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Hollow droplets impacting onto a solid surface

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Abstract

The impact process of spherical hollow droplets impinging onto a solid surface has been experimentally studied. Formation of a counter-jet in a wide range of Reynolds and Weber numbers was revealed, this jet being similar to a Worthington jet. For characterizing the regime of liquid flow in the hollow droplet, we propose using the Euler number. Theoretically, the problem was treated using a simple model of axisymmetric liquid flow. The obtained results proved to be consistent with experimental data.

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Abbreviations

Eu = P g0/ρU 2p :

Euler number

Re = ρD p U p /μ :

Reynolds number

We = ρD p U 2p /σ :

Weber number

D cont :

Mean diameter of the circumference round which the droplet shell contacts the spreading liquid layer (m)

D p :

Droplet diameter (m)

D s :

Splat diameter (m)

E tot(t), E kin(t), E surf(t):

Total, kinetic, and surface energy of spreading droplet at time t (J)

E visc(t):

Viscous loss of energy in droplet flow by time t (J)

m p :

Droplet mass (kg)

P g0 :

Initial pressure in gas cavity (Pa)

t d = D p /U p :

Characteristic time of droplet deformation (s)

U p :

Droplet velocity (m/s)

U jet :

Counter-jet velocity (m/s)

u z, u r :

Vertical and radial velocities of liquid flow in spreading layer (m/s)

V tot(t):

Total liquid volume having entered the spreading layer by time t (m3)

V disk(t):

Liquid volume having entered the peripheral spreading disk by time t (m3)

μ :

Dynamic viscosity of liquid (Pa s)

ρ :

Liquid density (kg/m3)

σ :

Liquid surface tension (N/m)

Δp :

Droplet shell thickness (m)

δ p = Δp/D p :

Relative droplet shell thickness

β = (1 − 2δ p)3 :

Part of droplet volume occupied by gas

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Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Siberian Branch, Novosibirsk, 630090, Russia

    I. P. Gulyaev & O. P. Solonenko

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  1. I. P. Gulyaev
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  2. O. P. Solonenko
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Correspondence to I. P. Gulyaev.

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Gulyaev, I.P., Solonenko, O.P. Hollow droplets impacting onto a solid surface. Exp Fluids 54, 1432 (2013). https://doi.org/10.1007/s00348-012-1432-z

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  • DOI: https://doi.org/10.1007/s00348-012-1432-z

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