Spherical-cap-shaped interfacial nanobubbles (NBs) forming on hydrophobic surfaces in aqueous solutions have extensively been studied both from a fundamental point of view and due to their relevance for various practical applications. In this study, the nucleation mechanism of spontaneously generated NBs at solid–liquid interfaces of immersed nanostructured hydrophobic surfaces is studied. Depending on the size and density of the surface nanostructures, NBs with different size and density were reproducibly and deterministically obtained. A two-step process can explain the NB nucleation, based on the crevice model, i.e., entrapped air pockets in surface cavities which grow by diffusion. The results show direct evidence for the spontaneous formation of NBs on a surface at its immersion. Next, the influence of size and shape of the nanostructures on the nucleated NBs are revealed. In particular, on non-circular nanopits we obtain NBs with a non-circular footprint, demonstrating the strong pinning forces at the three-phase contact line.

A second-order instability analysis has been performed for sinuous disturbances on two-dimensional planar viscous sheets moving in a stationary gas medium using a perturbation technique. The solutions of second-order interface disturbances have been derived for both temporal instability and spatial instability. It has been found that the second-order interface deformation of the fundamental sinuous wave is varicose or dilational, causing disintegration and resulting in ligaments which are interspaced by half a wavelength. The interface deformation has been presented; the breakup time for temporal instability and breakup length for spatial instability have been calculated. An increase in Weber number and gas-to-liquid density ratio extensively increases both the temporal or spatial growth rate and the second-order initial disturbance amplitude, resulting in a shorter breakup time or length, and a more distorted surface deformation. Under normal conditions, viscosity has a stabilizing effect on the first-order temporal or spatial growth rate, but it plays a dual role in the second-order disturbance amplitude. The overall effect of viscosity is minor and complicated. In the typical condition, in which the Weber number is 400 and the gas-to-liquid density ratio is 0.001, viscosity has a weak stabilizing effect when the Reynolds number is larger than 150 or smaller than 10; when the Reynolds number is between 150 and 10, viscosity has a weak destabilizing effect.

A linear instability analysis method has been used to investigate the breakup of an electrified viscoelastic liquid jet. The liquid is assumed to be a dilute polymer solution modeled by the linear viscoelastic constitutive equation. As for its electric properties, the liquid is assumed to be of perfect electrical conductivity. The axisymmetric and nonaxisymmetric disturbance wave growth rate has been worked out by solving the dispersion equation of an electrified viscoelastic liquid jet, which was obtained by combining the linear instability model of an electrified Newtonian liquid jet with the linear viscoelastic model. The maximum growth rate and corresponding dominant wavenumbers have been observed. The electrical Euler number, non-Newtonian rheological parameters and some flow parameters have been tested for their influence on the instability of the electrified viscoelastic liquid jet. The results show that the disturbance growth rate of electrified viscoelastic liquid jets is higher than that of Newtonian ones for axisymmetric mode disturbance and almost the same for the nonaxisymmetric mode. The growth rate of the axisymmetric mode is greater than that of the nonaxisymmetric mode for large wavenumbers, and the trend is opposite in the small wavenumber range. The ratio of gas to liquid density, electrical Euler number, and elasticity number can accelerate the breakup of the electrified viscoelastic liquid jet for both modes. The increase of the time constant ratio, zero shear viscosity, and jet radius can decrease the growth rate of the axisymmetric mode; however, their effects on the nonaxisymmetric mode are different. As for the effect of surface tension and jet velocity, there is a critical value. The variation trend is opposite when the surface tension or jet velocity is larger or smaller than the critical value.

The stability of a thin viscoelastic film of Oldroyd-B fluid falling down an incline is investigated. In the weak viscoelasticity limit, a reduced model is derived using the weighted residual techniques, which consists of two coupled equations for the film thickness and local flow rate. Through the normal mode analysis, temporal growth rates and neutral stability curves are calculated to explore linear stability of the film. Results show that the viscoelasticity acts to destabilize the film and decrease the phase speed of linear waves. Good agreement is found between the reduced model and full linearized equations solved by the Chebyshev spectral collocation method when viscoelastic effect is relatively weak. Nonlinear traveling waves are further determined. The speed of fast/slow-wave families is promoted/reduced in the presence of the viscoelasticity, resulting in a dispersion effect on the system; while the wave amplitudes are augmented for both fast and slow waves. Besides, the temporal evolution of surface waves is numerically resolved, which validates the linear prediction of the instability threshold. Steady permanent waves are observed in the final stage; the surface deformation and perturbation energy are enhanced by the viscoelasticity as expected.

The stability of a thin film of Walters-type B″ viscoelastic fluid flowing down a heated inclined plane is investigated. Both the weighted residual method (WRM) and the Benney-type equation (BE) are derived to simplify the original two-dimensional problem. Normal mode analysis is conducted to determine the instability threshold. We also employ the Chebyshev spectral collocation method to solve the eigenvalue problem of the full linearized Navier-Stokes/energy equations, which provides a technique to test the performance of the analytical approximations. The self-similar velocity and temperature profile assumptions made in WRM are validated by a spectral method. The results show that WRM and BE yield the same expression for the critical Reynolds number, which is in agreement with the full equations. The effects of the viscoelastic parameter, Marangoni number, and Biot number are discussed. Both heating and viscoelasticity are found to destabilize the flow, while a critical value of the Biot number is determined at which the flow is the most unstable. Nonlinear simulations are further conducted based on the method of lines, which support the predictions of instability threshold using the linear theory.