The overall objective of this research is to develop models to predict drop-size-distribution evolutions due to droplet collisions and coalescence during processing within the miscibility gap of bimetallic liquid-phase-miscibility-gap materials. The individual and collective action of gravitational and nongravitational mechanisms on the relative motion and coalescence of drops are considered

Davis, Robert H.

English

NASA Technical Reports Server

NASA-CR-191247
/ .
FINAL REPORT TO THE
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
ON RESEARCH SUPPORTED BY GRANT NAG3-993:
/O
MODELING OF COALESCENCE, AGGLOMERATION AND PHASE
SEGREGATION IN MICROGRAVITY PROCESSING OF
BIMETALLIC COMPOSITE MATERIALS
Narn¢ _nd Address of Institution:
Time Period of Suvvort:
The Regents of the University of Colorado
Campus Box 19
Boulder, CO 80309-0019
2/2189-9130/92
Principal Investimator;
Responsible NASA Official:
Date of Final Report:
Robert H. Davis, Professor
Department of Chemical Engineering
University of Colorado
Boulder, CO 80309-0424
Telephone: (303) 492-7314
R. Balasubramanian
Mail Stop 500-217
NASA Lewis Research Center
21000 Brookpark Road
Cleveland,OH 44135
Telephone: (216)433-2878
11/10/92
PH.AC,_ ":;_'_::c.-C;_TIqN Iq _'!ICv, f_uPAVITY
P_:)C_q_[_C n[ :,T_'_TALLIC CQN_pOSITF
" • 2_ Feb. 19F3'_:,_,TL,£,_L3 _:intl R_port t
_ ,_} c_:_. i_2 (Culor ,Io Univ.)
[C'
N?3-12?z"
Unc 1 _s
0t_0507
https://ntrs.nasa.gov/search.jsp?R=19930003540 2020-03-17T10:37:02+00:00Z
Summary of Technical Progress
Objectives: The overall objective of this research is to develop models to predict drop-size-
distribution evolutions due to droplet collisions and coalescence during processing within
the miscibility gap of bimetallic liquid-phase-miscibility-gap materials. The individual and
collective action of gravitational and nongravitational mechanisms on the relative motion
and coalescence of drops are considered.
Research Task Description: When bimetallic liquid-phase-miscibility-gap materials, which
are thought to have a variety of desirable properties, are cooled through the miscibility gap,
droplets rich in one of the metals form in the liquid matrix rich in the other metal. Droplet
coalescence and phase segregation then occur due to buoyancy and to thermocapillary and
other nongravitational mechanisms. In order to gain a predl"ctive understanding of these
phenomena, population dynamics models are used to follow drop-size distribution evolutions
in time as the droplets grow due to collisions and coalescence. Continuous drop size dis-
tributions are discretized into a large number of categories. Drops of a given mass are
destroyed by coalescing with other drops and are formed by the coalescence ofsmaller drops.
The population dynamics model tracks the formation anddestruction of drops in each size
category.
The relative motion of drops which gives rise to their collision and coalescence is considered
to occur by gravity sedimentation, Marangoni migration, Brownian motion, and bulk flow.
These collision mechanisms are considered either individually or collectively in the pop-
ulation dynamics models. In general, different mechanisms dominate for different pro-
cessing conditions, materials properties, and drop-size ranges.
The collision kernals appearing in the population dynamics models require expressions for
the collision rate between drops of two different sizes. Classical expressions attributed to
Smoluchowski are improved to include attractive, repulsive, and hydrodynamic interactions
between drops. In particular, trajectory calculations are used to predict collision efficiencies,
which represent the ratio of the collision rate with these interactions to the Smoluchowski
collision rate without these interactions, as functions of the size ratio, viscosity ratio, and
other relevant dimensionless parameters.
Accomplishments: During the three years of NASA support, the following progress was
made:
o A computer program has been completed for solving the population dynamics model
to follow droplet size evolutions with time in homogeneous dispersions due to col-
lisions arising from gravity sedimentation, Marangoni migration, and/or Brownian
motion. Some of the key results are that a bimodal initial distribution will exhibit
much more rapid coalescence due to gravity sedimentation or Marangoni migration
than will a unimodal initial distribution (Figure 1), a unimodal initial distribution
will evolve into a bimodal distribution and then into a shifted and broadened uni-
modal distribution (Figure 2), and that coalescence may be greatly reduced by
antiparallel alignment of the gravity vector and the temperature gradient (Figure
3).
. Collision efficiencies for Brownian motion (Figure 4) and gravity sedimentation
(Figure 5) for drops having a range of viscosity and radius ratios have been computed
both in the presence and absence ofattractive forces. A key result is that, in contrast
to rigid particles, spherical liquid drops have nonzero collision efficiencies in the
absence of attractive forces.
. Theoreticalwork has been completed to predictcollisionefficienciesforMarangoni
migration oftwo drops ofdifferentsizesina temperature gradient Example results
are shown inFigure 6. Note thatthe collisionefficienciesforthermocapillary motion
are larger than those for gravity motion, because of the more rapid decay of the
velocityfieldscreated by drops undergoing thermocapillary motion, provided that
..
.
°
the thermal conductivity of the drops is not too large. Surprisingly, however, the
relative mobility function along the line-of-centers can become negative for large
thermal conductivities (Figure 7), indicating that the smaller drop moves away from
the larger drop and that there is a region of closed trajectories which prevents
coalescence in the absence of attractive forces (Figure 8).
In relatedexperimental work, drop sizedistributionsofbutyl benzoate inwater are
followed with time by holography as coalescenceoccurs due to gravity motion. We
are alsoexamining the interactionoftwo drops with video microscopy. An example
ofcoalescence isshown inFigure 9,and measured relativetrajectoriesoftwo drops
are shown in Figure 10 to be in good agreement with theory.
Theoretical work on combined mechanisms fordrop coalescence has been focused
on buoyancy and Marangoni motion with the gravity vector aligned parallelor
antiparallelto the temperature gradient. Our resultsshow that there isa finite
region inparameter space forwhich no collisionsoccur (Figure 11).This isbecause
the interactionoftwo drops due to thermocapillary migration decays more rapidly
(as 1/r3)with the separation distance (r)than does the interactionof two drops in
gravitymotion (which decays as 1/r).As a result,the largedrop which moves toward
a small drop below itdue to gravity may reach a separation distance where the
initiallyweaker thermocapillary effectsjust balance the buoyancy-driven relative
motion, and so the separation distance would then no longer decrease (Figure 12).
With appropriate antiparallelalignment of buoyancy and Marangoni velocities,a
polydisperse suspension of small drops ispredicted to evolve intoa monodisperse
suspension of largerdrops (Figure 13).
Time scales have been determined for phase segregation and drop coalescence,
together with criteriaforpredictingwhether ornot significantcoalescencewilloccur
riortophase segregation.A computer model has been developed tosolvepopulation
alances for drop sizedistributionswhich vary in space due to buoyancy or ther-
mocapillary motion. Resultsshow thatthe phase segregationrateinitiallyincreases
due to coalescence and subsequently decreases as the largerdrops migrate out of
suspension (Figure 14).
Physical data on a variety of bimetallicand transparent immiscibles have been
collected,and dimensionless parameters representingvarious effectshave been
tabulated as functionsofdrop size.Data on com_p0siteHamaker constants (forvan
der Waals attractions)and temperature coefficientsof interfacialtension (for
thermocapillary migration) are sparse,and order-of-magnitude estimates are typ-
icallyused. Calculationsofcollisionefficiencieshave been made forbismuth drops
in a zinc melt, forethylsalicytatedrops in diethylene glycol,and forlead drops in
an aluminum melt.
Publications
Barnocky, G. and Davis, R.H., "The Lubrication Force Between Spherical Drops, Bubbles
and Rigid Particles in a Viscous Fluid," Int. J. Multiphase Flow 15, 627-638 (1989).
Davis, R.H., Schonberg, J.A., and Rallison, J.M., "The Lubrication Force Between Two
Viscous Drops," Phys. Fluids A 1, 77-81 (1989).
Rogers, J.R. and Davis, R.H., "Modeling of Coalescence in Microgravity Processing of Zn-Bi
Immiscible Alloys," Met. Trans. A. 21, 59-68 (1990).
Rogers, J.R. and Davis, R.H., "The Influence of van der Waals Attractions on Cloud Droplet
Growth by Coalescence," J. Atmos. Sci. 47, 1075-1080 (1990).
Yiantsios, S.G. and Davis, R.H., "On the Buoyancy Driven Motion of a Drop Towards a Rigid
Surface or a Deformable Interface," J. Fluid Mech. 217, 547-573 (1990).
3
Zhang, X. and Davis, R.H., "The Rate of Collisions of Viscous Drops Due to Gravity or
Brownian Motion," J. Fluid Mech. 230, 479-504 (1991).
Yiantsios, S.G. and Davis, R.H., "The Deformation of Two Unequal Drops in Near-Contact
Buoyancy Driven Motion," J. Colloid Interface Sci. 144, 412-433 (1991).
Rogers, J.R., Experimental and Modeling Studies of Droplet Growth Due to Coalescence,
PhD Thesis, University of Colorado (1991).
Zhang, X. and Davis, R.H., "Collision Efficiencies of Small Drops," Proc. Chinese Acad. Sci.
Workshop (1991).
Zhang, X. and Davis, R.H., "The Collision Rate of Small Drops Undergoing Thermocapillary
Migration," J. Colloid Interface Sci. 152,548-561 (1992).
Davis, R.H., Zhang, X., and Wang, H., "Hydrodynamics of Dispersions and Coagulation,"
Proc. Int. Workshop on Systems witha Miscibility Gap (ed. L. Ratke), Bad Honnef,
Germany, 157-174 (1992).
Zhang, X., Relative Motion, Collision and Coalescence of Small Spherical Drops, PhD Thesis,
University of Colorado (1992).
Zhang, X., Davis, R.H., and Ruth, M.F., "Experimental Study of Two Interacting Drops in
an Immiscible Fluid," J. Fluid Mech. (in press).
Wang, H. and Davis, R.H., "Droplet Growth due to Brownian, Gravitational, or Thermo-
capillary Motion and Coalescence in Dilute Dispersions," J. Colloid Interface Sci.
(under review).
Zhang, X., Wang, H., and Davis, R.H., _Collective Effects of Temperature Gradients and
Gravity on Droplet Coalescence," Phys. Fluids A (under review).
9°°'I'"'"eoo 'iil_I"'_li'_'"""i"_"'o
700_
i 6001 ./IZl /I001
500
400 _" il t _
200 _-- _l
Oltj 4 i Iilll Ij "}'l I I I I f f ; t I I S'_'i] I I i
2.3 6,* 16.7 45 4
OROPLET RAOIUS (_m)
400
1200
i tO00
000
600
400
ZOO
0
1600, ]: 11 [ _ liiill_[il i;ii; : l, ; .; ;!: :1
a i11,/I "0
"Ii -IOOs. AS _\
, %
It l! III Ilkl'rJ-III Ill IilII_LI t II
2.3 6.1 t6.7
DROPLET RADIUS (/J.m)
Figure la. Time evolution of the cLrop,size
distribution for a bimodal initial distri-
bution of bismuth drops undergoing
15hu-angoni migration in molten zinc.
Figure lb. Time evolution of the.dTop "size
distribution for a unimodal initzal distri-
bution of bismuth drops undergoing
Marangoni migration in molten zinc.
L2
i0
[- r L.l.Oelll| | ,., .,,o
. r rr ,,.,z.. .
,. 0.$ 3Ore.., 4
";
_ ,o,,.,e Z
Z ,0,0 _6 ,04} I00 ,00@
, (#ill
Figure % Time evolution of the .drop. size
distribution for a unzmodal initial distri-
bution of water drops subject to gravity
sedimentation in air.
[ I i I
m
o I I [ 1
-0 z2 -001 -004 0 00a OOI
Figure 8. Mass average drop radius at t=45
seconds due to combined gravity and
Marangom motion of bismuth drops in
zinc as a function ct gravity strength
relative to normal for parallel (/> O) and
antiparallel (i <0) orientation of gravity
_._e_o..r and temperature gradient. The
itial mass average radius is r_=2
w0,8
0.6
0.4
0.2
0.0
1000.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Figure 4. Collision efficlencies for viscous drops of various viscosity ratios (_) and
size ratios (_) undergoing Brownian motion in the absence of attractive
forces.
m
LJ
Figure 5.
0.15
0.05
0.0
O.IS
0 1 2 3 4 5
Col//sion efficiencles for viscous drops of various size ratios (;L) and viscosity
ratios (_) undeq_oing gravity sedimentation in the absence of attractive forces.
6
0.7
LaJ
1.0
]L_IFL"e 6.
-,J
Figure 7.
Collision efficienc4es as a function of the drop size rat/o (_.)for drops of various
thermal conductivity ratios (_c)and viscosity ratios (_) undergoing thermoca-
pillary migration in the absence of attractive forces.
1.0
0.8
0.6
0.4
0.2
0.0
-- ;I | .0 'klO.01 /- -: o,_,=oj
-- -- -- _l 1.0l_(l 1,0 i/ / / O_ /
.. ^ ,/ , _,'
--- _,-i o,.-5 o f / ._;'
- - _-, o..-,oo ,/ : U"
A /w 0 #° • ii I..... _,n 1.0.kl 100.0 fi./'
/," : /I.'"
/; / /i,'
// , .# ,.
.# • °•
_.,.,..,,'_ ;o O° i" I ."
...... I ........ 1 ...... 1 ........ 1 " ' '
0.0010 0.0100 0.1000 1.0000
Relative mobility function venus the dimensionless separation distance for
two unequal drops 0,.= 0_) in relative, motion along their line of centers due
to thermocapUlary migration, for various thermal eonductivity ratios (k) and
viscosity ratios _
Figure 8.
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
q
--- _=C.25
--- XzO.9
_k
_ .-. _-._ Stable
- . i° ou . ° o ° -_
Unstable
1 1 I t l i T I I
0 1 2 3 4. 5 6 7 8 9
Stability diagram showing regions of no collisions (stable) and collisions
(unstable) for two spherical drops undergoing thennocapillary migration in
the absence of attractive forces.
t=0sec t=3sec t=10sec t=17sec
Figure 9.
4
3
° . - -
2 o •
....... . -O" _ " " "
. . .
0 " " ",'" " _" " " i
-8 -6
Figure 10.
Time sequence of approach and coalescence due to gravity of two castor oil
drops in a silicon fired.
I
-4
._°_°°'° °°'_°_O.
o Q" .@ - . ° ° . . . . . _ _
i
-44- . . ° . Q Q ....
I I I
4 6-2 0 2
Dimensionless relative trajectories of two different sized castor oil drops
moving due to gravity in a silicon fluid. The symbols are experimental data
and the dashed lines are theory.
8
8
LLJ
Figure 11.
10 °
;_=0, _=0
"= _=0
1
2, 2
0 10 20
Nv
The collision efficiency versus the ratio of buoyancy and thermocapillary
relative velocities for two widely spaced dropsof size ratio k = O_ for various
viscosity (_) and thermal conductivity ratios (k).
,m
(J
O
a)
>
a)
>
O
k-
(n
{fl
r"
O
It}
¢-
E
D_
"O
Figure 12.
1.0
0.5
0.0
L
-0.5
0 1 2 3 4 5
dimensionless separation distance
The dimensionless gravitational (L), thermocaplllary (L_No) and combined
relative velocities versus separation distance for two drops w/th k = 0.5, _ = I,
= l, and N, = -2.5.
9
EFigure 13,
4000-
3000
2OOO
1000
0
50
5
t:O s
2 4 6 8 10
°
Evolution of the size distribution of lead drops in an aluminum melt for
antipara]l, el alignment of the gravity vector (9_ m/s z) and temperature gra-
dient (I0" K/m).
0.012
E
"!3
t"
"t3
Figure 14.
0.010
0.008
0.006
0.004
0.002
0.000
. :::-
0 10 20 30 40
t(s)
The rate of phase separation versus time for a dispersion of bismuth drops
undergoing simultaneous buoyancy motion and coalescence/n a zinc meltin
containers of increasing height (left to right), the dashed curves are the cot-
responding results in the absence of coalescence.
10


Modeling of coalescence, agglomeration, and phase segregation in microgravity processing of bimetallic composite materials

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server