We study numerically the nonlinear stationary states of a droplet covered with an insoluble surfactant in a uniaxial extensional flow. We calculate both the eigenfunctions to reveal the instability mechanism and the time-dependent states resulting from it, which provides a coherent picture of the phenomenon. The transition is of the saddle-node type, both with and without surfactant. The flow becomes unstable under stationary linear perturbations. Surfactant considerably reduces the interval of stable capillary numbers. Inertia increases the droplet deformation and decreases the critical capillary number. In the presence of the surfactant monolayer, neither the droplet deformation nor the stability is significantly affected by the droplet viscosity. The transient state resulting from instability is fundamentally different for drops with and without surfactant. Tip streaming occurs only in the presence of surfactants. The critical eigenmode leading to tip streaming is qualitatively the same as that yielding the central pinching mode for a clean interface, which indicates that the small local scale characterizing tip streaming is set during the nonlinear droplet deformation. The viscous surface stress does not significantly affect the droplet deformation and the critical capillary number. However, the damping rate of the dominant mode considerably decreases for viscous surfactants. Interestingly, shear viscous surface stress considerably alters the tip streaming arising in the supercritical regime, even for very small surface viscosities. The viscous surface stresses alter the balance of normal interfacial stresses and affect the surfactant transport over the stretched interface.

The commercial Computational Fluid Dynamics (CFD) software STAR-CCM+ was used to simulate the flow and breakup characteristics of a Liquid Jet Injected into the gaseous Crossflow (LJIC) under real engine operating conditions. The reasonable calculation domain geometry and flow boundary conditions were obtained based on a civil aviation engine performance model similar to the Leap-1B engine which was developed using the GasTurb software and the preliminary design results of its low-emission combustor. The Volume of Fluid (VOF) model was applied to simulate the breakup feature of the near field of LJIC. The numerical method was validated and calibrated through comparison with the public test data at atmospheric conditions. The results showed that the numerical method can capture most of the jet breakup structure and predict the jet trajectory with an error not exceeding ±5%. The verified numerical method was applied to simulate the breakup of LJIC at the real engine operating condition. The breakup mode of LJIC was shown to be surface shear breakup at elevated condition. The trajectory of the liquid jet showed good agreement with Ragucci’s empirical correlation.

The effect of a relationship separation on wellbeing is substantial. However, without divorce parameters, individuals in dating or cohabiting relationships may struggle to access support mechanisms. A systematic review was conducted to identify controlled trials of interventions targeting individuals who have experienced a non-marital relationship separation, to supplement the divorce literature. The aim of the review was to assess the impact of these interventions on mental health. Five articles were identified through PsycINFO, PsycARTICLES and Medline databases. Overall, two of the trials reported a significant improvement in specific mental health outcomes at post-test and/or follow-up. Of the two trials demonstrating efficacy in mental health outcomes, one used a weekly, forgiveness-based group intervention and the other was a writing-based, self-initiated intervention. A lack of trials testing theory-driven interventions for relationship separation is of particular concern. Limitations of the existing literature and corresponding directions for future research are discussed.

Experiments on high-pressure vessel decompression have shown that vaporization occurs in ‘boiling shocks’ moving with a velocity of . To explain this phenomenon, a model accounting for bubble breakup was suggested (Ivashnyov, Ivashneva & Smirnov, J. Fluid. Mech., vol. 413, 2000, pp. 149–180). It was shown that the explosive boiling was caused by chain bubble fragmentation, which led to a sharp increase in the interface area and instantaneous transformation of the mixture into an equilibrium state. In the present study, this model is used to simulate nozzle flows with no change in the free parameters chosen earlier for modelling a tube decompression. It is shown that an advanced model ensures the best correspondence to experiments for flashing flows in comparison with an equilibrium model and with a model of boiling at a constant number of centres. It is also shown that the formation of a boiling shock in a critical nozzle flow leads to autovibrations.

A two-dimensional lattice Boltzmann model has been employed to simulate the impingement of a liquid drop on a dry surface. For a range of Weber number, Reynolds number and low density ratios, multiple phases leading to breakup have been obtained. An analytical solution for breakup as function of Reynolds and Weber number based on the conservation of energy is shown to match well with the simulations. At the moment breakup occurs, the spread diameter is maximum; it increases with Weber number and reaches an asymptotic value at a density ratio of 10. Droplet breakup is found to be more viable for the case when the wall is non-wetting or neutral as compared to a wetting surface. Upon breakup, the distance between the daughter droplets is much higher for the case with a non-wetting wall, which illustrates the role of the surface interactions in the outcome of the impact.

Experiments and numerical simulations have been performed to investigate the deformation and break-up of a cloud of rigid fibres falling under gravity through a viscous fluid in the absence of inertia and interfacial tension. The cloud of fibres is observed to evolve into a torus that subsequently becomes unstable and breaks up into secondary droplets which themselves deform into tori in a repeating cascade. This behaviour is similar to that of clouds of spherical particles, though the evolution of the cloud of fibres occurs more rapidly. The simulations, which use two different levels of approximation of the far-field hydrodynamic interactions, capture the evolution of the cloud and demonstrate that the coupling between the self-motion and hydrodynamically induced fluctuations are responsible for the faster break-up time of the cloud. The dynamics of the cloud are controlled by a single parameter which is related to the self-motion of the anisotropic particles. The experiments confirm these findings.

We present experimental observations of hole formation in ejecta crowns, when a viscous drop impacts onto a thin film of low-viscosity liquid with significantly lower surface tension than the drop liquid. The holes are promoted by Marangoni-driven flows in the sheet, resulting from a spray of fine droplets ejected from the thin film hitting the inner side of the crown. The puncturing of the sheet takes place in three distinct steps. First a circular patch of the sheet thins by Marangoni-driven flows. Then this thinner film ruptures and a hole quickly opens up spanning the patch. Finally, the hole opens up further at an accelerated rate, driven by the unbalanced surface tension at its edge. The holes grow until they meet adjacent holes, thus leaving a foam-like network of liquid filaments, which then breaks up into a cloud of droplets.