The effect of an externally applied electric field on the motion of an interface between two viscous dielectric fluids is investigated. We first develop a powerful, efficient and widely applicable boundary integral method to compute the interface dynamics in a general multiphysics model comprising coupled Laplace and Stokes flow problems in a periodic half-space. In particular, we exploit the relevant Stokes and Laplace Green's functions to reduce the problem to one defined on the interfacial part of the domain alone. Secondly, motivated by recent experimental work that seeks to underpin the development of switchable liquid optical devices, we concentrate on a fluid–air interface and derive asymptotic approximations suitable to describe the behaviour of a thin film of fluid above an array of electrodes. In this case, the problem is reduced to a single nonlinear partial differential equation describing the film height, coupled to the electrostatic problem via suitable numerical solution or via an asymptotic formula for electrostatic forcing. Comparison against numerical simulations of the full problem shows that the reduced models successfully capture key features of the film dynamics in appropriate regimes; all three approaches are shown to reproduce experimental results.

When a suspension of conducting particles is subjected to a shear flow, there is particle rotation due to the fluid vorticity. A conductor rotating in a uniform magnetic field experiences a torque due to eddy currents both parallel and perpendicular to the direction of rotation. Eddy currents induce a magnetic moment in a conducting particle, which disturbs the magnetic field around the particle. The effect of the Maxwell stress due to the magnetic field disturbance on the rheology of a dilute suspension is calculated in a manner similar to the Einstein viscosity for a suspension of rigid particles. The expression for the stress tensor contains three symmetric stress coefficients, and two normal stress coefficients, in addition to the three antisymmetric stress coefficients calculated in Kumaran (J. Fluid Mech., vol. 871, 2019, pp. 139–185). The stress coefficients depend on the relative orientation of the vorticity and magnetic field and two dimensionless parameters, $\beta$, the product of the vorticity and current relaxation time, and $\Sigma$, the ratio of the magnetic and hydrodynamic torques. In the ‘linear’ approximation, where only terms linear in the particle magnetic moment are retained, the particle stress depends on two dimensionless functions. For the physically important limit $\beta \ll 1$, as well as the limit $\beta \gg 1$ and $\Sigma \gg 1$, these two functions are independent of the vorticity, and depend only on the magnetic field and material properties.

This paper presents an experimental investigation of the evolution of the wetted surface and of the hydrodynamic force during the water exit of a body initially floating at the water surface, and during combined water entry and exit. The evolution of the surface of contact between the body and the water is measured using transparent mock-ups and an LED edge-lighting system. This technique makes it possible to follow the evolution of the wetted surface during both the entry and exit phases with a high-speed video camera placed above the mock-up. The feasibility of the technique is shown for different axisymmetric bodies: a circular disc, a cone and a sphere. The evolution of the hydrodynamic force and of the radius of the wetted surface measured during the experiments are compared with theoretical results obtained with a combined Wagner-modified von Karman approach (Tassin et al. J. Fluids Struct., vol. 40, 2013, pp. 317–336), the linearized water exit model of Korobkin et al. (J. Fluids Struct., vol. 69, 2017a, pp. 16–33) and the small-time self-similar solution of Korobkin et al. (J. Engng Maths, vol. 102, 2017b, pp. 117–130).

We report the first experiments on divergent shock-driven Richtmyer–Meshkov instability (RMI) at well-controlled single-mode interfaces. These experiments are performed in a novel divergent shock tube designed by shock dynamics theory. Generally, the perturbation growth can be divided into three successive stages: linear growth, quick reduction in growth rate and instability freeze-out. It is observed that the growth rate at each stage is far lower than its counterpart in planar or convergent geometry due to geometric divergence. We also found that nonlinearity is much weaker than that in planar or convergent RMI, and has a negligible influence on the overall amplitude growth even at late stages when it has become strong. This weak nonlinear effect is because the growth of the third harmonic counteracts its feedback to the fundamental mode. As a consequence, the linear theory of Bell (report no. LA-1321) accounting for geometric divergence and Rayleigh–Taylor (RT) stabilization caused by flow deceleration can reasonably predict the present results from early to late stages. The instability freeze-out at late times is ascribed to the negative growth induced by geometric divergence and RT stabilization, and is also well reproduced by the linear theory.

The present paper aims at establishing the synthetic jet technology capabilities in controlling the von Kármán street behind a circular cylinder. The circular cylinder, placed in an open-circuit wind tunnel, presents a slot in its rear position, through which the synthetic jet is issued. The Reynolds number, based on the circular cylinder diameter and the free-stream velocity, is equal to 4600 and the von Kármán street is characterized, in the baseline configuration (i.e. without synthetic jet), by a shedding frequency of 16.2 Hz. Several synthetic jet operating conditions are tested. Therefore, the effects of the momentum coefficient ($C_{\mu } = 5.4$%, 10.8% and 21.6%) and the dimensionless frequency ($f^{+} = 0.49$, 0.98 and 1.96) on the von Kármán street behaviour can be analysed. Instantaneous two-dimensional in-plane velocity fields are measured in a plane containing the synthetic jet slot axis using multigrid/multipass cross-correlation digital particle image velocimetry. These measurements have been used to investigate the mean flow quantities and turbulent statistics of the phenomenon. In addition, the wake extent and behaviour (i.e. symmetric or asymmetric) are analysed as well as the drag coefficient, for each configuration. The extent of the wake region decreases as the momentum coefficient and/or the dimensionless frequency increase, while the symmetric/asymmetric wake behaviour is found to be governed by a different control parameter: the synthetic jet Reynolds number based on its impulse. As regards the drag coefficient, a maximum reduction, of approximately 35%, is found for the configuration at $C_{\mu }=10.8\,\%$ and $f^{+}=0.98$.