We derive boundary conditions for two-dimensional parallel and non-parallel flows at the interface of a homogeneous and isotropic porous medium and an overlying fluid layer by solving a macroscopic closure problem based on the asymptotic solution to the generalised transport equations (GTE) in the interfacial region. We obtained jump boundary conditions at the effective sharp surface dividing the homogeneous fluid and porous layers for either the Darcy or the Darcy–Brinkman equations. We discuss the choice of the location of the dividing surface and propose choices which reduce the distance with the GTE solutions. We propose an ad hoc expression of the permeability distribution within the interfacial region which enables us to preserve the invariance of the fluid-side-averaged velocity profile with respect to the radius $r_0$ of the averaging volume. Solutions to the GTE, equipped with the proposed permeability distribution, compare favourably with the averaged solutions to the pore-scale simulations when the interfacial thickness $\delta$ is adjusted to $r_0$. Numerical tests for parallel and non-parallel flows using the obtained jump boundary conditions or the generalised transport equations show quantitative agreement with the GTE solutions, with experiments and pore-scale simulations. The proposed model of mass and momentum transport is predictive, requiring solely information on the bulk porosity and permeability and the location of the solid matrix of the porous medium. Our results suggest that the Brinkman corrections may be avoided if the ratio $a=\delta /\delta _B$ of the thickness $\delta$ of the interfacial region to the Brinkman penetration depth $\delta _B$ is large enough, as the Brinkman sub-layer is entirely contained within the interfacial region in that case. Our formulation has been extended to anisotropic porous media and can be easily dealt with for three-dimensional configurations.

We examined theoretically, experimentally and numerically the origin of the acoustothermal effect using a standing surface acoustic wave-actuated sessile water droplet system. Despite a wealth of experimental studies and a few recent theoretical explorations, a profound understanding of the acoustothermal mechanism remains elusive. This study bridges the existing knowledge gap by pinpointing the fundamental causes of acoustothermal heating. Theory broadly applicable to any acoustofluidic system at arbitrary Reynolds numbers, going beyond the regular perturbation analysis, is presented. Relevant parameters responsible for the phenomenon are identified and an exact closed-form expression delineating the underlining mechanism is presented. We also examined the impact of viscosity on acoustothermal phenomena by modelling temperature profiles in sessile glycerol–water droplets, underscoring its crucial role in modulating the acoustic field and shaping the resulting acoustothermal profile. Furthermore, an analogy between the acoustothermal effect and the electromagnetic heating is drawn, thereby deepening the understanding of the acoustothermal process.

We investigate experimentally the effect of salinity and atmospheric humidity on the drainage and lifetime of thin liquid films motivated by conditions relevant to air–sea exchanges. We show that the drainage is independent of humidity and that the effect of a change in salinity is reflected only through the associated change in viscosity. On the other hand, film lifetime displays a strong dependence on humidity, with more than a tenfold increase between low and high humidities: from a few seconds to tens of minutes. Mixing the air surrounding the film also has a very important effect on lifetime, modifying its distribution and reducing the mean lifetime of the film. From estimations of the evaporation rate, we are able to derive scaling laws that describe well the evolution of lifetime with a change of humidity. Observations of the black film, close to the top where the film ruptures, reveal that this region is very sensitive to local humidity conditions.

Noise source identification has been a long-standing challenge for decades. Although it is known that sound sources are closely related to flow structures, the underlying physical mechanisms remain controversial. This study develops a sound source identification method based on longitudinal and transverse process decomposition (LTD). Large-eddy simulations were performed on the flow around a cylinder at a Reynolds number of 3900. Using the new LTD method, sound sources in the cylinder flow were identified, and the mechanisms linking flow structures with noise generation were discussed in detail. Identifying the physical sound sources from two levels, low-order theory and high-order theory, the physical mechanism of wall sound sources was also analysed. Results indicate that the sound sources in the flow field mainly come from the leading edge, shear layer and wake region of the cylinder. The high-order theory reveals that sound sources are correlated with the spatio-temporal evolution of enstrophy, vortex stretching and surface deformation processes, this reflecting the coupling between transversal and longitudinal flow fields. The boundary thermodynamic flux and boundary dilatation flux distribution of the cylinder were analysed. Results indicate that the wall sound sources mainly come from the separation point and have a disorderly distribution on the leeward side of the cylinder, which is the main region where longitudinal variables enter the fluid from the wall surface, and the wall sound source is related to the boundary enstrophy flux.

Numerous studies showed that the flow and transport phenomena in angstrom channels are different from existing understandings. In this work, we investigate the electrokinetic phenomena in a charged angstrom channel, including homogeneous and heterogeneous charge distributions at the wall to mimic the charging mechanisms of electrified metal-like surfaces and deprotonated dielectric surfaces, respectively. Our results show that both the streaming current and the flow velocity linearly increase as the applied pressure increases in a homogeneously charged system. However, in a heterogeneously charged system, the streaming current is activated only when the applied pressure exceeds a critical threshold. This behaviour arises from the strong Coulomb interactions between counterions and the surface charge, manifesting as an obvious nonlinear feature. The dissociation of counterions from the surface charge may not only cause pressure-dependent streaming conductance but also reduce the friction coefficient of the system, thus the flow resistance, when the system friction is governed by the bound ions. We found that such pressure-dependent streaming conductance gradually weakens as the channel size increases and reaches the regime of classical nanofluidic theories. Taking one-dimensional non-equilibrium statistics and Markov chains for the sequence evolution of bound-ion dissociation, our theory can well explain the pressure-dependent streaming conductance and water permeability in angstrom charged channels. Voltage-driven nonlinear ionic transport and electro-osmosis were also observed in heterogeneously charged systems. Our findings will be helpful for understanding the ionic transport in angstrom-scale channels and possibly useful in ion separations.

Embedding the intrinsic symmetry of a flow system in training its machine learning algorithms has become a significant trend in the recent surge of their application in fluid mechanics. This paper leverages the geometric symmetry of a four-roll mill (FRM) to enhance its training efficiency. Stabilising and precisely controlling droplet trajectories in an FRM is challenging due to the unstable nature of the extensional flow with a saddle point. Extending the work of Vona & Lauga (Phys. Rev. E, vol. 104(5), 2021, p. 055108), this study applies deep reinforcement learning (DRL) to effectively guide a displaced droplet to the centre of the FRM. Through direct numerical simulations, we explore the applicability of DRL in controlling FRM flow with moderate inertial effects, i.e. Reynolds number $\sim \mathcal{O}(1)$, a nonlinear regime previously unexplored. The FRM’s geometric symmetry allows control policies trained in one of the eight sub-quadrants to be extended to the entire domain, reducing training costs. Our results indicate that the DRL-based control method can successfully guide a displaced droplet to the target centre with robust performance across various starting positions, even from substantially far distances. The work also highlights potential directions for future research, particularly focusing on efficiently addressing the delay effects in flow response caused by inertia. This study presents new advances in controlling droplet trajectories in more nonlinear and complex situations, with potential applications to other nonlinear flows. The geometric symmetry used in this cutting-edge reinforcement learning approach can also be applied to other control methods.

The dynamics of flow over an isolated surface-mounted hemisphere are investigated with tomographic particle image velocimetry (PIV). The 10 mm height hemisphere is completely submerged in the laminar boundary layer, and the height-based Reynolds number is 1530. The evolution of typical coherent structures around the hemisphere are discussed, with emphasis on the hairpin vortex (HV) and side hairpin vortex (SHV) formed periodically in the middle and both sides of the wake, respectively. Proper orthogonal decomposition (POD) analysis is conducted to explore the vortex dynamics. The shedding processes of the HV and SHV are each dominated by two different POD modes with correspondingly different characteristic frequencies, which has not been reported before in the literature. Furthermore, the coexistence of symmetric and asymmetric shedding patterns is explored for the first time in the shedding process of the HV at such a low Reynolds number. The asymmetric behaviour is controlled by the asymmetric shedding POD mode, whose dominant frequency is exactly half of the symmetric mode. In addition, SHVs on both sides of the wake are throughout formed and shed alternately, and the streamwise extensions of a horseshoe vortex also oscillate asymmetrically, which are responsible for the formation of the asymmetric shedding pattern of the HV. These findings help to fill the gaps in the related field and contribute to studies on the vortex dynamics of the flow over a hemisphere.