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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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