The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.

Particles dispersion on fluid-liquid interfaces

This paper is concerned with the dispersion of particles on the fluid-liquid interface. In a previous study we have shown that when small particles, e.g., flour, pollen, glass beads, etc., contact an air-liquid interface, they disperse rapidly as if they were in an explosion. The rapid dispersion is due to the fact that the capillary force pulls particles into the interface causing them to accelerate to a large velocity. In this paper we show that motion of particles normal to the interface is inertia dominated; they oscillate vertically about their equilibrium position before coming to rest under viscous drag. This vertical motion of a particle causes a radially-outward lateral （secondary） flow on the interface that causes nearby particles to move away. The dispersion on a liquid-liquid interface, which is the primary focus of this study, was relatively weaker than on an air-liquid interface, and occurred over a longer period of time. When falling through an upper liquid the particles have a slower velocity than when falling through air because the liquid has a greater viscosity. Another difference for the liquid-liquid interface is that the separation of particles begins in the upper liquid before the particles reach the interface. The rate of dispersion depended on the size of the particles, the densities of the particle and liquids, the viscosities of the liquids involved, and the contact angle. For small particles, partial pinning and hysteresis of the three-phase contact line on the surface of the particle during adsorption on liquid-liquid interfaces was also important. The frequency of oscillation of particles about their floating equilibrium increased with decreasing particle size on both air-water and liquid-liquid interfaces, and the time to reach equilibrium decreased with decreasing particle size. These results are in agreement with our analysis.