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Solidification contact angles of molten droplets deposited on solid surfaces

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Abstract

Droplet impact and equilibrium contact angle have been extensively studied. However, solidification contact angle, which is the final contact angle formed by molten droplets impacting on cold surfaces, has never been a study focus. The formation of this type of contact angle was investigated by experimentally studying the deposition of micro-size droplets (∼39 μm in diameter) of molten wax ink on cold solid surfaces. Scanning Electron Microscope (SEM) was used to visualize dots formed by droplets impacted under various impact conditions, and parameters varied included droplet initial temperature, substrate temperature, flight distance of droplet, and type of substrate surface. It was found that the solidification contact angle was not single-valued for given droplet and substrate materials and substrate temperature, but was strongly dependent on the impact history of droplet. The angle decreased with increasing substrate and droplet temperatures. Smaller angles were formed on the surface with high wettability, and this wetting effect increased with increasing substrate temperature. Applying oil lubricant to solid surfaces could change solidification contact angle by affecting the local fluid dynamics near the contact line of spreading droplets. Assuming final shape as hemispheres did not give correct data of contact angles, since the final shape of deposited droplets significantly differs from a hemispherical shape.

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Abbreviations

C p :

Specific heat of droplet

D :

Diameter of spherical droplet

G :

Shear modulus of substrate

h :

Height of sessile droplet

H :

Elastic displacement of viton surface

k 0 :

Thermal conductivity of substrate

k c :

Thermal conductivity of substrate coating

k d :

Thermal conductivity of droplet

l :

Thickness of substrate coating

L :

Flight distance of droplet

L f :

Latent heat of fusion of droplet

R c :

Thermal resistance of substrate coating

R d :

Thermal resistance of droplet

t :

Time

t solid :

Solidification time scale of droplet

t spr :

Spreading time scale of droplet

T d :

Droplet temperature upon impact

T j :

Jetting temperature

T m :

Droplet melting temperature

T s :

Substrate temperature

U :

Velocity of droplet upon impact

X :

Thickness of solidified layer

α0 :

Thermal diffusivity of substrate

αd :

Thermal diffusivity of droplet

θc :

Calculated contact angle of sessile droplet

θe :

Equilibrium contact angle

θl :

Contact angle measured on the left of photographs

θr :

Contact angle measured on the right of photographs

θs :

Solidification contact angle

λ:

Parameter defined in Eq. 7

μ:

Viscosity of droplet

ρ:

Density of droplet

σ:

Surface tension of droplet

Ca:

μ U/σ (Capillary number)

Pr:

μ C p /k d (Prandtl number)

Re:

ρ UD/μ (Reynolds number)

Ste:

C p (T m−T s)/L f (Stefan number)

We:

ρ U 2 D/σ (Weber number)

β:

(T d−T m)/(T m−T s) (Superheat parameter)

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Acknowledgements

The authors greatly thank Dr. Stephan Drappel from Xerox Research Centre of Canada for his help and discussion. The authors are indebted to Chris Wagner and Bradley Gerner from Xerox Corporation for their assistance in setting up the jetting fixture and to David Gervasi from Xerox Corporation for the viton coating. This work is supported by Xerox Foundation and Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada, M5S3G8

    Ri Li, Nasser Ashgriz & Sanjeev Chandra

  2. Xerox Corporation, Wilson Center for Research and Technology, 800 Phillips Rd. M/S 114-44D, Webster, NY, 14580, USA

    John R. Andrews

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  1. Ri Li
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  2. Nasser Ashgriz
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  3. Sanjeev Chandra
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Correspondence to Nasser Ashgriz.

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Li, R., Ashgriz, N., Chandra, S. et al. Solidification contact angles of molten droplets deposited on solid surfaces. J Mater Sci 42, 9511–9523 (2007). https://doi.org/10.1007/s10853-007-1757-9

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  • DOI: https://doi.org/10.1007/s10853-007-1757-9

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