Complex Fluids &
Multiphase Transport
Laboratory
Heat transfer characteristics of an evaporating meniscus on nanostructured surfaces
Han Hu and Ying Sun
Department of Mechanical Engineering and Mechanics, Drexel University
Motivation
• Thermal management challenges
Thermal
management
requirements:
• Capillary pumping of water in a nanochannel
• Heat transfer rate of thin film evaporation
Steady state temperature profile
CPU
Power supply
LED array
− Heat transfer coefficient
l hfg 
 2hfg  M  

 






2


2

RT
T

T
T

v  
s
v
v 
h 
12

 2h fg  M   l hfg   0


  RK 

1  

 2    2RTv  Tv  rkl

12
500
Ts,i
Liquid
z
Tw
Nonevaporating film thickness
Steady state:
N = const
1
0
1000
2000
Time (ps)
0
10
20
30
40
50
− Heat flux (J): J  Nhfg An
J
− Heat transfer coefficient (h): h 
Ts,i  Tv
1.4
How to design nanostructures for highest heat transfer coefficient (HTC) and critical
heat flux (CHF).
• Objective
Investigate the effect of nanostructures and film thickness on meniscus shape and heat
transfer coefficient of an evaporating thin film
Heat transfer coefficient, h (W/cm2K)
• Challenge
4000
3000
Rcond dominates
Revap
dominates
2000
1000
Model predictions
MD results
0
0
1
2
3
4
5
6
Rcond
RK
Flat meniscus
− Extended meniscus in a nanopore
− Disjoining pressure driven flow
d
u 
dz
3D pore
(η: viscosity)
(Evaporation flux =
liquid delivery flux)
Evaporation x
m"
0
12
0
200
400
600
800
1000
1200
Time, t (ps)
0.8
0.6
0.4
0.2
0.0
0
• Evaporating meniscus in a nanochannel
6
20
40
60
80
4
100
Heat transfer coefficient (Nanostructures)
z
4000
3000
2000
1000
δcrit for
D=5.71nm
D (nm)
0
1
2
3
2.85 5.71
4
5
2
MD, w/ evaporation
MD, w/o evaporation
Model for 2D meniscus
0
-2
-4
-6
Assumptions:
i) Pore diameter >> film thickness
ii) Evaporation kinetics & vapor removal much
faster than liquid delivery
MD
0
w/ evaporation
3 l n kl Ts  Tv   1
d *
*
*2 
2
*2


4


3


tan




A
*2
dx*
Ahfg



Model
0
w/o evaporation
Model for 2D meniscus
0
1
2
3
4
z axis (nm)
Extended meniscus is observed for
cases with evaporation.
6
D increases, Rcond decreases, Revap increases.
10
z
MD results
Fitting equation
8
6
4
Wenzel roughness ratio:
2
0
δ
Critical film thickness
Critical film thickness, crit (nm)
Revap
L
10
Washburn model using advancing contact angle agrees well with MD.
1.0
Interfacial thermal resistance
Revap
Rcond
Kapitza resistance, RK (m K/W)
Conformal meniscus
D
8
z axis (nm)
• Evaporating meniscus in a 3D nanopore
x
x
δ(x)
6
Note: θA is the advancing
contact angle >
equilibrium contact angle
4
z axis (nm)
δ0 < δcrit, Revap dominates, h increases with δ0; δ0 > δcrit, Rcond dominates, h decreases with δ0.
− Heat transfer coefficient (h)
 RK: interfacial
resistance
 Rcond: conduction
resistance
 Revap: evaporation
resistance
4
8
A
2
− Meniscus shape and disjoining
pressure on nanostructured surface
2
 cos  A Dporet
LI 
3
12
Liquid film thickness, 0 (nm)
δ0 increase, Rcond increases, Revap decreases
Theoretical model
RK
MD, D = 0
MD, D = 2.85nm
Model for flat surface
1.2
Liquid film thickness, 0 (nm)
1 h  RK  Rcond  Revap
0
x
Introduction
− Real TIP4P-Ew water rather than
simple L-J liquids
4
L-V inteface temperature drop, Tli-Tv (K)
Heat transfer coefficient (Flat surface)
Molecular dynamics (MD)
12
8
Ts,i  Tl,i
− Interfacial thermal
RK 
resistance (RK):
J
− Meniscus is extended in pores for larger heat transfer area.
− Disjoining pressure (Π) drives liquid flow to thin film region for high heat transfer
rate.
13
MD results
Washburn model
S  L intefacial area
2D
r
 1
Normal area
L
1.0
1.2
1.4
1.6
1.8
2.0
Wenzel roughness ratio, r
Increasing r, stronger S-L interaction, smaller RK.
14
5000
12
4500
10
8
4000
6
4
3500
Critical film thickness
Max. heat transfer coef.
2
0
0
20
40
60
80
3000
100
Nanostructure depth, D (nm)
hmax saturates at RK → 0 (when D → ∞).
y
z
A-A
A
z axis (nm)
Nanoporous alumina membrane
(Synkera, Inc.)
16
2
z axis (nm)
δ
t=500ps
crit
 crit


ArTv
n  



6

h
T

T

l fg
li
v 

3
t=250ps
t=1000ps
Dpore =
10nm
m"
hmax  h 
&
t = 1000ps
16
t=20ps
t=750ps
− Nonevaporating film thickness (δn)
400
350
0
20
Max. heat transfer coef. hmax (W/cm2K)
500 nm
dh
d 0
Tv
250
Tv , Pv
92
Solid
0
x
64
Vapor
300
Intrinsic
meniscus
Evaporating thin
film
42
t = 750ps
Infiltration length
x axis (nm)
Extended meniscus in a nanopore
22
t = 500ps
t = 250ps
Dpore =
10nm
• Thin film evaporation in a nanopore
ΔT (K)
Tl,i
Evaporation rate, N (/ps)
Temperature (K)
Thin film evaporation (thickness ~ 1μm) reveals CHF > 500W/cm2 and HTC > 105
W/m2K, ×3 higher cooling rate than nucleate boiling.
interface
t = 20ps
Dynamic meniscus shape
x axis (nm)
Theoretical
450
Nonevaporating
− Critical film thickness (δcrit) & Maximum
heat transfer coefficient (hmax)
h decreases with D
Thin film evaporation
z
δn increases
with D
Pool boiling
x
Infiltrated length, LI (nm)
104
Heat flux (W/cm2)
h decreases with D
Convection
103
Non-evaporating filmthickness, n (nm)
102
Heat transfer coefficient, h (W/cm2K)
101
2D pore
LI
Model prediction
Au H2O
Cooling
techniques:
Extended meniscus in a nanopore
Effect of nanostructures on heat transfer
x
z
References
[1] Nam, Y., Sharratt, S., Cha, G., Ju, Y.S., J. Heat Transfer, 133, (2011) 101502
[2] Gerasopoulos, K., McCarthy, M., Royston, E., Culver, J.N., Ghodssi, R., J. Micromech.
Microeng., 18, (2008) 104003
[3] Hu, H. and Sun, Y., J. Appl. Phys., 112, (2012) 053508
[4] Hu, H., Weinberger, C., and Sun, Y., Nano. Lett., 14 , (2014) 7131-7137
This work was supported by the U.S. National Science Foundation under Grant No. DMR-1104835.