A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a unified and concise mathematical form, with clear physical meanings and extensibility. The bubble oscillation equation can be simplified to the Keller–Miksis equation by neglecting the effects of phase transition and bubble migration. The present theoretical model effectively captures the experimental results for bubbles generated in free fields, near free surfaces, adjacent to rigid walls, and in the vicinity of other bubbles. Based on the present theory, we explore the effect of the bubble content by changing the vapour proportion inside the cavitation bubble for an initial high-pressure bubble. It is found that the energy loss of the bubble shows a consistent increase with increasing Mach number and initial vapour proportion. However, the radiated pressure peak by the bubble at the collapse stage increases with decreasing Mach number and increasing vapour proportion. The energy analyses of the bubble reveal that the presence of vapour inside the bubble not only directly contributes to the energy loss of the bubble through phase transition but also intensifies the bubble collapse, which leads to greater radiation of energy into the surrounding flow field due to the fluid compressibility.

The evolution of the water-entry cavity affects the impact load and the motion of the body. This paper adopts the Eulerian finite element method for multiphase flow for simulations of the high-speed water-entry process. The accuracy and convergence of the numerical method are verified by comparing it with the experimental data and the results of the transient cavity dynamics theory. Based on the results, the representative characteristics of the cavity are discussed from the perspective of the cavity cross-section. It is found that the asymmetry of the cavity expansion and contraction durations is related to the motion of the free surface and the closure of the cavity. The uplift of the free surface suppresses cavity expansion, while the jet generated from free surface closure accelerates cavity contraction. The duration of the contraction of the cavity near the free surface is shorter than the expansion duration due to the change in the velocity distribution caused by the free surface motion. The necking phenomenon during deep closure leads to an increase in the internal pressure of the cavity, prolonging cavity contraction near the deep closure area. This work provides new insights into the cavity dynamics in high-speed water entry.

An additional distant wall is known to highly alter the jetting scenarios of wall-proximal bubbles. Here, we combine high-speed photography and axisymmetric volume of fluid (VoF) simulations to quantitatively describe its role in enhancing the micro-jet dynamics within the directed jet regime (Zeng et al., J. Fluid Mech., vol. 896, 2020, A28). Upon a favourable agreement on the bubble and micro-jet dynamics, both experimental and simulation results indicate that the micro-jet velocity increases dramatically as $\eta$ decreases, where $\eta =H/R_{max}$ is the distance between two walls $H$ normalized by the maximum bubble radius $R_{max}$. The mechanism is related to the collapsing flow, which is constrained by the distant wall into a reverse stagnation-point flow that builds up pressure near the bubble's top surface and accelerates it into micro-jets. We further derive an equation expressing the micro-jet velocity $U_{jet}=87.94\gamma ^{0.5}(1+(1/3)(\eta -\lambda ^{1.2})^{-2})$, where ${\gamma =d/R_{max}}$ is the stand-off distance to the proximal wall with $d$ the distance between the initial bubble centre and the wall, $\lambda =R_{y,m}/R_{max}$ with $R_{y,m}$ the distance between the top surface and the proximal wall at the bubble's maximum expansion. Viscosity has a minimal impact on the jet velocity for small $\gamma$, where the pressure buildup is predominantly influenced by geometry.

This study gives insights into the interfacial instabilities of a ventilation cavity by injecting gas vertically into the horizontal liquid crossflow through both numerical and experimental investigations. We identified four distinct regimes of the ventilation cavity based on their topological characteristics: (I) discrete bubble, (II) continuous cavity, (III) bifurcated cavity, and (IV) bubble plume. The boundaries for these regimes are delineated within the parameter space of crossflow velocity and jet speed. A comprehensive analysis of the flow characteristics associated with each regime is presented, encompassing the phase mixing properties, the dominant frequency of pulsation, and the time-averaged profile of the cavity. This study conducted a detailed investigation of the periodic pulsation at the leading-edge interface of the cavity, also known as the ‘puffing phenomenon’. The results of local spectral analysis and dynamic mode decomposition indicate that the high-frequency instability in the near-field region exhibits the most significant growth rate. In contrast, the low-frequency mode with the largest amplitude spans a broader region from the orifice to the cavity branches. A conceptual model has been proposed to elucidate the mechanism behind the pulsation phenomenon observed along the cavity interface: the pulsation results from the alternate intrusion of the crossflow and the cavity recovery at the leading edge, being governed mainly by the periodic oscillating imbalance between the static pressure of gas near the orifice and the stagnation pressure of crossflow at the leading edge.

In this paper, we present a theoretical, experimental and numerical study of the dynamics of cavitation bubbles inside a droplet suspended in another host fluid. On the theoretical side, we provided a modified Rayleigh collapse time and natural frequency for spherical bubbles in our particular context, characterized by the density ratio between the two liquids and the bubble-to-droplet size ratio. Regarding the experimental aspect, experiments were carried out for laser-induced cavitation bubbles inside oil-in-water (O/W) or water-in-oil (W/O) droplets. Two distinct fluid-mixing mechanisms were unveiled in the two systems, respectively. In the case of O/W droplets, a liquid jet emerges around the end of the bubble collapse phase, effectively penetrating the droplet interface. We offer a detailed analysis of the criteria governing jet penetration, involving the standoff parameter and impact velocity of the bubble jet on the droplet surface. Conversely, in the scenario involving W/O droplets, the bubble traverses the droplet interior, inducing global motion and eventually leading to droplet pinch-off when the local Weber number exceeds a critical value. This phenomenon is elucidated through the equilibrium between interfacial and kinetic energies. Lastly, our boundary integral model faithfully reproduces the essential physics of the non-spherical bubble dynamics observed in the experiments. We conduct a parametric study spanning a wide parameter space to investigate bubble–droplet interactions. The insights from this study could serve as a valuable reference for practical applications in the field of ultrasonic emulsification, pharmacy, etc.

Kaolinite is often a cause of deformation in soft-rock tunnel engineering, leading to safety problems. In order to gain a better predictive understanding of the governing principles associated with this phenomenon, the physical and chemical properties of kaolinite were investigated using an efficient, firstprinciples scheme for studying isomorphic substitution of Al ions in kaolinite by two kinds of other elements (namely, the dual defect). Elements that are relatively common in natural kaolinite were chosen from groups II (Be, Mg, Ca, and Sr) and III (Fe and Sc) of the Periodic Table as dual-defect ions to substitute for Al ions in kaolinite. By systematically calculating the impurity-formation energies (which characterize the difference in the total crystal energy before and after the defect arises) and transitionenergy levels, which characterize the energy cost for the transformation between two different charge states, the (Be + Sc)Al (i.e. the replacement of two specific Al ions in kaolinite by external Be and Sc ions), (Ca + Sc)Al, (Mg + Sc)Al, and (Sr + Sc)Al ion pairs were determined to have low formation energies, suggesting that these combinations of ions can easily substitute for Al ions in kaolinite. The (Be + Fe)Al, (Ca + Fe)Al, (Mg + Fe)Al, and (Sr + Fe)Al ion pairs have relatively high formation energies which make isomorphic substitution (or doping) in kaolinite difficult. Moreover, these combinations of elements from groups II and III were found to have relatively low transition-energy levels compared with other element pairs. Among them, (Sr + Sc)Al have the lowest transition-energy level at 0.06 eV above the valence band maximum. When compared with single external substitutional defects in kaolinite, remarkably, the dual defects have relatively low formation energies and transition-energy levels. The results are helpful in understanding the chemical and physical properties of natural kaolinite.

Vitrification has been widely used for oocyte cryopreservation, but there is still a need for optimization to improve clinical outcomes. In this study, we compared the routine droplet merge protocol with modified multi-gradient equilibration vitrification for cryopreservation of mouse oocytes at metaphase II. Subsequently, the oocytes were thawed and subjected to intracytoplasmic sperm injection (ICSI). Oocyte survival and spindle status were evaluated by morphology and immunofluorescence staining. Moreover, the fertilization rates and blastocyst development were examined in vitro. The results showed that multi-gradient equilibration vitrification outperformed droplet merge vitrification in terms of oocyte survival, spindle morphology, blastocyst formation, and embryo quality. In contrast, droplet merge vitrification exhibited decreasing survival rates, a reduced proportion of oocytes with normal spindle morphology, and lower blastocyst rates as the number of loaded oocytes increased. Notably, when more than six oocytes were loaded, reduced oocyte survival rates, abnormal oocyte spindle morphology, and poor embryo quality were observed. These findings highlight that the vitrification of mouse metaphase II oocytes by the modified multi-gradient equilibration vitrification has the advantage of maintaining oocyte survival, spindle morphology, and subsequent embryonic development.

Let $G=(V, E)$ be a locally finite graph with the vertex set V and the edge set E, where both V and E are infinite sets. By dividing the graph G into a sequence of finite subgraphs, the existence of a sequence of local solutions to several equations involving the p-Laplacian and the poly-Laplacian systems is confirmed on each subgraph, and the global existence for each equation on graph G is derived by the convergence of these local solutions. Such results extend the recent work of Grigor’yan, Lin and Yang [J. Differential Equations, 261 (2016), 4924–4943; Rev. Mat. Complut., 35 (2022), 791–813]. The method in this paper also provides an idea for investigating similar problems on infinite graphs.

The behaviour of granular column collapses is associated with the dynamics of geohazards, such as debris flows, landslides and pyroclastic flows, yet their underlying physics is still not well understood. In this paper, we explore granular column collapses using the sphero-polyhedral discrete element method, where the system contains two types of particles with different frictional properties. We impose three different mixing ratios and multiple different particle frictional coefficients, which lead to different run-out distances and deposition heights. Based on our previous work and a simple mixture theory, we propose a new effective initial aspect ratio for the bi-frictional granular mixture, which helps unify the description of the relative run-out distances. We analyse the kinematics of bi-frictional granular column collapses and find that deviations from classical power-law scaling in both the dimensionless terminal time and the dimensionless time when the system reaches the maximum kinetic energy may result from differences in the initial solid fraction and initial structures. To clarify the influence of initial states, we further decrease the initial solid fraction of granular column collapses, and propose a trial function to quantitatively describe its influence. Due to the utilization of a simple mixture theory of contact occurrence probability, this study can be associated with the friction-dependent rheology of granular systems and friction-induced granular segregations, and further generalized to applications with multiple species of particles in various natural and engineering mixtures.

Vertically neutral collapse of a pulsating bubble occurs when the boundaries above or below the bubble balance the buoyancy effect over a pulsation. In this study, the vertically neutral collapse of a bubble near a vertical rigid wall below the free surface is investigated. The boundary integral method (BIM) is employed to model the bubble dynamics with an open-domain free surface. Moreover, this method is validated against several buoyant bubble experiments. Bubble dynamics in such conditions are associated with three dimensionless parameters: the bubble-free surface distance $\gamma _{{f}}$, bubble–wall distance $\gamma _{{w}}$ and buoyancy parameter $\delta$. We derive the Kelvin impulse of a spherical bubble and the algebraic relationship for vertically neutral collapse, which proves to be accurate for predicting vertically neutral collapse when the bubble is relatively far from the boundaries. Four patterns of the vertically neutral collapse of the bubble for different $\gamma _{{w}}$ and $\gamma _{{f}}$ are identified: (i) formally downward jet; (ii) annular collapse; (iii) horizontal jet; and (iv) weak jet. Despite the downward jet shape, the ‘formally downward jet’ is in the vertically neutral collapse state in terms of the profile of toroidal bubbles and the orientation of local high-pressure zones around the bubble at jet impact. A bulge with a high curvature above the bubble in the ‘annular collapse’ pattern is formed during bubble collapse under two local high-pressure zones at the left and right extremities of the bubble. The ‘horizontal jet’ pattern has the greatest potential to attack the wall, and the power laws of the moment of the jet impact, jet velocity and bubble displacement with respect to the theoretical Kelvin impulse are discussed. In particular, we quantitatively illustrate the role of the free surface on bubble migration towards the wall through the variational power-law exponents of the bubble displacement with respect to $\gamma _{{w}}$.

Shape memory polymers (SMPs) are a type of programmable materials capable of transforming their shapes in a pre-programmed way upon the application of an external stimulus. These materials have been tested for various potential applications particularly in the biomedical field for polymers with general and specific requirements. This review focuses on the recent advances in biomedical applications, including self-tightening sutures, pressure bandages, self-expansion stents, tissue engineering scaffolds, artificial muscles, drug delivery, and orthodontic archwires, after a brief description of the concepts, classifications, programming procedures, and material requirements of SMPs.

High-speed water entry is a transient hydrodynamic process that is accompanied by strongly compressible flow, free surface splash, cavity evolution and other nonlinear hydrodynamic phenomena. To address these problems, a novel fluid–structure interaction (FSI) scheme based on the immersed boundary method is proposed which is suitable for strongly compressible multiphase flows. In this scheme, considering the multiphase interfaces at the immersed boundary, an improved immersed boundary method for effectively suppressing the non-physical force oscillation is proposed. Additionally, a quaternion-based six degrees of freedom motion system is used to describe rigid body motion, and the multiphase flow Eulerian finite element method is applied as the fluid solver. Using analytical solutions, experimental data and literature data, the accuracy and robustness of the FSI scheme are validated. Finally, the high-speed water entry of the slender body with different noses is investigated, and the hydrodynamic loads including the axial and normal drag forces and the bending moment are extensively discussed. The hydrodynamic load and motion trajectory are determined by the nose configuration. The tail slamming phenomenon is the primary focus, and it is revealed that its formation is primarily related to the pitch moment formed at the stage of crossing the free surface. Tail slamming also causes violent impact loads, especially bending moments, which may cause slender projectiles to break off. Finally, to combine the features of the flat and hemispherical noses, the water entry of the projectile with a truncated hemispherical nose is simulated and discussed.

The essence of sub-critical transition of oscillatory boundary-layer flows is the non-modal growth of finite-amplitude disturbances. The current understanding of the mechanisms of the orderly and bypass transitions of oscillatory boundary-layer flows is limited. The present study adopts optimisation approaches to predict the maximum energy amplification of two- and three-dimensional perturbations in response to the optimal initial disturbance with or without external forcing. A series of direct numerical simulations are also performed to compare with the results obtained from the stability analyses. In particular, the optimal initial perturbation similar to a Tollmien–Schlichting (T–S) wave yields the largest transient growth under the combined effects of the Orr mechanism and inflectional point instability. With a considerable level of two-dimensional disturbance, the vortex tube nonlinearly develops from the T–S-like wave, and then either deforms into a $\varLambda$-vortex in the near-wall region or rolls up to the free shear region. The further burst of turbulence can follow the first pathway as K-type transition or the second one as vortex tube breakdown due to the elliptical instability. Additionally, non-modal growth can initiate the inception of streaky structures by favourable three-dimensional initial perturbations and/or forcing. The secondary instabilities responsible for the streak breakdown are classified as the varicose (symmetric) and sinuous (anti-symmetric) modes. Under a sufficiently high level of three-dimensional disturbance, the bypass transition is predominantly characterised by the formation of the sinuous mode and turbulent spots, which leads to the suppression of inflection point instability.

Violent respiratory events play critical roles in the transmission of respiratory diseases, such as coughing and sneezing, between infectious and susceptible individuals. In this work, large-scale multiphase flow large-eddy simulations have been performed to simulate the coughing jet from a human's mouth carrying pathogenic or virus-laden droplets by using a weakly compressible smoothed particle hydrodynamics method. We explicitly model the cough jet ejected from a human mouth in the form of a mixture of two-phase fluids based on the cough velocity profile of the exhalation flow obtained from experimental data and the statistics of the droplets’ sizes. The coupling and interaction between the two expiratory phases and ambient surrounding air are examined based on the interaction between the gas particles and droplet particles. First, the results reveal that the turbulence of the cough jet determines the dispersion of the virus-laden droplets, i.e. whether they fly up evolving into aerosols or fall down to the ground. Second, the droplet particles have significant effects on the evolution of the cough jet turbulence; for example, they increase the complexity and butterfly effect introduced by the turbulence disturbance. Our results show that the prediction of the spreading distance of droplet particles often goes beyond the social distancing rules recommended by the World Health Organization, which reminds us of the risks of exposure if we do not take any protecting protocol.

Very few studies have emphasized the effects of high-pressure sintering on snow density evolution, even though snow as a type of engineering material is widely used in construction engineering in cold regions for snow pavement, snow runway and polar infrastructure. This study presents new experimental results of snow densification under high pressures of up to 100 MPa for a temperature range from −3.5 to −17.3°C and uniaxial compression at the temperature of −10°C and constant strain rates from 5 × 10−4 to 10−1 s−1. Results reveal that density evolution of snow to ice under high-pressure sintering can be achieved in a wide temperature range within a duration as short as 5 min. The compressive strength of snow-sintered ice was ~1.2–2.2 times as large as that of water-frozen ice reported by previous work. The orthogonal experiment showed that pressure is a more significant factor affecting the final density in comparison with sintering temperature and time. The increased rates of ice fabrication, low limitations on temperature and reliable sintered snow strength indicate that snow-ice engineering, such as airport construction in Greenland and Antarctica, can be improved by high-pressure sintering of snow to overcome the harsh environment.