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TECHNICAL PAPERS: Bubbles, Particles, and Droplets

Marangoni and Variable Viscosity Phenomena in Picoliter Size Solder Droplet Deposition

[+] Author and Article Information
M. Dietzel, S. Haferl, Y. Ventikos, D. Poulikakos

Laboratory of Thermodynamics in Emerging Technologies, Institute of Energy Technology, Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology, ETH Center, 8092 Zurich, Switzerland

J. Heat Transfer 125(2), 365-376 (Mar 21, 2003) (12 pages) doi:10.1115/1.1532014 History: Received April 22, 2002; Revised October 11, 2002; Online March 21, 2003
Copyright © 2003 by ASME
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References

Maronnier,  V., Picasso,  M., and Rappaz,  J., 1999, “Numerical Simulation of Free Surface Flows,” J. Comput. Phys., 155(2), pp. 439–455.
Attinger,  D., Zhao,  Z., and Poulikakos,  D., 2000, “An Experimental Study of Molten Microdroplet Surface Deposition and Solidification: Transient Behavior and Wetting Angle Dynamics,” Journal of Heat Transfer—Transactions of the Asme, 122(3), pp. 544–556.
Haferl,  S., Butty,  V., Poulikakos,  D., Giannakouros,  J., Boomsma,  K., Megaridis,  C. M., and Nayagam,  V., 2001, “Freezing Dynamics of Molten Solder Droplets Impacting onto Flat Substrates in Reduced Gravity,” Int. J. Heat Mass Transf., 44(18), pp. 3513–3528.
Monti,  R., Savino,  R., and Tempesta,  S., 1998, “Wetting Prevention by Thermal Marangoni Effect. Experimental and Numerical Simulation,” Eur. J. Mech. B/Fluids, 17(1), pp. 51–77.
Cao,  C. D., Wang,  N., Wei,  B. B., and de Groh,  H. C., 1999, “Rapid Solidification of Ag-Si Eutectic Alloys in Drop Tube,” Prog. Nat. Sci., 9(9), pp. 687–695.
Khodadadi,  J. M., and Zhang,  Y., 2000, “Effects of Thermocapillary Convection on Melting within Droplets,” Numer. Heat Transfer, Part A, 37(2), pp. 133–153.
Song,  S. P., and Li,  B. Q., 2000, “Free Surface Profiles and Thermal Convection in Electrostatically Levitated Droplets,” Int. J. Heat Mass Transf., 43(19), pp. 3589–3606.
Ehrhard,  P., and Davis,  S. H., 1991, “Nonisothermal Spreading of Liquid-Drops on Horizontal Plates,” J. Fluid Mech., 229, pp. 365–388.
Braun,  R. J., Murray,  B. T., Boettinger,  W. J., and McFadden,  G. B., 1995, “Lubrication Theory for Reactive Spreading of a Thin Drop,” Phys. Fluids, 7(8), pp. 1797–1810.
Waldvogel,  J. M., and Poulikakos,  D., 1997, “Solidification Phenomena in Picoliter Size Solder Droplet Deposition on a Composite Substrate,” Int. J. Heat Mass Transf., 40(2), pp. 295–309.
den Boer, A. W. J. P., 1996, “Marangoni Convection: Numerical Model and Experiments,” doctoral thesis, Technische Universiteit Eindhoven, Eindhoven.
Fowler,  R. H., 1937, “A Tentative Statistical Theory of Macleod’s Equation for Surface Tension, and the Parachor,” Proc. R. Soc. London, Ser. A: Mathematical Physical and Engineering Sciences, , A159(896), pp. 229–246.
Jasper,  J. J., 1972, “The Surface Tension of Pure Liquid Compounds,” J. Phys. Chem. Ref. Data, 1(4), pp. 841–1009.
Born,  M., and Green,  H. S., 1947, “A General Kinetic Theory of Liquids,” Proc. R. Soc. London, Ser. A: Mathematical Physical and Engineering Sciences, , 190(1020), pp. 455–474.
Egry,  I., 1993, “On the Relation between Surface-Tension and Viscosity for Liquid-Metals,” Scr. Metall. Mater., 28(10), pp. 1273–1276.
Koke, J., 2001, “Rheologie Teilerstarrter Metalllegierunger,” doctoral thesis, RWTH Aachen, Aachen.
Thresh,  H. R., and Crawley,  A. F., 1970, “The Viscosities of Lead, Tin and Pb-Sn Alloys,” Metall. Trans., 1, pp. 1531–1535.
Keene,  B. J., 1993, “Review of Data for the Surface-Tension of Pure Metals,” Int. Mater. Rev., 38(4), pp. 157–192.
Schwaneke,  A. E., Falke,  W. L., and Miller,  V. R., 1978, “Surface-Tension and Density of Liquid Tin-Lead Solder Alloys,” J. Chem. Eng. Data, 23(4), pp. 298–301.
White,  D. W. G., 1971, “Surface Tensions of Pb, Sn, and Pb-Sn Alloys,” Metall. Trans., 2(11), pp. 3067–3071.
NIST, 2001, “Properties of Solder,” http://www.boulder.nist.gov/div853/lead%20free/part2.html#%202.2.5.
Carroll,  M. A., and Warwick,  M. E., 1987, “Surface-Tension of Some Sn-Pb Alloys.1. Effect of Bi, Sb, P, Ag, and Cu on 60sn-40pb Solder,” Mater. Sci. Technol., 3(12), pp. 1040–1045.
Landau, L. D., and Lifshitz, E. M., 1959, Fluid Mechanics, Pergamon Press, Oxford; New York, 6 , pp. 238–241.
Baer,  T. A., Cairncross,  R. A., Schunk,  P. R., Rao,  R. R., and Sackinger,  P. A., 2000, “A Finite Element Method for Free Surface Flows of Incompressible Fluids in Three Dimensions. Part Ii. Dynamic Wetting Lines,” Int. J. Numer. Methods Fluids, 33(3), pp. 405–427.
Bushko,  W., and Grosse,  I. R., 1991, “New Finite-Element Method for Multidimensional Phase-Change Heat-Transfer Problems,” Numer. Heat Transfer, Part B, 19(1), pp. 31–48.
Arafune,  K., Sugiura,  M., and Hirata,  A., 1999, “Investigation of Thermal Marangoni Convection in Low and High- Prandtl-Number Fluids,” J. Chem. Eng. Jpn., 32(1), pp. 104–109.
Bach,  P., and Hassager,  O., 1985, “An Algorithm for the Use of the Lagrangian Specification in Newtonian Fluid-Mechanics and Applications to Free-Surface Flow,” J. Fluid Mech., 152, pp. 173–190.

Figures

Grahic Jump Location
Comparison of different correlations for viscosity μ
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Sketch of the impingement process
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Maximum change of tangential vector
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Change of spreading with increasing droplet superheat (bold dotted line: constant viscosity and surface tension; thin dashed line: constant viscosity and variable surface tension; bold solid line: variable viscosity and surface tension): (a) T1,0=200°C; (b) T1,0=250°C; (c) T1,0=300°C; (d) T1,0=350°C; (e) T1,0=400°C; (f ) T1,0=450°C; and (g) T1,0=500°C.
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Spreading versus absolute Ma-number
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Vorticity and relative change in surface tension at time τ=0.3 for: (a) invariant; and (b) variant thermal properties (Ma=−49).
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(a) Illustration of spreading mechanism (left) and surface velocity vectors (right) at time τ=0.3; (b) vorticity field without Marangoni effect, τ=0.3; and (c) vorticity field with Marangoni effect, Ma=−49,τ=0.3.
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(a) Contact line freezing time versus absolute value of Ma-number; and (b) contact line freezing time versus superheat temperature.
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(a) Droplet spread radius; and (b) droplet top center of symmetry as a function of time τ.
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Evolution of surface temperature (a) and surface tension in time (b)
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Streamlines and isotherms in droplet at τ=0.6

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