Numerical simulation of liquid droplet solidification on substrates

A mathematical model describing the deformation and solidification behavior of liquid droplets impinging on substrates is presented. The mathematical model is numerically solved using a finite element method. In the experiment, a molten tin droplet (2.2–4.3 mm diameter) impacts copper, stainless steel and glass substrates at various preimpact velocities (1.4–4.0 m/s). The values of the heat transfer coefficient at the droplet/substrate interface are evaluated by comparing the calculated splat diameters to the experimental ones. The estimated values are within the previously reported ranges. The model almost predicts the Weber number dependence of the experimental splat diameters. The time variations of the numerical splat diameters also agree with the experimental results. The simulation reveals that the frozen layer at the splat edge, rather than at the center region, affects deceleration of the droplet spreading. The effect of the solidification on the splat diameter is explained from the freezing rate at the splat edge.

[1]  J. Fukai,et al.  Maximum spreading of liquid droplets colliding with flat surfaces , 1998 .

[2]  Albert Y. Tong,et al.  NUMERICAL STUDY ON THE SOLIDIFICATION OF LIQUID METAL DROPLETS IMPACTING ONTO A SUBSTRATE , 1997 .

[3]  Dimos Poulikakos,et al.  Transport Phenomena in Picoliter Size Solder Droplet Dispension , 1995 .

[4]  I. Doltsinis,et al.  Thermomechanical Simulation of the Splashing of Ceramic Droplets on a Rigid Substrate , 1997 .

[5]  Dimos Poulikakos,et al.  Modeling of the deformation of a liquid droplet impinging upon a flat surface , 1993 .

[6]  E. Matthys,et al.  Modelling of heat transfer and solidification during splat cooling : effect of splat thickness and splat/substrate thermal contact , 1991 .

[7]  J. Szekely,et al.  Fluid flow, heat transfer, and solidification of molten metal droplets impinging on substrates: Comparison of numerical and experimental results , 1992 .

[8]  D. Poulikakos,et al.  An Investigation of Key Factors Affecting Solder Microdroplet Deposition , 1998 .

[9]  D. Poulikakos,et al.  Solidification of Liquid Metal Droplets Impacting Sequentially on a Solid Surface , 1994 .

[10]  Takayuki Watanabe,et al.  Deformation and solidification of a droplet on a cold substrate , 1992 .

[11]  Dimos Poulikakos,et al.  Solidification phenomena in picoliter size solder droplet deposition on a composite substrate , 1997 .

[12]  Mutsuto Kawahara,et al.  A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme , 1983 .

[13]  Roger H. Rangel,et al.  Numerical simulation of substrate impact and freezing of droplets in plasma spray processes , 1993 .

[14]  J. Delplanque,et al.  An improved model for droplet solidification on a flat surface , 1997 .

[15]  Eric F. Matthys,et al.  Thermal analysis and measurements for a molten metal drop impacting on a substrate: cooling, solidification and heat transfer coefficient , 1995 .

[16]  W. Bushko,et al.  NEW FINITE ELEMENT METHOD FOR MULTIDIMENSIONAL PHASE CHANGE HEAT TRANSFER PROBLEMS , 1991 .

[17]  Roger H. Rangel,et al.  Numerical analysis of the deformation and solidification of a single droplet impinging onto a flat substrate , 1993 .

[18]  J. Madejski,et al.  Solidification of droplets on a cold surface , 1976 .

[19]  R. Rangel,et al.  Metal-droplet deposition model including liquid deformation and substrate remelting , 1997 .

[20]  Roger H. Rangel,et al.  Multidirectional solidification model for the description of micropore formation in spray deposition processes , 1996 .

[21]  Dimos Poulikakos,et al.  Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling , 1995 .

[22]  Javad Mostaghimi,et al.  Deposition of tin droplets on a steel plate: simulations and experiments , 1998 .

[23]  Dimos Poulikakos,et al.  Heat transfer aspects of splat-quench solidification: modelling and experiment , 1994 .

[24]  Guo-xiang Wang,et al.  Experimental Investigation of Interfacial Thermal Conductance for Molten Metal Solidification on a Substrate , 1996 .