The working
conditions are: Q = 193 kg/m2 s,  = 0.1 for (a1 - a6), Q = 193 kg/m2 s,  = 0.266 for (b1 - b7) and
Q = 193 kg/m2 s,  = 0.328 for (c1-c6).
In summary, the supplementary materials in the section provide more evidences to support the
conclusion in our article. The diversified flow patterns in classical microchannels are unified into
12
single periodic annular flow. This flow pattern exists at various conditions with different mass fluxes,
heat fluxes and vapor qualities. Without flow boiling occurs, the single periodic annular flow remains
the same without periodic rewetting process.
Movie Legends
Movie S1: Single periodic annular flow near inlet. Video was captured at 3000 FPS (Frame per
second) and replayed at 5 FPS.
Movie S2: Single periodic annular flow during flushed out. Video was taken at 30000 FPS and
replayed at 15 FPS.
Reference:
1
Y.Y. Hsu,
Journal Name: Journal of Heat Transfer (U.S.); Journal Volume: Vol: 84; Other Information: Orig.
Receipt Date: 31-DEC-62, Medium: X; Size: Pages: 207 (1962).
2
M. L. Zhang, K. Q. Peng, X. Fan, J. S. Jie, R. Q. Zhang, S. T. Lee, and N. B. Wong,
Journal of Physical
Chemistry C 112 (12), 4444 (2008).
3
Tiejun Zhang, Tao Tong, Je-Young Chang, Yoav Peles, Ravi Prasher, Michael K. Jensen, John T. Wen, and
Patrick Phelan,
4
International Journal of Heat and Mass Transfer 52 (25-26), 5661 (2009).
S. J. Kline and F. A. McClintock,
Mechanical Engineering 75 (1), 3 (1953).
13