1) The document describes numerical simulations and experiments of droplet impacts on highly viscous liquid basins. It studies how varying the viscosity ratio between the droplet liquid and basin liquid affects the impact dynamics, allowing for a transition from liquid/liquid impact to liquid/solid impact. 2) Experiments were conducted with ethanol droplets impacting on a honey basin, with the honey having a much higher viscosity than the ethanol. Decreasing the air pressure above the impact was found to suppress splashing. 3) Numerical simulations using the Gerris code were able to qualitatively and quantitatively match the experiments. Increasing the viscosity ratio over 5000 caused the basin to behave similarly to a solid surface during impact.

1. Droplet impact on a highly viscous liquid basin
Zhen JIAN∗
, Guy-Jean Michon, Christophe Josserand, St´ephane Zaleski & Pascal Ray
Institut Jean Le Rond D’Alembert, CNRS & UPMC, UMR 7190, 4 place Jussieu, 75005 Paris, France
jian@dalembert.upmc.fr
Ethanol drop impacting on honey basin under different air background pressures
d0 = 3.6 ± 0.1 mm, U0 = 4 ± 0.04 m · s−1
, ∆t = 0.2ms; top: 1.01325 × 105
Pa (SAP), bottom: 21325 Pa (1/5 SAP)
Proposed numerical model
• Simulation with the code Gerris
• Variation of ρ and γ in mixed liquid area neglected
• ρ(c1) = c1ρl + (1 − c1)ρg, γ = constant
• Viscosity of the system:
µ(c1, c2) = c1c2µl2 + c1(1 − c2)µl1 + (1 − c1)µg
c1, c2: volume fraction, liquid 1, liquid 2 and gas.
• Liquid-viscosity ratio ml = µl2/µl1 (µl1: normal liquid):
measure viscosity deviation from normal liquid
• r = ρg/ρl1, m = µg/µl1: control properties of normal liquid
Numerical setup
Axisymmetric
Semi-circular drop:
normal liquid,
initial U0, without gravity
Basin:
highly-viscous liquid
VOF tracers:
T : distinguish L/S,
Tl : track drop,
Tls : track liquid basin
γ
γ
D
U0
ρl1, µl1
ρl2, µl2
ρg, µg
r
z
0
h
d
T
Tl
Tls
Physical parameters in simulations
ρ∗
l1 ρ∗
l2 ρ∗
g µ∗
l1 µ∗
l2 µ∗
g γ∗ U∗
0 D∗ d∗ h∗
1 1 0.001 0.001 0.001ml 0.0001 0.0027 1 1 0.5 0.1
Continuous transition from L/L impact to L/S impact by varying liquid-viscosity ratio ml = µl2/µl1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
z/D
r/D
t=0
t=0.04
t=0.05
t=0.07
t=0.09
t=0.11
t=0.20
t=0.30
t=0.90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
z/D
r/D
t=0
t=0.04
t=0.05
t=0.07
t=0.11
t=0.20
t=0.30
t=0.90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
z/D
r/D
t=0
t=0.04
t=0.05
t=0.07
t=0.09
t=0.11
t=0.20
t=0.30
t=0.90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
z/D
r/D
t=0
t=0.04
t=0.05
t=0.07
t=0.09
t=0.11
t=0.20
t=0.30
t=0.90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
z/D
r/D
t=0
t=0.04
t=0.05
t=0.07
t=0.09
t=0.11
t=0.20
t=0.30
t=0.90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
z/D
r/D
t=0
t=0.04
t=0.05
t=0.07
t=0.09
t=0.11
t=0.20
t=0.30
t=0.90
ml = 1 ml = 5 ml = 20 ml = 50 ml = 500 ml = 10000
Interface evolution in time for different liquid-viscosity ratio ml
Physical properties
Drops : Ethanol Basin : Honey of Acacia ml = 7407.4
Physical parameters in experiments and simulations∗
ρl ρg µethanol µhoney
R 789 kg · m−3 1 kg · m−3 0.0027 Pa · s 20 Pa · s
Dl 1 1.267 × 10−3 2.376 × 10−3 0.8802
µg γ U0 D
R 1.8444 × 10−5 Pa · s 0.0224 N · m−1 4 m · s−1 3.6 mm
Dl 1.623 × 10−6 4.929 × 10−4 1 1
∗:R denotes real parameters, Dl denotes dimensionless parameters
Manipulation setup
• Drops generated by a syringe system with different diameters.
• Stepping-motor system to insure reproducible diameter of drops.
• Drops released from rest in a vacuum chamber.
• Impact velocity controlled by changing initial falling height.
• Gas pressure in the vacuum chamber varied from ambient to low pressures by a pump system.
• Ultra-high-speed camera (Photron FASTCAM SA5 model 1000K-M1) to record impact dynamics.
• Record rate is 10000 fps ⇔ temporal distinction of 0.1 ms.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7 8
z(mm)
r(mm)
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7 8
z(mm)
r(mm)
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7 8
z(mm)
r(mm)
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7 8
z(mm)
r(mm)
Qualitative (top and middle) and quantitative (bottom) comparison of photographs (top) with simulations (middle) of an ethanol drop impacting on a honey basin
under the standard atmospheric pressure pg = 1.01325 × 105
Pa, d0 = 3.6 mm, U0 = 4 m · s−1
, ∆t = 0.1ms
Conclusion
A numerical model is proposed to deal with the three-phase impact dynamics, of which a droplet of normal liquid impacts on a highly viscous liquid basin. Viscous effect is dominant as compared
to the inertial and surface tension effects during the dynamics. By varying liquid viscosity ratio ml = µbasin/µdroplet,normal, a continuous transition from L/L impact to L/S impact can be
achieved. For highly-viscous liquid (ml > 5000), the basin performs as a solid substrate. Experiments of ethanol drop impacting on honey basin is executed. The honey basin performs as a solid
and the complete suppression of splash by decreasing the gas pressure is observed. Agreement of the drop shapes predicted by our simulations with the experiments is encouraging.