This study investigates experimentally the pressure fluctuations of liquids in a column under short-time acceleration. It demonstrates that the Strouhal number $St=L/(c\,\Delta t)$, where $L$, $c$ and $\Delta t$ are the liquid column length, speed of sound, and acceleration duration, respectively, provides a measure of the pressure fluctuations for intermediate $St$ values. On the one hand, the incompressible fluid theory implies that the magnitude of the averaged pressure fluctuation $\bar {P}$ becomes negligible for $St\ll 1$. On the other hand, the water hammer theory predicts that the pressure tends to $\rho cu_0$ (where $u_0$ is the change in the liquid velocity) for $St\geq O(1)$. For intermediate $St$ values, there is no consensus on the value of $\bar {P}$. In our experiments, $L$, $c$ and $\Delta t$ are varied so that $0.02 \leq St \leq 2.2$. The results suggest that the incompressible fluid theory holds only up to $St\sim 0.2$, and that $St$ governs the pressure fluctuations under different experimental conditions for higher $St$ values. The data relating to a hydrogel also tend to collapse to a unified trend. The inception of cavitation in the liquid starts at $St\sim 0.2$ for various $\Delta t$, indicating that the liquid pressure goes lower than the liquid vapour pressure. To understand this mechanism, we employ a one-dimensional wave propagation model with a pressure wavefront of finite thickness that scales with $\Delta t$. The model provides a reasonable description of the experimental results as a function of $St$.

This study reveals the morphological evolution of a splashing drop by a newly proposed feature extraction method, and a subsequent interpretation of the classification of splashing and non-splashing drops performed by an explainable artificial intelligence (XAI) video classifier. Notably, the values of the weight matrix elements of the XAI that correspond to the extracted features are found to change with the temporal evolution of the drop morphology. We compute the rate of change of the contributions of each frame with respect to the classification value of a video as an importance index to quantify the contributions of the extracted features at different impact times to the classification. Remarkably, the rate computed for the extracted splashing features of ethanol and 1 cSt silicone oil is found to have a peak value at the early impact times, while the extracted features of 5 cSt silicone oil are more obvious at a later time when the lamella is more developed. This study provides an example that clarifies the complex morphological evolution of a splashing drop by interpreting the XAI.

We investigate experimentally and theoretically the interactions between a cavitation bubble and a hemispherical pendant oil droplet immersed in water. In experiments, the cavitation bubble is generated by a focused laser pulse right below the pendant droplet with well-controlled bubble–wall distances and bubble–droplet size ratios. By high-speed imaging, four typical interactions are observed, namely: oil droplet rupture; water droplet entrapment; oil droplet large deformation; and oil droplet mild deformation. The bubble jetting at the end of collapse and the migration of the bubble centroid are particularly different in each bubble–droplet interaction. We propose theoretical models based on the method of images for calculating the Kelvin impulse and the anisotropy parameter which quantitatively reflects the migration of the bubble centroid at the end of the collapse. Finally, we explain that a combination of the Weber number and the anisotropy parameter determines the regimes of the bubble–droplet interactions.

An on-demand painting system with a simple structure device that ejects highly viscous liquids as microjets is introduced. An impulsive motion of the container results in the ejection of a viscous liquid jet from the nozzle. This system enabled us to paint letters on a section of a car body using commercial car paint with a zero-shear viscosity of 100 $\textrm {Pa} \cdot \textrm {s}$. To understand the jet velocity, we conducted systematic experiments. Experimental results showed that the jet velocity increases with the ratio between the liquid depths in the container and the nozzle, up to approximately 30 times faster than the initial velocity. However, a linear relation between the jet velocity and the ratio predicted by the previous model, which considers only the pressure impulse, does not hold for the high length ratios since the actual position of the stagnation point is different from the position predicted by the previous model. By solving the Laplace equation and using the model proposed by Gordillo et al. (J. Fluid Mech., vol. 894, 2020, pp. A3–11), we reproduce the non-monotonic behaviour of the jet velocity as a function of the length ratio. For practical use, we improve the jet-velocity model by considering mass conservation as well as the pressure impulse.

Here we characterize the origin and subsequent disintegration into droplets of the type of high-speed jets formed after the sudden implosion of a locally spherical cavity. The full spatio-temporal evolution of these types of impulsively generated jets is described here making use of just the initial values of the interfacial normal velocity at the axis of symmetry and of its corresponding second derivative along the azimuthal direction, obtained straightforwardly from the solution of the Laplace equation subjected to standard boundary conditions. The predicted time evolutions of the jet tip radius and velocity, and of the radii of the ejected droplets, are shown to agree well with experimental observations.

We investigate the impact and penetration of a solid sphere passing through gelatine at various impact speeds up to $143.2~\text{m}~\text{s}^{-1}$. Tests were performed with several concentrations of gelatine. Impacts for low elastic Froude number $\mathit{Fr}_{e}$, a ratio between inertia and gelatine elasticity, resulted in rebound. Higher $\mathit{Fr}_{e}$ values resulted in penetration, forming cavities with prominent surface textures. The overall shape of the cavities resembles those observed in water-entry experiments, yet they appear in a different order with respect to increasing inertia: rebound, quasi-seal, deep-seal, shallow-seal and surface-seal. Remarkably, similar to the $We$–$Bo$ phase diagram in water-entry experiments, the elastic Froude number $\mathit{Fr}_{e}$ and elastic Grashof number $\mathit{Gr}_{e}$ (a ratio between gravity and gelatine elasticity) classify all five different phenomena into distinguishable regimes. We find that $\mathit{Fr}_{e}$ can be a good indicator to describe the cavity length $H$, particularly in the shallow-seal regime. Finally, the evolution of cavity shape, pinch-off depth, and lower cavity radius are investigated for different $\mathit{Fr}_{e}$ values.

In isothermal non-coalescence behaviours of a droplet against a wall, an air film of micrometre thickness plays a crucial role. We experimentally study this phenomenon by letting a droplet levitate over a moving glass wall. The three-dimensional shape of the air film is measured using an interferometric method. The mean curvature distribution of the deformed free surface and the distributions of the lubrication pressure are derived from the experimental measurements. We vary experimental parameters, namely wall velocity, droplet diameter and viscosity of the droplets, over a wide range; for example, the droplet viscosity is varied over two orders of magnitude. For the same wall velocity, the air film of low-viscosity droplets shows little shape oscillation with constant film thickness (defined as the steady state), while that of highly viscous droplets shows a significant shape oscillation with varying film thickness (defined as the unsteady state). The droplet viscosity also affects the surface velocity of a droplet. Under our experimental conditions, where the air film shape can be assumed to be steady, we present experimental evidence showing that the lift force generated inside the air film balances with the droplet’s weight. We also verify that the lubrication pressure locally balances with the surface tension and hydrostatic pressures. This indicates that lubrication pressure and the shape of the free surface are mutually determined. Based on the local pressure balance, we discuss a process of determining the steady shape of an air film that has two areas of minimum thickness in the vicinity of the downstream rim.

We experimentally examine a laser-induced underwater shock wave paying special attention to the pressure impulse, the time integral of the pressure evolution. Plasma formation, shock-wave expansion and the pressure in water are observed simultaneously using a combined measurement system that obtains high-resolution nanosecond-order image sequences. These detailed measurements reveal a distribution of the pressure peak which is not spherically symmetric. In contrast, remarkably, the pressure impulse is found to be symmetrically distributed for a wide range of experimental parameters, even when the shock waves are emitted from an elongated region. The structure is determined to be a collection of multiple spherical shock waves originating from point-like plasmas in the elongated region.

We investigate the motion of a gas–liquid interface in a test tube induced by a large acceleration via impulsive force. We conduct simple experiments in which the tube partially filled with a liquid falls under gravity and hits a rigid floor. A curved gas–liquid interface inside the tube reverses and eventually forms a so-called focused jet. In our experiments, there arises either vibration of the interface or an increment in the velocity of the liquid jet, accompanied by the onset of cavitation in the liquid column. These phenomena cannot be explained by a considering pressure impulse in a classical potential flow analysis, which does not account for finite speeds of sound or phase changes. Here we model such water-hammer events as a result of the one-dimensional propagation of a pressure wave and its interaction with boundaries through acoustic impedance mismatching. The method of characteristics is applied to describe pressure-wave interactions and the subsequent cavitation. The model proposed is found to be able to capture the time-dependent characteristics of the liquid jet.

We report results from the first systematic experiments for investigating surfactant effects on path instability of an air bubble rising in quiescent water. The addition of surfactant to a gas–water system causes a non-uniform distribution of surfactant concentration along the bubble surface, resulting in variations in the gas–water boundary condition from zero shear stress to non-zero shear stress due to the Marangoni effect. This leads to retarded surface velocity and ends up with immobilization of the bubble surface with increasing surfactant concentration, where the drag corresponds to that of a solid sphere of the same size. Using two high-speed cameras and vertical traverse systems, we measure three-dimensional trajectories, velocities and aspect ratios of a millimetre-sized bubble simultaneously for ${\sim }1~\mathrm{m} $. Experimental parameters are the diameter of the bubble and the surfactant concentration of 1-Pentanol or Triton X-100. We explore the surfactant effect on the drag and lift forces acting on the bubble in helical motion. While the drag force monotonically increases with the surfactant concentration as expected, the lift force shows a non-monotonic behaviour. Nevertheless, the direction of the lift force in a reference frame that rotates with the bubble along its trajectory is kept almost constant. We also observe the transient trajectory starting from helical motion to zigzag, which has never been reported in the case of purified water. The instantaneous amplitude and frequency of the transient motion agree with those of the motion regarded as steady. Finally the bubble motions are categorized as straight/helical/zigzag and experimentally examined in the field of two dimensionless numbers: Reynolds number $\mathit{Re}\in $ [300 900] and the normalized drag coefficient ${ C}_{D}^{\ast } $ which represents the slip condition. Remarkably it is found that the motions of a bubble with the intermediate slip conditions between free-slip and no-slip are helical for a broad range of $\mathit{Re}$.

We investigate the levitation of a drop gently deposited onto the inner wall of a rotating hollow cylinder. For a sufficiently large velocity of the wall, the drop steadily levitates over a thin air film and reaches a stable angular position in the cylinder, where the drag and lift balance the weight of the drop. Interferometric measurements yield the three-dimensional (3D) air film thickness under the drop and reveal the asymmetry of the profile along the direction of the wall motion. A two-dimensional (2D) model is presented which explains the levitation mechanism, captures the main characteristics of the air film shape and predicts two asymptotic regimes for the film thickness ${h}_{0} $: for large drops ${h}_{0} \sim {\mathit{Ca}}^{2/ 3} { \kappa }_{b}^{- 1} $, as in the Bretherton problem, where $\mathit{Ca}$ is the capillary number based on the air viscosity and ${\kappa }_{b} $ is the curvature at the bottom of the drop; for small drops ${h}_{0} \sim {\mathit{Ca}}^{4/ 5} {(a{\kappa }_{b} )}^{4/ 5} { \kappa }_{b}^{- 1} $, where $a$ is the capillary length.

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Voronoï analysis enables us to distinguish quantitatively between two typical preferential clustering configurations: a regular lattice arrangement and irregular clustering. The bubble data are obtained from direct numerical simulations using the front-tracking method. It is found that the bubble deformation, represented by the aspect ratio $\chi $, plays a significant role in determining which type of clustering is realized: nearly spherical bubbles form a regular lattice arrangement, while more deformed bubbles show irregular clustering. Remarkably, this criterion for the clustering morphology holds for different diameters of the bubbles, surface tensions and viscosities of the liquid in the studied parameter regime. The mechanism of this clustering behaviour is most likely connected to the amount of vorticity generated at the bubble surfaces.

By focusing a laser pulse inside a capillary partially filled with liquid, a vapour bubble is created that emits a pressure wave. This pressure wave travels through the liquid and creates a fast, focused axisymmetric microjet when it is reflected at the meniscus. We numerically investigate the formation of this microjet using axisymmetric boundary integral simulations, where we model the pressure wave as a pressure pulse applied on the bubble. We find a good agreement between the simulations and experimental results in terms of the time evolution of the jet and on all parameters that can be compared directly. We present a simple analytical model that accurately predicts the velocity of the jet after the pressure pulse and its maximum velocity.

Three-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers ) and two Taylor–Reynolds numbers ( and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher . Light particles show maximum clustering for around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.