The dynamic behavior of droplets impacting cylindrical superhydrophobic surfaces with different structures (azimuthal groove, axial groove, pillar) is studied in this work. The rebound and splash thresholds with different structures were also proposed, which depended on D/D₀ (where D is the ratio of cylinder diameter and D₀ is the initial droplet diameter) and the surface structure of the substrate. Based on the energy conservation approach, a complete rebound threshold semi-empirical model is constructed for cylindrical superhydrophobic surfaces. The recovery coefficient is used to measure the energy loss during the droplet impacting the superhydrophobic cylindrical surface. At the same time, the energy loss was significant on the cylindrical superhydrophobic surface with different structures, and the surface structure of the substrate played a vital role in the energy loss of the collision process. Then a prediction formula for the maximum spread diameter on the cylindrical superhydrophobic surface with different structures is presented to understand the droplet collision behavior further. In addition, a level wing-like splash morphology could reduce contact time on grooved superhydrophobic surfaces. Based on the contact time as a function of the Weber number, the azimuthal grooved structure surface has the least contact time.

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 oscillatory Kelvin–Helmholtz (K–H) instability of a planar liquid sheet was experimentally investigated in the presence of an axial oscillating gas flow. An experimental system was initiated to study the oscillatory K–H instability. The surface wave growth rates were measured and compared with theoretical results obtained using the authors’ early linear method. Furthermore, in a larger parameter range experimentally studied, it is interesting that there are four different unstable modes: first disordered mode (FDM), second disordered mode (SDM), K–H harmonic unstable mode (KHH) and K–H subharmonic unstable mode (KHS). These unstable modes are determined by the oscillating amplitude, oscillating frequency and liquid inertia force. The frequencies of KHH are equal to the oscillating frequency; the frequency of KHS equals half the oscillating frequency, while the frequencies of FDM and SDM are irregular. By considering the mechanism of instability, the instability regime maps on the relative Weber number versus liquid Weber number (We_rel–We_l) and the Weber number ratio versus the oscillating frequency (We_rel/We_l– $\varOmega$ _s2) were plotted. Among these four modes, KHS is the most unexpected: the frequency of this mode is not equal to the oscillating frequency, but the surface wave can also couple with the oscillating gas flow. Linear instability theory was applied to divide the parameter range between the different unstable modes. According to linear instability theory, K–H and parametric unstable regions both exist. However, note that all four modes (KHH, KHS, FDM and SDM) corresponded primarily to the K–H unstable region obtained from the theoretical analysis. Nevertheless, the parametric unstable mode was also observed when the oscillating frequency and amplitude were relatively low, and the liquid inertia force was relatively high. The surface wave amplitude was small but regular, and the evolution of this wave was similar to that of Faraday waves. The wave oscillating frequency was half that of the surface wave.

Micro-thrusters based on the mechanism of electro-atomization are widely used in space engines and play an important role in spacecraft power supply and attitude adjustment. However, current research on the dynamic characteristics of electro-atomization is focused on a steady electric field, and the effect of an alternating electric field is helpful in order to realize the attitude adjustment of the micro-thruster pulse working mode and the self-neutralization of a plume by alternating polarity. For this reason, this work focuses on experimental investigation; the oscillation behavior of a Taylor cone under an alternating electric field excitation has also been systematically examined. Using a high-speed camera, the pulsating modes of a Taylor cone under the disturbance of a continuous sinusoidal waveform and a single pulse waveform were recorded, and the responses of different oscillation modes and geometric characteristics to different disturbance parameters analyzed and discussed. This research has shown that the oscillation of a Taylor cone under a continuous sinusoidal waveform disturbance can be divided into six different modes; the dynamic characteristics of each mode are discussed, and each mode has been assigned its own unique matching relationship for different disturbance parameters. The three-dimensional distribution phase diagrams of the six modes were drawn after the relevant parameters were made dimensionless. Under the disturbance of a single pulse waveform, the geometric oscillation of the Taylor cone displayed a specific law: the oscillation period of the diameter and cone angle was consistent and showed a strong correlation with the charge relaxation time of the liquid.

Pressure fluctuation produced in liquid rocket engines affects atomization of the annular liquid jet in the combustion chamber. A linear stability analysis of an annular liquid jet under acoustic oscillations was conducted in this work. Parametric instability was applied to study the problem, and the oscillations of the gas velocity were considered. The Floquet theory was used to solve the disturbance, from which the dispersion equation containing the coefficients of the infinite order matrix was derived; the order of the coefficient matrix affected the accuracy of the results. There were several unstable regions in the wavenumber range, obtained by solving the dispersion matrix. When the gas velocity oscillated, the amplitude of the surface wave displacement also oscillated. In various unstable regions, the growth of the surface wave of the annular liquid sheet was also different, but the crest never passed through the equilibrium position, which was more complicated than in the planar liquid sheet. Increasing oscillation frequency contributed to an increase in the wavenumber corresponding to the unstable area. Increasing the oscillation amplitude increased the maximum growth rate. The effect of physical parameters on the instability of the annular liquid jet was also discussed.

When combustion instability occurs—in addition to periodic change in the nozzle flow rate caused by pressure oscillation—the instability of the liquid sheet is also affected by pressure oscillation, reflected mainly in oscillation of the internal parameters of the fluid. In this work, the parametric instability of a liquid sheet under a standing wave acoustic field was studied theoretically, and the influence of acoustic parameters on the instability of a liquid sheet was analyzed. It was found that sinuous and varicose modes were coupled in the subharmonic region. Atomization characteristics of slit nozzles under a standing wave acoustic field were studied experimentally; the effects of acoustic pressure and injector position were analyzed with respect to the acoustic field on atomization characteristics and the characteristics of nozzles in the critical state. It was found that under the same acoustic pressure, the effect of the acoustic field at the velocity antinode (VAN) was stronger than the effect at the acoustic intensity antinode (IAN), and there was little effect at the acoustic pressure antinode. There was also a critical value of acoustic pressure: when the pressure threshold was exceeded, Faraday waves were motivated at VAN and IAN. An interesting phenomenon is that the frequency of the surface wave is the same as the acoustic frequency, but the Faraday wave was found to be subharmonic rather than harmonic. The effect of flow rate on atomization characteristics was analyzed. The wavelength of the Faraday wave and breakup length of the liquid sheet were well in accord with the theoretical wavelength calculated in the analysis of liquid sheet instability.