Unsteady Motion of a Single Droplet in Surfactant Solutions

Abstract

Abstract: A numerical investigation of the unsteady motion of a deformed drop released freely in
another quiescent liquid contaminated by surfactant is presented in this paper. The finite
difference method was used to solve numerically the coupled time-dependent Navier-Stokes
and convective-diffusion equations in a body-fitted orthogonal coordinate system. Numerical
simulation was conducted on the experimental cases, in which MIBK drops with the size
ranging from 1.24 mm to 1.97 mm rose and accelerated freely in pure water and in dilute
sodium dodecyl sulphate (SDS) aqueous solution. The applicability of the numerical scheme
was validated by the agreement between the simulation results and the experimental data.
Both the numerical and experimental results showed that the velocitytime profile exhibited
a maximum rising velocity for drops in SDS solutions, which was close to the terminal
velocity in pure water, before it dropped down to a steady-state value. The effect of the
sorption kinetics of surfactant on the accelerating motion was also evaluated. It is also
suggested that introduction of virtual mass force into the formulation improved obviously
the precision of numerical simulation of transient drop motion.

Key words: surfactant, single drop, unsteady motion, sorption kinetics, numerical simulation

摘要： A numerical investigation of the unsteady motion of a deformed drop released freely in
another quiescent liquid contaminated by surfactant is presented in this paper. The finite
difference method was used to solve numerically the coupled time-dependent Navier-Stokes
and convective-diffusion equations in a body-fitted orthogonal coordinate system. Numerical
simulation was conducted on the experimental cases, in which MIBK drops with the size
ranging from 1.24 mm to 1.97 mm rose and accelerated freely in pure water and in dilute
sodium dodecyl sulphate (SDS) aqueous solution. The applicability of the numerical scheme
was validated by the agreement between the simulation results and the experimental data.
Both the numerical and experimental results showed that the velocitytime profile exhibited
a maximum rising velocity for drops in SDS solutions, which was close to the terminal
velocity in pure water, before it dropped down to a steady-state value. The effect of the
sorption kinetics of surfactant on the accelerating motion was also evaluated. It is also
suggested that introduction of virtual mass force into the formulation improved obviously
the precision of numerical simulation of transient drop motion.

关键词: surfactant;single drop;unsteady motion;sorption kinetics;numerical simulation

LI Xiaojin, MAO Zaisha, FEI Weiyang. Unsteady Motion of a Single Droplet in Surfactant Solutions[J]. .

李晓锦, 毛在砂, 费维扬. 表面活性剂溶液中单液滴的非稳态运动[J]. CIESC Journal.

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