Zijing Ding

Three-dimensional dynamics of thin liquid films on vertical cylinders with Marangoni effect

The effects of thermocapillary force on the three dimensional dynamics of thin liquid films flowing down a uniformly heated vertical cylinder are investigated using a thin film model. Linear and nonlinear analyses predict the existence of a non-axisymmetric mode due to the Marangoni effect. Symmetry-breaking of axisymmetric steady traveling waves is observed when the Marangoni number exceeds a critical value. Linear stability analysis demonstrates that the steady traveling wave can be unstable to azimuthal disturbances due to the Marangoni effect, leading to the formation of non-axisymmetric patterns.

Viscous liquid films on a porous vertical cylinder: Dynamics and stability

In this paper, liquid films flowing down a porous vertical cylinder were investigated by an integral boundary layer model. Linear stability and nonlinear evolution were studied. Linear stability results of the integral boundary layer model were in good agreement with the linearized Navier-Stokes equations which indicated that the permeability of the porous medium enhanced the instability of the flow system. The growth rate and cut-off wave number increased with increasing the permeability and the Reynolds number. Linear stability analysis showed that the system was more unstable for a larger Reynolds number Re. Nonlinear studies showed that, for a very small Re, the film evolved with time while a saturated state was not observed. In addition, it was observed that the film ruptured when the permeability parameter beta > 0, and the rupture time decreased with increasing beta. However, for a moderate Reynolds number, a small finite harmonic disturbance evolved to a saturated traveling wave. Further investigation was conducted on the droplet-like wave solution. Results showed that the wave speed increased as the permeability parameter increased.

Stability of two immiscible leaky-dielectric liquids subjected to a radial electric field in an annulus duct

In this paper, we investigated the stability of a two coaxial leaky dielectric fluid system flowing in an annulus duct. A constant pressure gradient was applied to drive the flow in the duct. A radial electric field was imposed between the outer and inner surfaces of the duct. Linear stability analysis was employed to discuss the influences of electric field on the capillary and interface wave instabilities. The former instability is caused by surface tension and the latter is caused by viscosity stratification at the interface. It was found that, depending on the electrical permittivities and conductivities of the two liquids, the electric field either stabilized or destabilized the flow system. Apart from that, it was found that an external electric field could impede the capillary and interface wave instabilities. Influences of the inner radius of the duct, viscosity ratio, thickness ratio, and Reynolds number on the stability of the system were discussed as well.