Spreading of a Droplet on Surface of an Immiscible Liquid with High Viscosity Ratios

doi:10.19596/j.cnki.1001-246x.8421

Abstract

Abstract:

A mathematical model of droplet spreading on surface of an immiscible liquid based on lubrication approximation was used. Influence of viscosity ratio on evolution and equilibrium state of droplet at high viscosity ratios was investigated. Crucial parameters including droplet thickness and spreading radius were examined. It shows that deformation of the liquid-liquid interface near the contact line is affected by the viscosity ratio and the surface tension ratio; Increase of viscosity ratio reduces the spreading rate and the time constant, thereby, prolongs the spreading evolution. It does not affect the final stable shape of the droplet; Relation between spreading radius and time satisfies x_max= 1 - 0.2 exp(- βt). Inertial oscillation does not appear at the final stage of droplet spreading in the case of high viscosity ratios.

Key words: liquid lens, high viscosity ratio, immiscible liquid, spreading properties

Jiaming TONG, Chunxi LI, Haozhe SU, Xuemin YE. Spreading of a Droplet on Surface of an Immiscible Liquid with High Viscosity Ratios[J]. Chinese Journal of Computational Physics, 2022, 39(3): 318-326.

Figures/Tables 12

Fig.1 A two-dimensional sketch of an equilibrium liquid lens

Fig.2 Steady lens shapes at σ = 0.5, 1.0 and 2.0

Fig.3 Evolution of liquid lens at (a) early-stage: t = 0.05, 0.1, 0.2; (b) late-stage: t = 1, 10, 100

Fig.4 Deformation degree of liquid-liquid interface with σ = 0.5, 1.0 and 2.0 at different times

Fig.5 Deformation degree of liquid-liquid interface with μ = 0.5, 1.0 and 2.0 at different times

Fig.6 (a) Temporal evolution of (h2- h1)max and xmax; (b) Effect of μon the balance time and balance position of lens; (c) Effect of μ on us at the same position

Fig.7 Effect of μon the temporal evolution of θ1 and θ2

Fig.8 Log-log plot of temporal evolution of spreading radius with different viscosity ratio μ

Fig.9 (h2- h1)max in experiment and calculation

Fig.10 xmax in experiment and calculation

Fig.11 Temporal evolutions of the maximal lens thickness at different viscosity ratio μ

Fig.12 Temporal evolution of the maximal lens thickness and spreading radius at μ = 0.1

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