Solidification phenomena in picoliter size solder droplet deposition on a composite substrate

Waldvogel, J.M.; Poulikakos, Dimos

doi:10.1016/0017-9310(96)00107-x

Cited by 140 publications

(82 citation statements)

References 14 publications

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“…In contrast, Madejski's method assumes that no energy losses occur in the initial spreading of the droplet. Figure 6 shows a comparison of the results of Madejski's model with those of Waldvogel et al (1996) Waldvogel et al (1996) shown in Figure 6, partly due to the higher Reynolds number and partly due to freezing. Figure 7 shows that Madejski's model predicts the freezing time reasonably well.…”

Section: Resultsmentioning

confidence: 98%

“…These results indicate that the modified Madejski's model of droplet spreading presented in this paper can be used to give reasonable predictions of maximum droplet diameter and minimum splat thickness. Zhao et al, 1996Waldvogel et al, 1996 Reynolds Weber This report describes the calculations done for predicting droplet speed and temperature at the moment of impact with a metallic substrate, for application to a droplet-based manufacturing project. Figure 1 shows a schematic of the experimental apparatus being used at UC Irvine for this project.…”

Section: Discussionmentioning

confidence: 99%

“…Some numerical analyses of the process of droplet spreading have heen presented to date Trapaga et al, 1992;Fukai et al, 1993;Fukai et al, 1995;Waldvogel et al, 1996;Zhao et al, 1996;Waldvogel and Poulikakos, 1997;. These solve for the continuity equation, for the Navier-Stokes equations, and for the'energy equation in the liquid and solid phases (and ideally in the substrate too).…”

Section: An Accuracy Evaluation For the Madejski Splat-mentioning

confidence: 99%

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High precision droplet based new form manufacturing

Aceves¹,

Hadjiconstantinou²,

Miller³

et al. 1999

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Section: Resultsmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

Section: An Accuracy Evaluation For the Madejski Splat-mentioning

confidence: 99%

See 1 more Smart Citation

High precision droplet based new form manufacturing

Aceves¹,

Hadjiconstantinou²,

Miller³

et al. 1999

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“…Later, Tsurutani et al (1990) and Trapaga and Szekely (1991) studied the impact of molten droplets in thermal spray processes. More studies were done by Sicilian and Hirt (1988), Kothe et al (1991), Brackbill et al (1992), Pasandideh-Fard et al (1996, Zhao et al (1996), Fukai et al (1995), Bertagnolli et al (1997), and Waldvogel and Poulikakos (1997). Moreover, Bussmann et al (1999Bussmann et al ( & 2000 developed a 3D model to simulate water droplet impacts and extended it to study metal droplet impacts.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Droplet Impact and Solidification Including Thermal Shrinkage in a Thermal Spray Process

Alavi¹,

Passandideh-Fard²

2011

Frontiers in Heat and Mass Transfer

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In this paper, a numerical study is performed to investigate the effects of thermal shrinkage on the deposition of molten particles on a substrate in a thermal spray process using the Volume-of-Fluid (VOF) method. Thermal shrinkage is a phenomenon caused by the variation of density during cooling and solidification of a molten metal. The Navier-Stokes equations along with the energy equation including phase change are solved using a 2D/axisymmetric mesh. The VOF method is used to track the free surface of molten particles, and an enthalpy-porosity formulation is used to model solidification. For the normal impact of tin particles in the order of 2 mm in diameter and 1 m/s in impact velocity, the final splat had a single cavity inside due to shrinkage. For cases with the scales of a typical thermal spray process, the effect of shrinkage appeared as a reduction in the droplet splashing on the substrate. Keywords INTRODUCTIONIn thermal spray processes, coatings such as various metals and alloys, carbides, and ceramics are applied to metal surfaces by a spray gun with a stream of oxyfuel flame, electric arc, or plasma arc. These coatings are formed by spraying and deposition of molten droplets on the substrate. The properties and quality of these coatings depend on many factors such as flame/laser/arc, material used for spraying, substrate material and its surface conditions, and spray characteristics. Another phenomenon that affects the shape of droplets in thermal spraying is thermal shrinkage. Because of their thermal expansion characteristics and changes in density, metals shrink or contract during solidification and cooling. Shrinkage, which causes dimensional changes and sometimes cracking, is the result of these three phases:a) Contraction of a molten metal as it cools prior to its solidification.b) Contraction of the metal during phase change from liquid to solid (release of the latent heat of fusion).c) Contraction of the solidified metal (casting) as its temperature drops to the ambient temperature.The shrinkage occurs because in most of the materials, the volume decreases due to an increase in density when the material undergoes solidification and cooling. Shrinkage can cause various defects in manufacturing processes. These defects can affect the appearance or even the structural integrity of the final product. Some examples are cavities, porosities, discontinuities such as cracks, defective surface, etc. In a thermal spray process, shrinkage has some effects on the deposition of droplets on the substrate and the formation of coating including porosity, cavity, curl-up of splat and surface depression.Developing a model to simulate impacts and solidification of molten droplets on to a substrate is a complex problem. It involves simultaneous computing of heat transfer and fluid flow in a droplet with a moving free surface. Adding phase change and density variation in this phenomenon makes the problem more complex. Modeling droplet impacts has a long history. Harlow and Shannon (1967) were the firs...

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“…The spreading of a droplet on a solid surface was quantified analytically assuming energy conservation in [3], [4], [5], while a detailed simulation of the phenomenon has been treated with the solution of the Navier-Stokes equations. Such methodologies are the Marker and Cell (MAC) by [6], [7], the Lagrangian formulation in a body fitted grid by [8], [9], [10], [11], [12], [13], the Immersed Boundary Method (IBM) by [14], [15], the Level-Set (LS) methodology by [16], the VOF methodology initially proposed by [17] and used in the works of [18], [19], [20], [21], [22], [23], [24]. In the aforementioned works the limiting conditions that separate the different regimes of the phenomenon were identified in the case of a droplet impact onto a wall and the maximum droplet spreading is estimated.…”

Section: Introductionmentioning

confidence: 99%

Single Droplet Impacts Onto Deposited Drops. Numerical Analysis and Comparison

et al. 2010

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Abstract. The impact of a spherical water droplet onto a stationary sessile droplet lying onto a solid wall is studied numerically using the VOF methodology. The governing Navier-Stokes equations are solved both for the gas and liquid phase coupled with an additional equation for the transport of the liquid interface. An unstructured numerical grid is used along with an adaptive local grid refinement technique, which enhances the accuracy of the numerical results along the liquid-gas interface and decreases the computational cost. The stationary sessile droplet has been created from the prior impact of one or two water droplets falling onto the solid wall, while two solid walls have been studied; an aluminium substrate and a glass substrate. The material of the wall plays an important role since it has an impact on the droplet's wetting behavior. The 2 numerical model is validated against corresponding experimental data presented in the first part of the present work [1], showing a good agreement. Furthermore, the numerical investigation sheds light into the governing physics of the phenomenon.

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Solidification phenomena in picoliter size solder droplet deposition on a composite substrate

Cited by 140 publications

References 14 publications

High precision droplet based new form manufacturing

High precision droplet based new form manufacturing

Numerical Simulation of Droplet Impact and Solidification Including Thermal Shrinkage in a Thermal Spray Process

Single Droplet Impacts Onto Deposited Drops. Numerical Analysis and Comparison

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