An implicit surface tension model for the analysis of droplet dynamics

A study of the normal impact of liquid droplets on a dry horizontal substrate is presented in this paper. The impact dynamics, spreading and recoil behavior are captured using a high-speed digital video camera at 2000 frames per second. A digital image processing software was used to determine the drop spread and height of the liquid on the surface from each frame. To ascertain the effects of liquid viscosity and surface tension, experiments were conducted with four liquids (water, ethanol, propylene glycol and glycerin) that have vastly different fluid properties. Three different Weber numbers (20, 40, and 80) were considered by altering the height from which the drop is released. The high-speed photographs of impact, spreading and recoil are shown and the temporal variations of dimensionless drop spread and height are provided in the paper. The results show that changes in liquid viscosity and surface tension significantly affect the spreading and recoil behavior. For a fixed Weber number, lower surface tension promotes greater spreading and higher viscosity dampens spreading and recoil. Using a simple scale analysis of energy balance, it was found that the maximum spread factor varies as Re1/5 when liquid viscosity is high and viscous effects govern the spreading behavior.

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On the classification of solutions to the zero-surface-tension model for Hele-Shaw free boundary flows

Quarterly of Applied Mathematics ◽

10.1090/qam/1247441 ◽

1993 ◽

Vol 51 (4) ◽

pp. 777-789 ◽

Cited By ~ 29

Author(s):

Y. E. Hohlov ◽

S. D. Howison

Keyword(s):

Surface Tension ◽

Free Boundary ◽

Classification Of Solutions ◽

Surface Tension Model

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Spreading-Droplet Simulation With Surface Tension Model Using Inter-Particle Force in Particle Method

Volume 7A: Fluids Engineering Systems and Technologies ◽

10.1115/imece2013-62542 ◽

2013 ◽

Cited By ~ 2

Author(s):

Eiji Ishii ◽

Taisuke Sugii

Keyword(s):

Surface Tension ◽

Contact Angle ◽

Dynamic Contact Angle ◽

Particle Method ◽

Dynamic Contact ◽

Contact Angles ◽

Particle Methods ◽

Static Contact ◽

Particle Force ◽

Surface Tension Model

Predicting the spreading behavior of droplets on a wall is important for designing micro/nano devices used for reagent dispensation in micro-electro-mechanical systems, printing processes of ink-jet printers, and condensation of droplets on a wall during spray forming in atomizers. Particle methods are useful for simulating the behavior of many droplets generated by micro/nano devices in practical computational time; the motion of each droplet is simulated using a group of particles, and no particles are assigned in the gas region if interactions between the droplets and gas are weak. Furthermore, liquid-gas interfaces obtained from the particle method remain sharp by using the Lagrangian description. However, conventional surface tension models used in the particle methods are used for predicting the static contact angle at a three-phase interface, not for predicting the dynamic contact angle. The dynamic contact angle defines the shape of a spreading droplet on a wall. We previously developed a surface tension model using inter-particle force in the particle method; the static contact angle of droplets on the wall was verified at various contact angles, and the heights of droplets agreed well with those obtained theoretically. In this study, we applied our surface tension model to the simulation of a spreading droplet on a wall. The simulated dynamic contact angles for some Weber numbers were compared with those measured by Šikalo et al, and they agreed well. Our surface tension model was useful for simulating droplet motion under static and dynamic conditions.

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Solder Joint Formation in Surface Mount Technology—Part II: Design

Journal of Electronic Packaging ◽

10.1115/1.2904370 ◽

1990 ◽

Vol 112 (3) ◽

pp. 219-222 ◽

Cited By ~ 11

Author(s):

S. M. Heinrich ◽

N. J. Nigro ◽

A. F. Elkouh ◽

P. S. Lee

Keyword(s):

Surface Tension ◽

Solder Joint ◽

Solder Joints ◽

Cross Sectional Area ◽

Surface Mount Technology ◽

Sectional Area ◽

Cross Sectional ◽

Joint Formation ◽

Surface Mount ◽

Surface Tension Model

In this paper dimensionless design curves relating fillet height and length to joint cross-sectional area are presented for surface-mount solder joints. Based on an analytical surface tension model, the advantage of these dimensionless curves is that they may be used for arbitrary values of solder density and surface tension. The range of applicability of previously developed approximate formulae for predicting joint dimensions is also investigated. A simple example problem is included to illustrate the use of both the design curves and the approximate formulae.

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