Microfluid Nanofluid (2005) 1: 137–145
DOI 10.1007/s10404-004-0021-8
R ES E AR C H P A PE R
Abhijit Mukherjee Æ Satish G. Kandlikar
Numerical simulation of growth of a vapor bubble during
flow boiling of water in a microchannel
Received: 20 July 2004 / Accepted: 5 October 2004 / Published online: 31 March 2005
Springer-Verlag 2005
Abstract The present study is performed to numerically
analyze the growth of a vapor bubble during flow of
water through a microchannel. The complete Navier–
Stokes equations, along with continuity and energy
equations, are solved using the SIMPLER (semi-implicit
method for pressure-linked equations revised) method.
The liquid–vapor interface is captured using the level set
technique. The microchannel is 200-lm square in crosssection and the bubble is placed at the center of the
channel with superheated liquid around it. The results
show steady initial bubble growth followed by a rapid
axial expansion after the bubble fills the channel crosssection. A trapped liquid layer is observed between the
bubble and the channel as it elongates. The bubble
growth rate increased with the incoming liquid superheat,
but decreased with Reynolds number. The formation of a
vapor patch at the walls is found to be dependent on the
time the bubble takes to fill up the channel. The upstream
interface of the bubble is found to exhibit both forward
and reverse movement during bubble growth. The results
show little effect of gravity on the bubble growth rate
under the specified conditions. The bubble growth features obtained from the numerical results are found to be
qualitatively similar to experimental observations.
l0
m
p
Re
r
T
DT
t
t0
u
u0
v
w
x
y
z
bT
j
l
m
q
r
s
/
u
Length scale
Mass transfer rate at interface
Pressure
Reynolds number
Radius
Temperature
Temperature difference, TwTsat
Time
Characteristic time
x direction velocity
Characteristic velocity
y direction velocity
z direction velocity
Distance in x direction
Distance in y direction
Distance in z direction
Coefficient of thermal expansion
Interfacial curvature
Dynamic viscosity
Kinematic viscosity
Density
Surface tension
Time period
Level set function
Contact angle
Keywords Bubble Æ Microchannel Æ Flow boiling
List
Cp
d
g
H
hfg
k
of symbols
Specific heat at constant pressure
Grid spacing
Gravity vector
Heaviside function
Latent heat of evaporation
Thermal conductivity
A. Mukherjee (&) Æ S. G. Kandlikar
Department of Mechanical Engineering,
Rochester Institute of Technology (RIT),
Rochester, NY, USA
E-mail: [email protected]
Tel.: +1-585-4755839
Fax: +1-585-4757710
Subscripts
evp
Evaporation
in
Inlet
l
Liquid
sat
Saturation
v
Vapor
w
Wall
x
¶/¶x
y
¶/¶y
z
¶/¶z
Superscripts
*
Non-dimensional quantity
fi
Vector quantity
138
1 Introduction
Two-phase flow through microchannels has been studied
extensively in the last decade, since it has the potential of
providing very high heat transfer rates in miniature heat
exchangers. The studies, however, were primarily confined to experiments. But, experiments at the microscale
have their own limitations, and a small inaccuracy in a
measurement can lead to a large error. Hence, there is a
need to numerically model two-phase flow through
microchannels, which would help us better interpret
the available experimental data and also explain the
underlying physics. When boiling takes place in a
microchannel, bubbles nucleate at the wall, but soon
grow large enough to fill the entire channel. Thus, the
behavior of individual bubbles determines the flow field
in the microchannel. The present work is undertaken to
numerically simulate the growth of a vapor bubble in a
microchannel and analyze its different characteristics.
2 Literature review
Jacobi and Thome (2002) developed a heat transfer
model for elongated bubbles in a microchannel. They
assumed that thin-film evaporation into elongated bubbles is the dominant heat transfer mechanism in microchannel flows. The model required the knowledge of two
parameters; the effective nucleation superheat and the
initial film thickness. The dependence of heat transfer
coefficient on heat flux was found to be low at small
heat fluxes, but high at large heat fluxes. The model
predicted the heat transfer coefficient to be insensitive to
mass flux.
Steinke and Kandlikar (2003) experimentally studied
flow boiling and pressure drop characteristics in parallel
microchannels. They used six parallel microchannels of
207-lm hydraulic diameter and observed conventional
flow boiling patterns. The flow patterns observed were
bubbly flow, slug flow, and annular flow, similar to
conventional flow boiling. They could maintain heat flux
up to 930 kW/m2 in the microchannel. One of the major
differences noted by them was the reversed flow during
rapid growth of a bubble.
Hetsroni et al. (2003) studied convective boiling in
parallel microchannels using pure water and surfactants.
They observed two flow regimes in steam–water flow.
The low heat flux regime was characterized by the
presence of a liquid phase in part of the parallel microchannels. The high heat flux regime was characterized by
convective boiling, accompanied by quasi-periodical
rewetting and refilling of the microchannels. They recommended that the boiling of surfactant solutions in
microchannels may be used to provide a nearly isothermal heat sink.
Peles (2003) studied two-phase boiling in microchannels and obtained flow regime maps. He used 16mm long parallel triangular microchannels with
hydraulic diameters ranging from 50 lm to 200 lm. He
also observed rapid bubble growth around a nucleating
bubble. He concluded that two-phase flow instabilities
were of primary importance at the microscale and
should be comprehensively addressed.
Fogg et al. (2003) numerically studied transient
boiling in microchannels. They used a homogeneous
model using mass-weighted averages of the local properties of the liquid and the vapor. The two phases were
considered to be uniformly distributed within each grid
element, precluding any models formulated for the
bubble or slug structures. In conjunction, they also
solved the one-dimensional transient heat conduction
equation at the wall. They concluded that future work
needs to model bubbles growing into slugs and annular
flow.
Ajaev and Homsy (2003) developed a mathematical
model of constrained vapor bubbles. They assumed that
the shape of the bubble is dominated by capillary forces
away from the wall. A lubrication-type analysis was
used to find the local vapor–liquid interface shapes and
mass fluxes near the wall. The microscopic adsorbed film
on the constraining walls was assumed to be in thermodynamic equilibrium with the vapor phase, due to the
action of London–van-der-Waals forces. Their solutions
indicate large values of mass flux near the contact line.
Longer bubbles were obtained for higher heater temperatures.
Son et al. (1999) developed a two-dimensional
numerical model of growth and departure of single vapor bubbles during nucleate pool boiling. They used the
level set technique to implicitly capture the liquid–vapor
interface. Mukherjee and Dhir (2003) extended the
model to three-dimensional cases and studied the merger
and departure of multiple bubbles during nucleate pool
boiling. The present analysis is done using a similar
model to study the growth of a vapor bubble inside a
microchannel.
3 Objectives
The objectives of the present work are as follows:
– Obtain the flow and thermal fields around a growing
vapor bubble inside a microchannel through numerical simulation
– Study the behavior of the liquid–vapor interface and
its interaction with the constraining walls
– Determine the effect of inlet liquid superheat, Reynolds number, and gravity on the bubble growth rate
4 Numerical model
4.1 Method
The complete incompressible Navier–Stokes equations
are solved using the SIMPLER method (Patankar 1980),
139
which stands for semi-implicit method for pressurelinked equations revised. The continuity equation is
turned into an equation for the pressure correction. A
pressure field is extracted from the given velocity field.
At each iteration, the velocities are corrected using
velocity-correction formulas. The computations proceed
to convergence via a series of continuity-satisfying
velocity fields. The algebraic equations are solved using
the line-by-line technique, which uses the tri-diagonal
matrix algorithm (TDMA) as the basic unit. The speed
of convergence of the line-by-line technique is further
increased by supplementing it with the block-correction
procedure (Patankar 1981). The multi-grid technique is
employed to solve the pressure equations.
Sussman et al. (1994) developed a level set approach
where the interface was captured implicitly as the zero
level set of a smooth function. The level set function was
typically a smooth function, denoted as /. This formulation eliminated the problems of adding/subtracting
points to a moving grid and automatically took care of
the merging and breaking of the interface. Furthermore,
the level set formulation generalized easily to three
dimensions. The present analysis is done using this level
set technique.
The liquid–vapor interface is identified as the zero
level set of a smooth distance function /. The level set
function / is negative inside the bubble and positive
outside the bubble. The interface is located by solving
the level set equation. A fifth-order weighted, essentially
non-oscillatory (WENO) scheme is used for the left- and
right-sided discretization of / (Fedkiw et al. 1998).
While / is initially a distance function, it will not remain
so after solving the level set equation. Maintaining / as
a distance function is essential for providing the interface with a width fixed in time. This is achieved by the
reinitialization of /. A modification of Godunov’s
method is used to determine the upwind directions. The
reinitialization equation is solved in fictitious time after
each fully complete time step. With Ds ¼ 2ud 0 ; ten s steps
are taken with a third-order total variation diminishing
(TVD) Runge–Kutta method.
The curvature of the interface is defined as:
r/
j ð /Þ ¼ r jr/j
ð4Þ
The mass flux of liquid evaporating at the interface is
given by:
~¼
m
kl rT
hfg
ð5Þ
The vapor velocity at the interface due to evaporation is:
~
uevp ¼
~ kl rT
m
¼
qv qv hfg
ð6Þ
To prevent instabilities at the interface, the density and
viscosity are defined as:
q ¼ qv þ ðql qv ÞH
ð7Þ
l ¼ lv þ ðll lv ÞH
ð8Þ
H is the Heaviside function, given by:
H ¼1
H ¼0
/
H ¼ 0:5 þ 3d
þ
if />1:5d
if /6 1:5d
sin2p/
3d
2p
ð9Þ
if j/j61:5d
where d is the grid spacing.
Since the vapor is assumed to remain at saturation
temperature, the thermal conductivity is given by:
k ¼ kl H 1
ð10Þ
The level set equation is solved as:
@/ þ ~
u þ~
uevp r/ ¼ 0
@t
ð11Þ
After every time step, the level set function / is reinitialized as:
@/
@t
¼ S ð/0 Þð1 jr/jÞu0
/ðx; 0Þ ¼ /0 ð xÞ
ð12Þ
where S is the sign function, which is calculated as:
4.2 Governing equations
The momentum equation is written as:
@~
u
þ~
u r~
u ¼ rp þ q~
g qbT ðT Tsat Þ~
q
g rjrH
@t
þ r lr~
u þ rlr~
uT
The energy equation is written as:
u rT ¼ r krT for / > 0
qCp @T
@t þ ~
T ¼ Tsat
for /60
ð1Þ
ð2Þ
The continuity equation is written as:
r ~
u¼
~
m
rq
q2
ð3Þ
/0
S ð/0 Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
/20 þ d 2
ð13Þ
4.3 Scaling factors
The governing equations are made non-dimensional
using a length scale and a time scale. The length scale l0
given by the channel width is equal to 200 lm. Thus, for
the case of water at 100C and Re equal to 100, the
velocity scale u0 is calculated as 0.146 m/s. The corresponding time scale t0 is 1.373 ms. All non-dimensional
quantities hereafter are indicated with a * superscript.
The non-dimensional temperature is defined as:
140
T ¼
T Tsat
Tw Tsat
ð14Þ
4.6 Boundary conditions
The boundary conditions are as follows:
– At the inlet (x*=0):
4.4 Computational domain
u ¼ u0 ;
Figure 1 shows the typical computational domain. The
full domain is 4.95·0.99·0.99 non-dimensional units in
size. Cartesian coordinates are used with the uniform
grid.
Flow takes place in the x direction, with liquid
entering the domain at x*=0. To take advantage of
symmetry and reduce computation time, the bubble is
placed at the center of the microchannel cross-section,
equidistant from the walls in the y and the z directions.
The gravity vector acts in the negative y direction. It is
shown later in this paper that gravity has little effect on
the bubble growth under the given conditions in this
study. Thus, when neglecting gravity, calculations are
done only for one quarter of the domain shown in
Fig. 1. Otherwise, when gravity is considered, computations are done using one half of the domain (in the z
direction) shown in Fig. 1.
– At the plane of symmetry, (y*=0, if neglecting gravity):
v ¼ w ¼ 0;
uy ¼ v ¼ wy ¼ Ty ¼ 0;
T ¼ Tin ;
/x ¼ 0
/y ¼ 0
ð15Þ
ð16Þ
– At the plane of symmetry (z*=0):
uz ¼ vz ¼ w ¼ Tz ¼ 0;
/z ¼ 0
*
ð17Þ
*
– At the walls (y =0.495, y =0.495):
u ¼ v ¼ w ¼ 0;
T ¼ Tw ;
/y ¼ cos u
ð18Þ
where u is the contact angle.
– At the walls (z*=0.495, z*=0.495):
u ¼ v ¼ w ¼ 0;
T ¼ Tw ;
/z ¼ cos u
ð19Þ
– At the outlet (x*=4.95):
ux ¼ vx ¼ wx ¼ Tx ¼ 0;
/x ¼ 0
ð20Þ
4.5 Initial conditions
4.7 Effect of grid size
The bubble is placed at x*=0.99, y*=0, and z*=0, with
radius 0.1l0 in the domain shown in Fig. 1. All velocities
in the internal grid points are set to zero. The wall
temperatures are set to 107C (T*=1). The vapor inside
the bubble is set to a saturation temperature of 100C
(T*=0). The liquid temperature inside the domain is set
equal to the inlet liquid temperature. All physical
properties are taken at 100C. The inlet velocity is
specified as u0 and the inlet liquid temperatures Tin are
varied as 102C, 104C, and 107C. The Reynolds
number is varied as 50, 100, and 150. The contact angle
at the walls is specified as 50 for the situation when the
bubble touches the walls.
We have compared the bubble growth rates for five
different grid sizes. Figure 2 plots the time taken for the
downstream interface of the vapor bubble to cross fourfifths of the channel length for different grids. The differences in growth time decreases as the grid is refined.
To optimize the computation costs and numerical
accuracy, 96 grids are used per 0.99l0 for all subsequent
calculations. Thus, the number of computational cells in
the half-domain used for the calculations when considering gravity are 480·96·48.
Fig. 1 Computational domain
Fig. 2 Grid independence check
141
5 Results
First, the growth of a vapor bubble is considered at a
liquid inlet temperature of 102C, with no gravity. The
flow and thermal fields around the bubble is analyzed
and its interaction with the wall is studied. Next, the
effects of the inlet liquid superheat, Reynolds number,
and gravity on the bubble growth rates are determined.
Finally, the numerical results are compared with experimental observations.
5.1 Bubble growth with Tin=102C, Re=100, g=0
Figure 3 shows the growth of the vapor bubble inside
the microchannel. The wall superheat is 7C and the
liquid inlet temperature is 102C. The Reynolds number
is specified as 100. Gravity is neglected in this case,
specifying g=0 in Eq. 1. The time corresponding to each
frame is shown at the lower right corner. The frame at
0.00 ms shows the initial condition with a bubble of
radius 0.1l0 placed at the center of the channel equidistant from the walls.
At 0.082 ms, we see that the bubble has grown
bigger due to evaporation, but it still retains its
spherical shape. The bubble continues to grow and, at
the same time, moves downstream in the direction of
flow, as seen at 0.158 ms. At 0.232 ms, the bubble
starts to elongate in the direction of flow. Here, the
bubble has almost filled the channel cross-section and
cannot expand any further in the y–z plane, due to
resistance from the wall. At 0.256 ms, the bubble
elongates further and turns into a plug. A thin layer of
liquid separates the bubble from the walls on all sides.
At 0.278 ms, the bubble is seen to form vapor patches
at the walls near its upstream end. Our calculations
were stopped when the downstream interface crossed a
length of 4l0 of the channel, which corresponds to the
last frame at 0.278 ms.
Figure 4 shows the velocity vectors at a vertical x–y
plane through the center of the domain. The first frame
at 0.000 ms shows no velocity vectors since before the
start of the calculations, all internal velocities are set to
zero. Thereafter, as the bubble grows, the liquid is pushed towards downstream of the bubble, which can be
seen at 0.082 ms. The velocity vectors are much larger
downstream of the bubble compared to upstream. The
reference vector shown in the frame corresponds to 10u0.
At 0.158 ms, as the bubble interface approaches the
walls, vapor jets are seen inside the bubble due to
evaporation at the interface near the walls. At 0.232 ms,
the bubble has started to elongate along the channel axis
and more evaporation takes place from its interface near
the walls, causing the bubble to expand rapidly. Large
velocity vectors can be seen across the downstream
interface at 0.256 ms, which is pushing the liquid out of
the channel.
Fig. 3 Growth of vapor bubble in microchannel; Tin=102C,
Re=100, g=0
142
Fig. 4 Velocity vectors at the central vertical plane; Tin=102C,
Re=100, g=0
Fig. 5 Temperature field at the
central vertical plane;
Tin=102C, Re=100, g=0
The bubble touches the wall as it expands and forms
vapor patches, as seen at 0.278 ms. A thin layer of liquid
is trapped between the bubble and the wall in the
downstream of the vapor patch. Due to the presence of
saturated vapor on one side, and superheated wall on
the other side, very high rate of evaporation takes place
in this liquid layer.
Figure 5 shows the temperature field around the
bubble at 0.278 ms. Isotherms are plotted in ten intervals between 0 and 1. The wall is at T*=1 and the vapor
inside the bubble is at T*=0. Formation of a thermal
boundary layer can be seen in the liquid near the walls.
Crowding of isotherms between the bubble and the walls
at downstream of the vapor patch indicates very high
heat transfer rates in these regions.
Figure 6 shows the plot of the bubble diameter and
the bubble length in the axial direction against time. It
also shows the locations of the upstream and downstream interfaces of the bubble in the channel measured
from the channel inlet as a function of time. The bubble
equivalent diameter is calculated assuming a sphere of
equal volume. The bubble length is the length of the
bubble at the x axis through the center of the domain. It
is calculated as the difference between the upstream and
the downstream end locations.
The bubble growth rate, indicated by the equivalent
diameter, is constant initially, but increases as the bubble equivalent diameter approaches the channel width at
around 0.2 ms. The initial bubble growth is linear, as it
is inertia controlled. The constant bubble growth rate
(d r/d t) before 0.1 ms is found to be around 0.38 m/s.
The bubble growth rate is found to decrease slightly
after 0.27 ms, due to the formation of the vapor patches.
The bubble length is equal to the equivalent diameter
initially, as the small bubble grows spherically with
superheated liquid around it. However, as the bubble
equivalent diameter approaches the channel diameter, it
faces resistance from the wall and grows rapidly in the
axial direction. This is evident as the bubble length becomes greater than its equivalent diameter after 0.1 ms.
As the bubble elongates, more surface area becomes
available for evaporation, and the bubble length increases exponentially between 0.1 ms and 0.28 ms.
The bubble upstream interface location is seen to
decrease slightly until 0.1 ms, as the bubble grows uniformly at the initial stages. Thereafter, as the bubble
starts to elongate after 0.1 ms, the upstream interface
143
Fig. 6 Bubble growth rate; Tin=102C, Re=100, g=0
location increases, indicating that the entire bubble is
moving downstream with the flow.
The bubble downstream interface location increases
throughout the entire growth period. It initially increases
linearly, similar to the bubble diameter, until 0.1 ms, and
afterwards, exponentially as the bubble elongates into a
plug. The velocity of the bubble downstream interface is
around 6 m/s when the bubble length is 0.5 mm. This
is much higher than the inlet velocity of the liquid, which
is around 0.146 m/s. Thus, the liquid is pushed out of the
channel at a very high rate, due to evaporation and the
bubble growth.
inlet superheats of 2C, 4C, and 7C. Gravity is neglected in all these cases. The results indicate that the
bubble grows considerably faster with increasing liquid
inlet temperature, thereby, decreasing the time taken by
the bubble to fill the channel.
The upstream interface is found to move back initially in all cases, causing reversed flow, indicating the
dominance of the bubble growth over the incoming liquid flow. The amount by which the upstream interface
receded increased with the liquid inlet temperature, due
to higher growth rates. This reversed flow is, however,
different to that observed by investigators in parallel
microchannels. In the present case of a single channel,
the flow at the inlet is constant, and, hence, the backward movement of the upstream interface increases the
downstream liquid flow between the bubble and the
walls.
After some time, the location of the upstream interface becomes constant in all the three cases. In the case
of 102C inlet temperature, which has the lowest bubble
growth rate, the upstream interface is found to advance
considerably in the direction of flow after 0.16 ms. The
downstream interface moves forward with bubble
growth in all the cases and displays similar growth
patterns.
Formation of vapor patches at the walls was observed for an inlet superheat of 2C (Fig. 2). Interestingly, it was not observed for the cases of 4C and 7C
inlet superheats. This could be due to the fact that the
bubbles grew too quickly in the latter two cases. Thus,
there was insufficient time for the thin layer of liquid
between the bubbles and the walls to evaporate, thereby,
preventing the formation of vapor patches.
5.2 Effect of liquid inlet temperature
5.3 Effect of Reynolds number
Figure 7 compares the effect of the inlet liquid temperature on the bubble growth. The upstream and downstream interface locations are plotted against time for
Figure 8 compares the effect of the Reynolds number on
the bubble growth. The upstream and downstream
Fig. 7 Effect of inlet liquid temperature on bubble growth;
Re=100, g=0
Fig. 8 Effect of Re on bubble growth; Tin=102C, g=0
144
interface locations are plotted against time for a Reynolds number of 50, 100, and 150. Gravity is neglected in
all the cases and the liquid inlet temperature is 102C.
A higher Reynolds number signifies a higher liquid
inlet velocity that pushes the bubble downstream.
Hence, the bubble upstream interface is found to move
forwards faster with increasing Reynolds number.
The bubble downstream interface, however, exhibits
the opposite behavior. The case with a Reynolds number
equal to 50 shows the highest downstream interface
velocity after 0.2 ms. This is due to the fact that, when
the bubble interface approaches the walls, the bubble
growth rate depends on the thickness of the wall thermal
boundary layer. An increased Reynolds number causes
the thermal boundary layer at the walls to be thinner.
Therefore, a comparatively smaller area of the bubble
interface gets exposed to the superheated thermal
boundary layer near the walls. An increased Reynolds
number also causes the layer of liquid between the
bubble and the walls to be thicker due to an increased
supply of liquid. This, in turn, decreases the temperature
gradient across the liquid layer and the subsequent
evaporation rate. As a result, when the bubble has
turned into a plug, the bubble growth rate and the
downstream interface velocity is less for an increased
Reynolds number.
Formation of vapor patches at the walls was
observed for all the above three cases.
5.4 Effect of gravity
All the results so far were obtained neglecting gravity.
Figure 9 shows the effect of gravity on the bubble
growth rate for the case with Tin=107C. In the case
with gravity, calculations are carried out for half the
domain shown in Fig. 1. The gravity acts in the negative
y direction.
The plot shows the bubble equivalent diameter
against time, until the bubble diameter reaches 0.2 mm,
which is the channel width. It indicates an insignificant
Fig. 9 Effect of gravity; Tin=107C, Re=100
difference in the bubble growth rates for the two cases.
This justifies the assumption of neglecting gravity for the
present channel geometry and Reynolds number. It
helps to take advantage of symmetry in the y direction
and reduces computation time.
The above finding is in agreement with the experimental observations made by Kandlikar and Balasubramanian (2004). They found similar flow patterns for
horizontal flows, vertical up flows, and vertical down
flows during flow boiling of water in parallel minichannels.
5.5 Comparison with experimental observations
The numerical results qualitatively agree with the
experimental data obtained by Balasubramanian and
Kandlikar (2004). The experiments show an increase in
bubble/plug length growth rate with time, similar to
present calculations. The plug growth rate in the
experiments with subcooled liquid at the inlet was found
to be 0.3 m/s at the initial stages of bubble growth and
around 3.5 m/s at the later stages. This is comparable to
the respective values of 0.38 m/s and 6 m/s obtained
from numerical calculations at Tin=102C. However,
the above experimental study was undertaken in 1-mm
wide parallel channels, 63.5 mm in length.
Figure 10 compares the bubble shapes between
numerical calculations and experimental observations.
This comparison is only qualitative. The times indicated
on the frames for numerical results do not correspond to
the experimental observations.
Fig. 10 Comparison of bubble shapes
145
Both the experiments and the numerical calculations
show the formation of vapor patches at the wall and thin
layers of liquid between the bubble and channel corners.
The bubbles are seen to move downstream with flow as
it turns into a plug and fills up the entire channel crosssection. The upstream and downstream interfaces of the
plug have similar shapes in both of the cases.
6 Conclusions
1. A vapor bubble growing in superheated liquid inside
a microchannel is modeled using the level set technique.
2. The bubble initially grows at a constant rate, but its
length increases rapidly when it fills the channel
cross-section and expands in a longitudinal direction.
This increase in growth rate is due to the thin layer of
liquid between the walls and its interface, where a
high rate of evaporation takes place.
3. The upstream interface of the bubble is found to
exhibit both forward and reverse movement during
bubble growth.
4. The bubble growth rate is found to increase with the
incoming liquid superheat, but decrease with Reynolds number.
5. Vapor patch formation at the walls is found to be
dependent on the time taken by the bubble to fill up
the channel length.
6. The effect of gravity is found to be negligible on the
bubble growth rate under the specified conditions.
7. The bubble growth features obtained from numerical
calculations are found to be qualitatively similar to
the experimental observations.
Acknowledgments The work was conducted in the Thermal Analysis and Microfluidics Laboratory at the Rochester Institute of
Technology (RIT), Rochester, NY, USA.
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