The instabilities of thermocapillary–buoyancy convection in droplet migration are examined by linear stability analysis. The droplet is flattened by gravity and placed on a unidirectional heated solid surface. The velocity and temperature distributions of basic flow are derived as a function of the migration velocity and the Bond number. The critical Marangoni number is obtained, which depends on the Prandtl number (Pr), the Bond number, and the migration velocity. The preferred modes at small and moderate Pr are oblique waves, which travel either upstream or downstream. For high Pr, the preferred modes include oblique and streamwise waves, while the amplitude of temperature on the surface is much smaller than that of the hot spot in the flow region. The instability mechanism is discussed and comparisons are made with liquid layers.

The thermocapillary instabilities of the liquid layers on an inclined plane with zero heat flux are examined by linear stability analysis. There is an angle between the gravity and the thermocapillary force. The basic flow depends on the ratio of the gravity effect to thermocapillary effect. When the ratio is positive, the gravity always increases the velocity and destabilizes the flow. When the ratio is negative, the influence of gravity on the flow stability depends on the Prandtl (Pr) number. At high and moderate Pr, the critical Marangoni number always decreases with the ratio. The vertical convection is the key to the instability mechanism at high Pr, while the horizontal convection is dominant at moderate Pr. By contrast, at small Pr, the critical Marangoni number has a maximum and the energy from the basic flow is important for the perturbation energy.

Rough surfaces have been widely considered as negative factors affecting cavitation erosion resistance. However, this study presented the opposite result. Here, 316L stainless steel substrates and the arc-sprayed 316L stainless steel coatings were subjected to a specific grinding process that introduced scratches on the surfaces. The surface hardness values of these ground specimens were measured to evaluate the influence of the grinding-induced strain hardening. The cavitation erosion performance of the specimens was evaluated. The results showed that rough surfaces with scratches could enhance the cavitation erosion resistance, particularly at the early stage of cavitation erosion. The scratches had a greater effect on the cavitation erosion resistance of the coatings than on the substrates. Moreover, rough surfaces with initial surface scratches could extend the incubation period of the 316L stainless steel substrates due to the inhibition of the plastic deformation. The SEM observation showed that the scratch structure of the coating surface inhibited the growth of cracks and the propagation of cavitation pits. This study could also serve as a reference for investigating the cavitation erosion behaviors of materials with a particular surface feature.

The nonlinear waves in a sheared liquid film on a horizontal plate at small Reynolds numbers are examined by theoretical and numerical approaches. The analysis employs the long-wave approximation along with finite difference schemes. The results show that the surface tension can suppress disturbances and prevent the occurrence of singularities. While the film flow is driven by the shear stress on the interface, its instability highly depends on the magnitude and direction of gravity. Specifically, when the direction of gravity is opposite to the wall-normal direction, perturbations are stabilized by gravity. In contrast, when these two directions are the same, the gravitational force is destabilizing, and stationary travelling waves can exist if a balance is reached between the effects of gravity and surface tension. For the steady solitary waves, there are quasi-periodic oscillations occurring between two stationary points, indicating the presence of heteroclinic trajectories. For periodic waves, the evolutions are sensitive to several parameters and initial disturbances, while one steady-state wave exhibits a sine function-like behaviour.