A new thin-film evaporation model is presented that captures the unsimplified dispersion force along with an electronic disjoining pressure component that is unique to liquid metals. The resulting nonlinear fourth-order ordinary differential equation (ODE) is solved using implicit orthogonal collocation along with the Levenberg–Marquardt method. The electronic component of the disjoining pressure should be considered when modeling liquid metal extended meniscus evaporation for a wide range of work function boundary values, which represent physical properties of different liquid metals. For liquid sodium, as an example test material, variation in the work function produces order-of-magnitude differences in the film thickness and evaporation profile.

1.
Khrustalev
,
D.
, and
Faghri
,
A.
, 1994, “
Thermal Analysis of a Micro Heat Pipe
,”
ASME J. Heat Transfer
0022-1481,
116
, pp.
189
198
.
2.
Jiao
,
A. J.
,
Riegler
,
R.
,
Ma
,
H. B.
, and
Peterson
,
G. P.
, 2005, “
Thin Film Evaporation Effect on Heat Transport Capability in a Grooved Heat Pipe
,”
Microfluid. Nanofluid.
1613-4982,
1
, pp.
227
233
.
3.
Sobhan
,
C.
,
Rag
,
R.
, and
Peterson
,
G.
, 2007, “
A Review and Comparative Study of the Investigations on Micro Heat Pipes
,”
Int. J. Energy Res.
0363-907X,
31
, pp.
664
688
.
4.
Jiao
,
A.
,
Ma
,
H.
, and
Critser
,
J.
, 2008, “
Heat Transport Characteristics in a Miniature Flat Heat Pipe With Wire Core Wicks
,”
ASME J. Heat Transfer
0022-1481,
130
, pp.
051501
.
5.
Wayner
,
P. C.
, Jr.
, 1999, “
Intermolecular Forces in Phase-Change Heat Transfer: 1998 Kern Award Review
,”
AIChE J.
0001-1541,
45
, pp.
2055
2068
.
6.
Wee
,
S. -K.
,
Kihm
,
K. D.
, and
Hallinan
,
K. P.
, 2005, “
Effects of the Liquid Polarity and the Wall Slip on the Heat and Mass Transport Characteristics of the Micro-Scale Evaporating Transition Film
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
265
278
.
7.
Peterson
,
G.
, and
Ma
,
H.
, 1999, “
Temperature Response of Heat Transport in a Micro Heat Pipe
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
438
445
.
8.
Badran
,
B.
,
Albayyari
,
J. M.
,
Gerner
,
F. M.
,
Ramadas
,
P.
,
Henderson
,
H. T.
, and
Baker
,
K. W.
, 1993, “
Liquid-Metal Micro Heat Pipes
,”
Heat Pipes and Capillary Pumped Loops: Proceedings of the 29th National Heat Transfer Conference
, Atlanta, GA, Aug 8–11,
ASME
,
New York
, pp.
71
85
.
9.
Ramadas
,
P.
,
Henderson
,
H.
,
Badran
,
B.
,
Gerner
,
F.
, and
Baker
,
K.
, 1993, “
Liquid-Metal Micro Heat Pipes Incorporated in Waste-Heat Radiator Panels
,”
Proceedings of the Tenth Symposium on Space Nuclear Power and Propulsion
, Albuquerque, NM, January 10–14,
M.
El-Genk
and
M. D.
Hoover
, eds.,
American Institute of Physics
,
New York
, pp.
551
557
.
10.
Wayner
,
P.
, Jr.
, and
Schonberg
,
J.
, 1990, “
Heat Transfer and Fluid Flow in an Evaporating Extended Meniscus
,”
Heat Transfer 1990: Proceedings of the Ninth International Heat Transfer Conference
, Jerusalem, Israel,
G.
Hestroni
, ed.,
Hemisphere
,
New York
, Vol.
4
, pp.
228
234
,.
11.
Derjaguin
,
B.
,
Nerpin
,
S.
, and
Churaev
,
N.
, 1965, “
Effect of Film Transfer Upon Evaporation of Liquids From Capillaries
,”
RILEM Bull.
0534-7157,
29
, pp.
93
98
.
12.
Schrage
,
R. W.
, 1953,
A Theoretical Study of Interphase Mass Transfer
,
Columbia University Press
,
New York
.
13.
Wayner
,
P. C.
, Jr.
,
Kao
,
Y. K.
, and
LaCroix
,
L. V.
, 1976, “
The Interline Heat-Transfer Coefficient of an Evaporating Wetting Film
,”
Int. J. Heat Mass Transfer
0017-9310,
19
, pp.
487
491
.
14.
Potash
,
M.
, Jr.
, and
Wayner
,
P. C.
, Jr.
, 1972, “
Evaporation From a Two-Dimensional Extended Meniscus
,”
Int. J. Heat Mass Transfer
0017-9310,
15
, pp.
1851
1863
.
15.
Chebaro
,
H.
, and
Hallinan
,
K.
, 1993, “
Boundary Conditions for an Evaporating Thin Film for Isothermal Interfacial Conditions
,”
ASME J. Heat Transfer
0022-1481,
115
, pp.
816
819
.
16.
Chebaro
,
H.
,
Hallinan
,
K.
,
Kim
,
S.
, and
Chang
,
W.
, 1992, “
Evaporation From a Porous Wick Heat Pipe for Isothermal Interfacial Conditions
,” ASME HTD-Vol.
221
, pp.
23
28
.
17.
Hamaker
,
H.
, 1937, “
London-Van Der Waals Attraction Between Spherical Particles
,”
Physica
,
4
, pp.
1058
1072
. 0031-8914
18.
Lifshitz
,
E.
, 1955, “
The Theory of Molecular Attractive Forces Between Solids
,”
Sov. Phys. JETP
0038-5646,
2
, pp.
73
78
.
19.
Dzyaloshinskii
,
I.
,
Lifshitz
,
E.
, and
Pitaevskii
,
L.
, 1961, “
The General Theory of Van Der Waals Forces
,”
Adv. Phys.
0001-8732,
10
, pp.
165
209
.
20.
Israelachvili
,
J. N.
, 1985,
Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems
,
Academic
,
New York
.
21.
Moosman
,
S.
, and
Homsy
,
G.
, 1980, “
Evaporating Menisci of Wetting Fluids
,”
J. Colloid Interface Sci.
0021-9797,
73
, pp.
212
223
.
22.
Truong
,
J. G.
, and
Wayner
,
P. C.
, Jr.
, 1987, “
Effects of Capillary and Van Der Waals Dispersion Forces on the Equilibrium Profile of a Wetting Liquid: Theory and Experiment
,”
J. Chem. Phys.
0021-9606,
87
, pp.
4180
4188
.
23.
DasGupta
,
S.
,
Schonberg
,
J. A.
, and
Wayner
,
P. C.
, Jr.
, 1993, “
Investigation of an Evaporating Extended Meniscus Based on the Augmented Young-Laplace Equation
,”
ASME J. Heat Transfer
0022-1481,
115
, pp.
201
208
.
24.
Derjaguin
,
B.
,
Leonov
,
L.
, and
Roldughin
,
V.
, 1985, “
Disjoining Pressure in Liquid Metallic Films
,”
J. Colloid Interface Sci.
0021-9797,
108
, pp.
207
214
.
25.
Derjaguin
,
B.
, and
Roldughin
,
V.
, 1985, “
Influence of the Ambient Medium on the Disjoining Pressure of Liquid Metallic Films
,”
Surf. Sci.
0039-6028,
159
, pp.
69
82
.
26.
Kubo
,
R.
, 1962, “
Electronic Properties of Metallic Fine Particles
,”
J. Phys. Soc. Jpn.
0031-9015,
17
, pp.
975
986
.
27.
Roldughin
,
V.
, 2000, “
Quantum-Size Colloid Metal Systems
,”
Russ. Chem. Rev.
0036-021X,
69
, pp.
821
843
.
28.
Ajaev
,
V.
, and
Willis
,
D.
, 2003, “
Thermocapillary Flow and Rupture in Films of Molten Metal on a Substrate
,”
Phys. Fluids
1070-6631,
15
, pp.
3144
3150
.
29.
Ajaev
,
V. S.
, and
Willis
,
D. A.
, 2006, “
Heat Transfer, Phase Change, and Thermocapillary Flow in Films of Molten Metal on a Substrate
,”
Numer. Heat Transfer, Part A
1040-7782,
50
, pp.
301
313
.
30.
Hecht
,
E.
, 2004,
Optics
,
4th ed.
,
Pearson
,
New York
.
31.
Fink
,
J.
, and
Leibowitz
,
L.
, 1996, “
A Consistent Assessment of the Thermophysical Properties of Sodium
,”
High Temp. Mater. Sci.
1080-1278,
35
, pp.
65
103
.
32.
Takens
,
W.
,
Mischke
,
W.
,
Korving
,
J.
, and
Beenakker
,
J.
, 1984, “
A Spectroscopic Study of Free Evaporation of Sodium
,”
Rarefied Gas Dynamics: Proceedings of the 14th International Symposium on Rarefied Gas Dynamics
, Tsukuba, Science City, Japan, Jul. 16–20,
University of Tokyo Press
,
Tokyo
, pp.
967
974
.
33.
Hallinan
,
K.
,
Chebaro
,
H.
,
Kim
,
S.
, and
Chang
,
W.
, 1994, “
Evaporation From an Extended Meniscus for Nonisothermal Interfacial Conditions
,”
J. Thermophys. Heat Transfer
0887-8722,
8
, pp.
709
716
.
34.
Marquardt
,
D. W.
, 1963, “
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,”
J. Soc. Ind. Appl. Math.
0368-4245,
11
, pp.
431
441
.
35.
Henley
,
E. J.
, and
Rosen
,
E. M.
, 1969,
Material and Energy Balance Computations
,
Wiley
,
New York
.
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