The influence of parametric forcing on a viscoelastic fluid layer, in both gravitationally stable and unstable configurations, is investigated via linear stability analysis. When such a layer is vertically oscillated beyond a threshold amplitude, large interface deflections are caused by Faraday instability. Viscosity and elasticity affect the damping rate of momentary disturbances with arbitrary wavelength, thereby altering the threshold and temporal response of this instability. In gravitationally stable configurations, calculations show that increased elasticity can either stabilize or destabilize the viscoelastic system. In weakly elastic liquids, higher elasticity increases damping, raising the threshold for Faraday instability, whereas the opposite is observed in strongly elastic liquids. While oscillatory instability occurs in Newtonian fluids for all gravity levels, we find that parametric forcing below a critical frequency will cause a monotonic instability for viscoelastic systems at microgravity. Importantly, in gravitationally unstable configurations, parametric forcing above this frequency stabilizes viscoelastic fluids, until the occurrence of a second critical frequency. This result contrasts with the case of Newtonian liquids, where under the same conditions, forcing stabilizes a system for all frequencies below a single critical frequency. Analytical expressions are obtained under the assumption of long wavelength disturbances predicting the damping rate of momentary disturbances as well as the range of parameters that lead to a monotonic response under parametric forcing.

We explore the instability and oscillation dynamics of barrel-shaped droplets on cylindrical fibres, contributing to a deeper understanding of fibre–droplet interactions critical to both natural systems and industrial applications. Unlike sessile droplets on flat surfaces, droplets on fibres exhibit unique behaviours due to the curvature of the fibre, such as transitions from axisymmetric (barrel) to non-axisymmetric (clamshell) shapes governed by droplet volume, contact angle and fibre radius. Using a linear inviscid theory, we compute the frequency spectrum of barrel-shaped droplets and identify stability thresholds for the barrel-to-clamshell transition by examining the first rocking mode, with a focus on the role of contact line conditions. This analysis resolves experimental anomalies concerning the stability of half-barrel-shaped droplets on hydrophobic fibres. Our findings also reveals diverse frequency spectra: droplets on thin fibres exhibit Rayleigh–Lamb-like spectral features, while those on thicker fibres show reduced sensitivity to azimuthal wavenumber. Interestingly, the instability of sectoral modes on thick fibres resembles the Rayleigh–Plateau instability of static rivulets, with fibre curvature slightly reducing growth rates at small axial wavenumbers but increasing them at larger ones.

Being thicker and lighter than the oceanic lithosphere, the continental lithosphere exerts a thermal blanket effect on the convective mantle by locally accumulating heat and altering the flow structure, which in turn affects continent motion. This thermal–mechanic feedback has been studied through a simplified model of a thermally insulating plate floating over a bottom-heated convective fluid, which shows that plate mobility enhances with plate size and a unidirectionally moving mode (UMM) emerges for sufficiently large plates. Nevertheless, apart from bottom heating, the mantle is also subject to internal heating induced by radioactive decay. How the addition of internal heating affects the dynamic coupling is still unclear, which motivates the present study. Numerical simulation results show that the effect varies with plate size. For small plates, as internal heating intensifies, plate motion becomes increasingly persistent and the critical plate size for the UMM decreases. This results from the enhanced thermal blanket effect under intensified internal heating, which enables a faster generation of hot plumes to boost plate motion during its slowdown. Most notably, the addition of internal heating brings a new mode for large plates – a permanently stagnant mode (PSM) – in which the plate oscillates permanently above a hot up-welling with down-wellings locating far away. The critical size for the PSM decreases as internal heating intensifies. In the PSM, the symmetry between cold and hot plumes breaks. Implications of these findings for the dynamic coupling on Earth and Mars are discussed.

A new lattice Boltzmann model (LBM) is presented to describe chemically reacting multicomponent fluid flow in homogenised porous media. In this work, towards further generalising the multicomponent reactive lattice Boltzmann model, we propose a formulation which is capable of performing reactive multicomponent flow computation in porous media at the representative elementary volume (REV) scale. To that end, the submodel responsible for interspecies diffusion has been upgraded to include Knudsen diffusion, whereas the kinetic equations for the species, the momentum and the energy have been rewritten to accommodate the effects of volume fraction of porous media through careful choice of the equilibrium distribution functions. Verification of the mesoscale kinetic system of equations by a Chapman–Enskog analysis reveals that at the macroscopic scale, the homogenised Navier–Stokes equations for compressible multicomponent reactive flows are recovered. The dusty gas model (DGM) capability hence formulated is validated over a wide pressure range by comparison of experimental flow rates of component species counter diffusing through capillary tubes. Next, for developing a capability to compute heterogeneous reactions, source terms for maintaining energy and mass balance across the fluid phase species and the surface adsorbed phase species are proposed. The complete model is then used to perform detailed chemistry simulations in porous electrodes of a solid oxide fuel cell (SOFC), thereby predicting polarisation curves which are of practical interest.

The effect of nucleation on cavitation inception in a high-Reynolds-number von Kármán wake from a bluff two-dimensional hydrofoil is studied experimentally in a variable pressure water tunnel. Nucleation effects are studied by seeding the flow with sparse monodisperse nuclei populations, with the critical pressure nominally equal to vapour pressure. The injected nuclei population and incipient cavitation events were imaged simultaneously using high-speed cameras to precisely quantify the number of activated nuclei of the total available. Three-dimensional spatial characterisation (orientation and location) of the incipient structures is obtained using two high-speed cameras mounted to the side and below the tunnel test section. Inception was observed predominantly in the stretched cores of secondary structures, with a negligible proportion of events occurring in the primary vortices. A broad peak in the vertical angle distribution is observed about the streamwise axis; however, events at all angles are seen. A symmetric distribution was observed for the horizontal angle, with a dominant orientation $45^{\circ }$ from the free-stream direction. The majority of events occur at approximately one hydrofoil thickness downstream of the hydrofoil trailing edge, with a bimodal symmetric distribution about the hydrofoil vertical centre plane. Nuclei activation rate is determined from the acoustic measurements, and was found to be proportional to the number of the injected nuclei. A power law increase in activation rate was observed following a decrease in cavitation number and an increase in Reynolds number. The nuclei activation rate was of the order of $0.1{-}10 \, \mathrm {s^{-1}}$, which combined with seeding rates of the orderof $100{-}1000 \, \mathrm {s^{-1}}$ reveals inception to be a rare occurrence (0.001 %–10 % of nuclei being activated), requiring the confluence of two unlikely events, the occurrence of a subvapour pressure vortex core with capture of a sufficiently weak nuclei. The presented study provides new insights into the physics of cavitation nucleation and inception and provides a comprehensive dataset for development of computational models.