The fluid mechanics and heat transfer of motions driven by surface tension gradients (Marangoni convection) were analyzed theoretically to obtain an understanding of the convection accompanying the process of growing high quality single crystals from the melt in a mu-g environment. The geometries considered include two dimensional liquid filled slots and axisymmetric float zone configurations

Davis, S. H.

Homsy, G. M.

English

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https://ntrs.nasa.gov/search.jsp?R=19830003192 2020-03-21T06:50:36+00:00Z
AS A -CR-1 70t)54) TUEA MOCAPILLARY FLOWS AND
	 U83-11462
'
-'HEIR STABILITY- BFFECTS OF SUILFACE .LAYERS
xND CUNTABINATI;N Anjival Repqrt
(Northwestern Univ.) 5 P 11C A02/Mr- A01	 Unclas
CSCL 2UD GJ/34 00672
YEAR TWO ANNUAL 
REPORT
on
CONTRACT NAS 8-33881
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MATERIALS-PROCESSING-IN-SPACE PROGRAM
"Thermocapillary Flows and Their Stability:
Effects of Surface Layers and Contamination"
from
NORTHWESTERN UNIVERSITY
Dr. S. H. Davis - Northwestern University
Dr. G. M. Homsy - Stanford University
Prepared for	 44_36
George C. Marshall Space Flight Center
-NOV 1982
Marshall Space Flight Center, Alabama 35812
RECEIVED
t4ASA Stj FACIUTy
ACCESS DEPT.
October 1982
L^_A
PROGRESS REPORT
The research conce'e s the theoretical analysis of the fluid mechanics
and heat transfer of motions driven by surface-tension gradients (Marangoni
convection). The object of the work is to obtain an understanding of the
convection accompanying the process of growing high-quality single crystals
from the melt ire a U-g environment. The geometries considered in this
work include two-dimensional liquid filled slots and axisymmetric float-zone
configurations.
The following models were stu
STEADY MARANGONT FLOWS
1. When a slot is differentially
gradient along the liquid gas
be induced. We have obtained
lied during the past year:
heated so as to impose a temperature
interface, a steady Marangoni flow can
approximat_ solutions for the flow
field, temperature distribution and surface deflection as functions
of the Marangoni number M, the Pr.andtl number P and the capillary number
C for long, thin slots when the liquid-gas interface is clean.
reference: Sen and Davis (1982)
2.	 When the liquid-gas interface of the slot from #1 is contaminated
with surface active material, the steady Marangoni flow is retarded.
We have obtained such steady flows for cases in which the contaminant
material is a non-condensed monolayer and determined the dependence
of the flow on the surface Peclet number and the Gibbs surface elasticity.
reference: Meiburg and Homsy (1982).
-2-
3. In bath planar cases #1 and #2, we obtain flaws for thin slots. Tlivse
flaws have only small or nuocicsxate values of the Marangoni number so
that convective transport of heat is small compared Lo that due Lo
conduction. Here we examine die caso of clean interfaces when the
Marangoni number is large. We use a simplified geometry and obtain
estimates for the Nusselt: number, the measure of the transport of
heat clue to convection. I gor large Prandtl number, 'N - M2/7.
reference: Cowley and Davis (1982)
4. When the liquid forms a cylindrical float zone and axial temperature
gradients are imposed, steady Marangoni convection can be induced.
We have extended the work of Son and Davis (1982) to this new geometry
and obtained the flow and heat transfer possible when significant
liquid—gas interface deflection is possible.
reference: Xu and Davis (1982x).
STABT.LIT'Y Or MARANCONI FLOWS
8.	 We have examined the steady Marangoni flows of #1 above and analyzed
the stability characteristics of these. We find that if the Prandtl
number P is small that the instability is oscillatory in time and is
associated with the interaction of liquid—gas interface deflection with
the underlying shear flow. Thus, even though the thermocapi.11ary
effect drives the steady motion it has little effect on the instability
characteristics; the instability is a mechanical one. If P is large,
then the instability is either oscillatory in time or a steady cellular
1
one. In either case the instability is associated with the thermal
MiL-.. _
. '3
t	 A	
.	 1 ^
-3-
field and depends little c ►► t Lhu deflection a(' Lhe l iijuid-gat; Inner-
face; the in4tabi lit.1 is a 010r ►nal. one. We have made good comparisons
with the experiments of St-harmann et al. in Cern ►a ►ty. We NO now that
we can completely eharaCturl.zV histablI tles in Mrzratigoni sayers.
references: Smith and Davis (1982a), Sill tLIl and DaviS (19821)),
Smith and Davl.ti (1982c:)
6.	 We are in the process of studying the instabilities in a float-zone
geometry to obtain the analog of the results of 115.
reference: Ku and Davis (1982b)
SL► IriMARY
The work is proceeding on schedule. We are excited by the breadth
and depth of the results obtained so far.
WORK TO BE APPROACHED IN YEAR TH RE E
1. The work on the influence of contamination, #2 above, will be completed
and extended to more complex monolayer models.
2. The work on high Marangoni number convection, 113 above, will be com-
pleted. We shall try to extend this analysis to axisymmetric float-
zone geometries.
3. The instabilities of Marangoni flows in float-zone geometries, #6 above,
is under way and will be completed.
4.	 We wish to examine the effect of instabilities on the heat transport
within a melt. Hence, we shall examine the nonlinear instability theory
w a	 e s
	
.
	
-4-
a
of #5 and 06 abovo, '(hIti Mould 1,ivo ►►►; L-st 1111ates of the rain- llentation
of heat transport clue Lo instabiliLioso
REPEH NOES CITED
Cowley, S. J. and Davis, S. 11. 1982 "Viscous thermocaplllary convection at
high Marangoni number," Applied Mathematics Technical Report No, 8203,
Northwestern University.
Meiburg, E. and Homsy, G. M. 1.982 "The effect of surface: contamination on
thermocapillary flow in a two-dimensional slot," Annual meeting AIChE - 	
a
November.
Sen, A. K. and Davis, S. H. 1982 "Steady thermocapillary flows in two-
dimensional slots," Journal. of Fluid Mechanics, 121, 23.
Smith, M. K. and Davis, S. H. 1982a "The instability of sheared liquid
layers," Journal of Fluid Mechanics, 121, 7G.
Smith, M. K. and Davis, S. H. 1982b "Instabilities of dynamic Chermocapillary
liquid layers. Part 1. Convective instabilities," submitted to
the Journal of Fluid Mechanics. Also see Applied Mathematics Technical
Report No. 8116, Northwestern University.
Smith, M. K. and Davis, S. A. 1982c "Instabilities of dynamic thermocapillary
liquid layers. Part 2. Mechanical Instabilities," submitted to the
Journal of Fluid Mechanics. Also see Applied Mathematics Technical
Report No. 8116, Northwestern University.
Xu, J.-J. and Davis, S. H. 1982a "Liquid bridges with thermocapillarity,"
submitted to Physics of fluids. Also see Applied Mathematics `technical
Report No. 8115, Northwestern University.
Xu, J.-J. and Davis, S. H. 1982b "The convective instability of cylindrical
and liquid bridges with thermocapillarity," 35th meeting, Division
i	 of Fluid Dynamics, American 'Physical Society, November.


Thermocapillary flows and their stability: Effects of surface layers and contamination

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