We investigate the onset of thermosolutal instabilities in a moderately dense nanoparticle suspension layer with a deformable interface. The suspension is deposited on a solid substrate subjected to a specified constant heat flux. The Soret effect and the action of gravity are taken into account. A mathematical model for the system considered with nanoparticle concentration-dependent density, viscosity, thermal conductivity and the Soret coefficient is presented in dimensional and non-dimensional forms. Linear stability analysis of the obtained base state is carried out using disturbances in the normal mode, and the corresponding eigenvalue problem is derived and numerically investigated. The onset of various instabilities is investigated for cases of both heating and cooling at the substrate. The monotonic solutocapillary instability is found in the case of cooling at the substrate, which exhibits two competing mechanisms that belong to two different disturbance wavelength domains. We identify the occurrence of both monotonic and oscillatory thermocapillary instabilities when the system is heated at the substrate. Furthermore, we show the emergence of the solutal buoyancy instability due to density variation which is promoted by the Soret effect adding nanoparticles heavier than the carrier fluid in the proximity of the layer interface. Transitions from the monotonic to oscillatory thermocapillary instability are found with variation in the gravity- and solutocapillarity-related parameters. Notably, we identify a previously unknown transition from monotonic to the oscillatory thermocapillary instability due to the variation in the strength of the thermal-conductivity stratification coupled with the Soret effect.

Jet penetration into soft gels is essential for optimising fluid delivery in medical therapies, biomedical engineering, and soft robotics. In this work, we visualise the jet flow of a Newtonian fluid into a soft viscoplastic gel using camera imaging and time-resolved tomographic particle image velocimetry (PIV) systems. The flow is primarily governed by the Reynolds number ($Re = 350-5000$) and the effective viscosity ratio ($m$ up to 22). We observe three flow regimes – mixing, jellyfish, and fingering – with transitions between them quantified in the $Re-m$ plane. An experimentally informed, systematic, practical, semi-analytical modelling framework is developed to estimate jet penetration depth over time, incorporating PIV results and an approximate functional decomposition approach to describe the velocity distribution and Reynolds stress contributions. The model provides reasonable estimations across all three regimes.

Porous membranes, like nets or filters, are thin structures that allow fluid to flow through their pores. Homogenisation can be used to rigorously link the flow velocity with the stresses on the membrane via several coefficients (e.g. permeability and slip) stemming from the solution of Stokes problems at the pore level. For a periodic microstructure, the geometry of a single pore determines these coefficients for the whole membrane. However, many biological membranes are not periodic, and the porous microstructure of industrial membranes can be modified to address specific needs, resulting in non-periodic patterns of solid inclusions and pores. In this case, multiple microscopic calculations are needed to retrieve the local non-periodic membrane properties, negatively affecting the efficiency of the homogenised model. In this paper, we introduce an adjoint-based procedure that drastically reduces the computational cost of these operations by computing the pore-scale solution’s first- and second-order sensitivities to geometric modifications. This adjoint-based technique only requires the solution of a few problems on a reference geometry and allows us to find the homogenised solution on any number of modified geometries. This new adjoint-based homogenisation procedure predicts the macroscopic flow around a thin aperiodic porous membrane at a fraction of the computational cost of classical approaches while maintaining comparable accuracy.

Cargo carrying by a spring connected chiral micro-swimmer in a square channel is numerical studied by the three-dimensional lattice Boltzmann method and a chiral squirmer model. The effects of the driving type (β), swimming Reynolds number (Rep), spin coefficient (ξ) and diameter ratio (S) on the changes of the cargo-carrying velocity, spring length and motion modes are investigated, respectively. Four kinds of interesting motion modes are observed. When the chirality is not considered, the optimal combination for maximising swimming velocity are the pusher–cargo and cargo–puller configurations when Rep = 0.1 ∼ 1. When Rep is enhanced, the swimming velocities of the pusher–cargo, puller–cargo and cargo–pusher are increased, while the velocity of the cargo–puller is gradually decreased. When considering the chirality, only the swimming velocity of cargo–pusher and cargo–puller keep an interesting increment, and the reverse motion mode for the pusher-cargo and puller-cargo is firstly found in the present work when ξ exceeds a certain value. The impact of S on the cargo-carrying behaviour is complex, three kinds of oscillatory trajectories will appear under different ξ and S. The swimming velocity is reduced and even zero velocity will be observed when S is large. This work reveals key factors on the movement of microorganisms, offering guidance for improving cargo-carrying capabilities.