The wetting or dewetting of a solid substrate by a liquid involves the motion of the contact line between the two phases. One of the parameters that govern the dynamics of the flow near a moving contact line is the local Reynolds number, $\rho$. At sufficient proximity to the moving contact line, where $\rho \ll 1$, the flow is dominated by viscous forces over inertia. However, further away from the contact line, or at higher speeds of motion, inertia is also expected to be influential. In such cases, the current contact line models, which assume Stokes flow and neglect inertia entirely, would be inaccurate in describing the hydrodynamic flow fields. Hence, to account for inertia, here we perform a regular perturbation expansion in $\rho$, of the streamfunction near the Stokes solution. We, however, find that the leading-order inertial correction thus obtained is singular at a critical contact angle of $0.715 {\rm \pi}$. We resolve this spurious mathematical singularity by incorporating the eigenfunction terms, which physically represent flows due to disturbances originating far from the contact line. In particular, we propose a stick slip on the solid boundary – arising from local surface heterogeneities – as the mechanism that generates these disturbance flows. The resulting singularity-free, inertia-corrected streamfunction shows significant deviation from the Stokes solution in the visco-inertial regime ($\rho \sim 1$). Furthermore, we quantify the effect of inertia by analysing its contribution to the velocity at the liquid interface. We also provide the leading-order inertial correction to the dynamic contact angles predicted by the classical Cox–Voinov model; while inertia has considerable effect on the hydrodynamic flow fields, we find that it has little to no influence on the dynamic contact angles.

The propagation of a normal shock wave along a coupled convex–concave surface of equal radii has been analysed experimentally and numerically in this study. The experimental and numerical studies were conducted using a similar geometry as of that used by Ram et al. (J. Fluid Mech., vol. 768, 2015, pp. 219–239) for studying the shock wave transition from regular reflection to Mach reflection. Many interesting flow features such as shock wave transitions over the ramp, characteristics of the induced flow behind the shock wave and the development of a stationary separation shock wave have been observed in the study. The numerical results are validated with experimental data. While the shock wave transitions over the ramp are found to depend mainly on the ramp geometry, the characteristics of the stationary shock wave and the flow separation in the concave region of the ramp surface have been found to vary with the shock wave Mach numbers.

We experimentally observe and theoretically analyse oscillations of a spherical bubble in a gelatin gel under ultrasound irradiation to quantify viscoelastic effects on the nonlinear bubble dynamics. A bubble nucleus is generated by focusing a laser pulse into a 6 wt% gelatin gel supersaturated with dissolved air, which enables us to control the bubble radius at mechanical equilibrium via influx of the gas air into the bubble. Linearized and finite-amplitude oscillations of the bubble are driven by 28 kHz ultrasound and recorded by a high-speed camera; the resonance curves of the oscillation amplitude as a function of the equilibrium radius are constructed for different ultrasound intensities. First, the viscosity and shear modulus of the gel are obtained by fitting the resonance curve (for the lowest ultrasound intensity) to the linearized solution of the Rayleigh–Plesset model that accounts for the gel's nonlinear elasticity of neo-Hookean type and diffusive effects on the bubble dynamics. Next, finite-amplitude oscillations of the bubble are compared with the nonlinear Rayleigh–Plesset calculations. The comparison suggests a need to include the gel's elasticity in the calculations to more accurately reproduce the nonlinear bubble dynamics. Another important finding is that the so-called spring softening feature appears in the experimentally determined resonance curve as the oscillation amplitude increases, which can be predicted by the Rayleigh–Plesset model. Furthermore, our experiment with the highest ultrasound intensity shows non-spherical oscillation of mode 1 that does not appear in the case of water but can be predicted by shape instability theory.

The theoretical limit for absorption of energy in monochromatic water waves of wavelength $\lambda$ by axisymmetric wave energy converters operating in rigid-body motion was established in the 1970s. The maximum mean power generated by a device absorbing due to heave motion is equivalent to that contained in $\lambda /2{\rm \pi}$ length of an incident wave crest. For devices absorbing through surge and/or pitch motions the so-called capture width doubles to $\lambda /{\rm \pi}$. For devices absorbing in both heave and surge/pitch the capture width increases further to $3\lambda /2{\rm \pi}$. In this paper it is demonstrated that it is theoretically possible to extend the capture width for axisymmetric wave energy converters without bound through the use of generalised (non-rigid-body) modes of motion. This concept is applied to vertical cylinders whose surface is surrounded by an array of narrow vertical absorbing paddles. A continuum approximation is made to the paddle motion which simplifies the problem and allows strategies to be developed for setting the springs and dampers that control the power absorption. Results demonstrate that a cylinder of fixed size can absorb as much power as demanded from a plane incident wave although the practical limitations of linear theory are rapidly breached as that demand increases unless the size of the cylinder increases in proportion. In this paper we do not explore these limits in detail or further practical design considerations, such as imposing motion constraints. The continuum approximation is tested against a discrete paddle simulation for accuracy.

Three-scalar subgrid-scale (SGS) mixing in turbulent coaxial jets is investigated experimentally. The flow consists of a centre jet, an annulus and a co-flow. The SGS mixing process and its dependence on the velocity and length scale ratios of the annulus flow to the centre jet are investigated. For small SGS scalar variance the scalars are well mixed and the initial three-scalar mixing configuration is lost. For large SGS variance, the scalars are highly segregated with a bimodal scalar filtered joint density function (f.j.d.f.) at a range of radial locations. Two competing factors, the SGS variance and the scalar length scale, play an important role for the bimodal f.j.d.f. For the higher velocity ratio cases, the peak value of the SGS variance is higher, thereby resulting in stronger bimodality. For the lower velocity ratio cases, the wider mean SGS variance profiles and the smaller scalar length scale cause bimodal f.j.d.f.s over a wider range of physical locations. The scalar dissipation rate structures have similarities to those of mixture fraction and temperature in turbulent non-premixed/partially premixed flames. The observed SGS mixing characteristics present a challenging test for SGS mixing models as well as provides an understanding of the physics for developing improved models. The results also provide a basis for investigating multiscalar SGS mixing in turbulent reactive flows.

The electrophoretic motion of a non-uniformly charged particle in an Oldroyd-B fluid is analysed here in the limit of thin electrical double layers. To this end, we analytically derive expressions for the modified Smoluchowski slip velocity around the particle, carrying weak but otherwise arbitrary surface charge. Our analysis reveals that the modified Smoluchowski slip around a particle differs significantly in a viscoelastic medium as compared with Newtonian fluids. The flow field thus derived is applied to two special cases of non-uniformly charged particles to obtain a closed-form expression for their electrophoretic translational and rotational velocities. We show that the particle's velocity strongly depends on its size in a viscoelastic medium, even for weakly charged surfaces, which is in stark contrast to the well-established theory for Newtonian fluids for weakly charged particles with negligible surface conduction. We further demonstrate that the presence of non-uniform surface charge enhances the influence of the medium's viscoelasticity on the particle's translational as well as angular velocity and this effect strongly depends on the nature of surface charge distribution. Such a physical paradigm, which leads to a breaking of fore–aft symmetry that is unique to complex fluids despite operating in the regime of creeping flows. Our study provides new theoretical framework for understanding electrophoresis of charged entities (such as DNA or active matter) in complex fluids, including biologically relevant fluidic media.

We report on a theoretical and experimental study on the anisotropic diffusion of isolated prolate spheroidal particles in the presence of an aligning potential field. By analysing the microscopic stochastic equations of motion, we obtained the coarse-grained Fokker–Planck equations that govern the evolution of the probability distributions of particle orientation in various configurational spaces. In particular, we found explicit formulae for the diffusion coefficients parallel ($D_x$) and perpendicular ($D_y$) to the field direction in the long-time limit. The predicted results were experimentally validated by measuring the Brownian motions of fluid-suspended carbon nanotubes in an electric field. Good agreement was observed between theoretical and experimental results, both of which showed increasing $D_x$ and decreasing $D_y$ with increasing field strength up to a critical field strength beyond which both curves start to flatten. Our theory and experimental results provide a framework for understanding the coupling between rotation and translation in a diffusion process, and for controlling the diffusion of particles with aligning potential fields.

Emerging technologies such as deep-sea mining and geoengineering pose fundamentally new questions regarding the dynamics of gravity currents. Such activities can continuously release dense sediment plumes from moving locations, thereafter propagating as gravity currents. Here, we present the results of idealized numerical simulations of this novel configuration, and investigate the propagation of a gravity current that results from a moving source of buoyancy, as a function of the ratio of source speed to buoyancy velocity. We show that above a certain value of this ratio, the flow enters a supercritical regime in which the source moves more rapidly than the generated current, resulting in a statistically steady state in the reference frame of the moving source. Once in the supercritical regime, the current goes through a second transition beyond which fluid in the head of the current moves approximately in the direction normal to the direction of motion of the source, and the time evolution of the front in the lateral direction is well described by an equivalent constant volume lock-release gravity current. We use our findings to gain insight into the propagation of sediment plumes released by deep-sea mining collector vehicles, and present proof-of-concept tow-tank laboratory experiments of a model deep-sea mining collector discharging dense dyed fluid in its wake. The experiments reveal the formation a wedge-shaped gravity current front which narrows as the ratio of collector-to-buoyancy velocity increases. The time-averaged front position shows good agreement with the results of the numerical model in the supercritical regime.

Particles are a widespread tool for obtaining information from fluid flows. When Eulerian data are unavailable, they may be employed to estimate flow fields or to identify coherent flow structures. Here we numerically examine the possibility of using particles to capture the dynamics of isolated vortex rings propagating in a quiescent fluid. The analysis is performed starting from numerical simulations of the Navier–Stokes and the Hall–Vinen–Bekarevich–Khalatnikov equations, respectively describing the dynamics of a Newtonian fluid and a finite-temperature superfluid. The flow-induced positions and velocities of particles suspended in the fluid are specifically used to compute the Lagrangian pseudovorticity field, a proxy for the Eulerian vorticity field recently employed in the context of superfluid $^{4}\textrm {He}$ experiments. We show that, when calculated from ideal Lagrangian tracers or from particles with low inertia, the pseudovorticity field can be accurately used to estimate the propagation velocity and the growth of isolated vortex rings, although the quantitative reconstruction of the corresponding vorticity fields remains challenging. On the other hand, particles with high inertia tend to preferentially sample specific flow regions, resulting in biased pseudovorticity fields that pollute the estimation of the vortex ring properties. Overall, this work neatly demonstrates that the Lagrangian pseudovorticity is a valuable tool for estimating the strength of macroscopic vortical structures in the absence of Eulerian data, which is, for example, the case for superfluid $^{4}\textrm {He}$ experiments.