Abstract
This study investigates the mechanisms that contribute to determining the maximum spreading of a liquid droplet impacting a solid surface in connection with splat-quench solidification. This paper defines two domains, the viscous dissipation domain and the surface tension domain, which are characterized by the Weber and the Reynolds numbers, and that are discriminated by the principal mechanism responsible for arresting the splat spreading. This paper illustrates the importance of correctly determining the equilibrium contact angle (a surface tension characteristic that quantifies the wetting of the substrate) for predicting the maximum spreading of the splat. Conditions under which solidification of the splat would or would not be expected to contribute to terminating the spreading of the splat are considered. However, our a priori assumption is that the effect of solidification on the spreading of a droplet, superheated at impact, is secondary compared to the effects of viscous dissipation and surface tension.
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Abbreviations
- a :
-
Thermal diffusivity
- C s :
-
Correction factor
- C v :
-
Correction factor
- d :
-
Initial diameter of droplet
- D :
-
Final diameter of splat
- E k :
-
Initial kinetic energy at impact
- E s :
-
Rise in surface tension energy
- E v :
-
Viscous energy dissipated
- s :
-
Terminal thickness of splat
- t c :
-
Spreading time of splat
- u :
-
Velocity of impinging droplet
- V :
-
Volume of splat (droplet)
- x :
-
Space variable
- κ:
-
Madejski's solidification parameter
- μ:
-
dynamic viscosity
- φ:
-
Dissipation function
- ϱ:
-
Density of liquid
- σ:
-
Liquid-vapour surface tension
- θe :
-
Equilibrium contact angle
- ξ:
-
D/d (spreading factor)
- Pe :
-
ud/a (Péclet number)
- Re :
-
ρud/μ (Reynolds number)
- We :
-
ρu 2d/σ (Weber number)
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Bennett, T., Poulikakos, D. Splat-quench solidification: estimating the maximum spreading of a droplet impacting a solid surface. Journal of Materials Science 28, 963–970 (1993). https://doi.org/10.1007/BF00400880
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DOI: https://doi.org/10.1007/BF00400880