Understanding how bubbles on a substrate respond to ultrasound is crucial for applications from industrial cleaning to biomedical treatments. Under ultrasonic excitation, bubbles can undergo shape deformations due to Faraday instability, periodically producing high-speed jets that may cause damage. While recent studies have begun to elucidate this behaviour for free bubbles, the dynamics of wall-attached bubbles is still largely unexplored. In particular, the selection and evolution of non-spherical modes in these bounded systems have not previously been resolved in three dimensions, and the resulting jetting dynamics has yet to be compared with that observed in free bubbles. In this study, we investigate individual micrometric air bubbles in contact with a rigid substrate and subjected to ultrasound. We introduce a novel dual-view imaging technique that combines top-view bright-field microscopy with side-view phase-contrast X-ray imaging, enabling visualisation of bubble shape evolution from two orthogonal perspectives. This set-up reveals the progression of bubble shape through four distinct dynamic regimes: purely spherical oscillations, onset of harmonic axisymmetric meniscus waves, emergence of half-harmonic axisymmetric Faraday waves and the superposition of half-harmonic sectoral Faraday waves. This stepwise evolution contrasts with the behaviour of free bubbles, which exhibit their ultimate Faraday wave pattern immediately upon instability onset. For the substrate chosen, the resulting shape-mode spectrum appears to be degenerate and exhibits a continuous range of shape mode degrees, in line with our theoretical predictions derived from kinematic arguments. While free bubbles also display a degenerate spectrum, their shape mode degrees remain discrete, constrained by the bubble spherical periodicity. Experimentally measured ultrasound pressure thresholds for the onset of Faraday instability agree well with classical interface stability theory, modified to incorporate the effects of a rigid boundary. Complementary three-dimensional boundary element simulations of bubble shape evolution align closely with experimental observations, validating this method’s predictive capability. Finally, we determine the acceleration threshold at which shape mode lobes initiate cyclic jetting. Unlike free bubbles, jetting in wall-attached bubbles consistently emerges from the side not restricted by the substrate.

We focus on the wake of a cylinder placed in uniform flow and forced to rotate periodically at subcritical Reynolds numbers, i.e. for Reynolds numbers smaller than 47 calculated based on the incoming flow velocity and the cylinder diameter, where vortices are not shed in the wake of a fixed cylinder. We show that in the near wake, the imposed periodic rotation causes the Föppl vortices (the symmetric steady vortices that are formed right behind a fixed cylinder within the Reynolds number range of $5\lt {Re}\lt 47$) to appear only momentarily during each rotation cycle until they disappear at higher rotation rates. In the far wake, vortices can be induced for certain values of rotation rate, $\alpha$, and rotation frequency, $f$. The shedding of these vortices in the wake results in a periodic lift force that acts on the cylinder. We have defined a new parameter $\omega /(f\alpha )\equiv 1/F$, where $\omega$ is the angular velocity of the cylinder, which is significant in describing the system. For any values of angular velocity and the frequency of change in the rotation direction, the wake pattern remains the same if the value of $1/F$ stays constant. Subsequently, the fluctuating lift coefficient and the average drag coefficient peak at the same value of $1/F$ for any value of $\omega /f\equiv \alpha /F$. The Reynolds number for the onset of shedding decreases with increasing rotation rate at a constant $\alpha /F$. We have observed shedding at Reynolds numbers as low as ${Re}=1$ for higher rotation rates.

Axisymmetric turbulent boundary layers are of great significance in industry and the fluid dynamics community. In this paper, direct numerical simulations of an axially developing axisymmetric turbulent boundary layer along a slender cylinder are performed. Periodical suction and blowing perturbation are used to trigger the transition from laminar inflow to turbulent flow downstream, resulting in the boundary layer thickness varying from 7 to 13 times the cylinder radius, and the friction Reynolds number varying from 300 to 510. Turbulence statistics including wall friction coefficient, mean velocity profile and Reynolds stresses are obtained. The turbulence intensities are weakened compared with the planar turbulent layer, and the inter-component energy transfer is also inhibited. A curvature-weighted transformation is proposed, and the transformed Reynolds stresses and mean velocity deficit collapse well with the planar case in the near-wall region. The velocity streaks and vortical structures are explored. The wall-normal variation of the mean spanwise spacing of low-speed streaks is greatly influenced by the cylindrical geometry. Quasi-streamwise vortices dominate the near-wall region, and the arch vortices are prevalent in the outer region. The prograde hairpin vortices can be commonly observed.

A rotating detonation combustor exhibits corotating $N$-wave modes with $N$ detonation waves propagating in the same direction. These modes and their responses to ignition conditions and disturbances were studied using a surrogate model. Through numerical continuation, a mode curve (MC) is obtained, depicting the relationship between the wave speed of the one-wave mode and a defined baseline of the combustor circumference ($L_{{base}}$) under fixed equation parameters, limited by deflagration and flow choking. The modes’ existence is confirmed by the equivalence between a one-wave mode within a combustor with circumference $L_{{base}}$/$N$ on the MC and an $N$-wave mode in an $L_{{base}}$ combustor. The stability, measured by the real part of the eigenvalue from linear stability analysis (LSA), revealed the dynamic properties. When multiple stable modes exist under the same parameters, ignition conditions with a spatial period of $L_{{base}}$/$N$ are more likely to form $N$-wave modes. An unstable evolution in formed modes, occurs in the dynamics from stable to unstable modes through saddle-node bifurcation and Hopf bifurcation induced by parameter perturbations and from unstable to stable modes induced by state disturbances. Eigenmodes from LSA reveal mechanisms of the unstable evolution, including the effect of secondary deflagration in the unstable one-wave mode and competitive interaction between detonation waves in the unstable multiwave mode, crucial for the combustor to mode transition.

Uniform arrays of particles tend to cluster as they sediment in viscous fluids. Shape anisotropy of the particles enriches this dynamics by modifying the mode structure and the resulting instabilities of the array. A one-dimensional lattice of sedimenting spheroids in the Stokesian regime displays either an exponential or an algebraic rate of clustering depending on the initial lattice spacing (Chajwa et al. 2020 Phys. Rev. X vol. 10, pp. 041016). This is caused by an interplay between the Crowley mechanism, which promotes clumping, and a shape-induced drift mechanism, which subdues it. We theoretically and experimentally investigate the sedimentation dynamics of one-dimensional lattices of oblate spheroids or discs and show a stark difference in clustering behaviour: the Crowley mechanism results in clumps comprising several spheroids, whereas the drift mechanism results in pairs of spheroids whose asymptotic behaviour is determined by pair–hydrodynamic interactions. We find that a Stokeslet, or point-particle, approximation is insufficient to accurately describe the instability and that the corrections provided by the first reflection are necessary for obtaining some crucial dynamical features. As opposed to a sharp boundary between exponential growth and neutral eigenvalues under the Stokeslet approximation, the first-reflection correction leads to exponential growth for all initial perturbations, but far more rapid algebraic growth than exponential growth at large dimensionless lattice spacing $\tilde {d}$. For discs with aspect ratio $0.125$, corresponding to the experimental value, the instability growth rate is found to decrease with increasing lattice spacing $\tilde {d}$, approximately as $\tilde {d}^{ -4.5}$, which is faster than the $\tilde {d}^{-2}$ for spheres (Crowley 1971 J. Fluid Mech. vol. 45, pp. 151–159). It is shown that the first-reflection correction has a stabilising effect for small lattice spacing and a destabilising effect for large lattice spacing. Sedimenting pairs predominantly come together to form an inverted ‘T’, or ‘$\perp$’, which our theory accounts for through an analysis that builds on Koch & Shaqfeh (1989 J. Fluid Mech. vol. 209, pp. 521–542). This structure remains stable for a significant amount of time.

Suspensions of microswimmers exhibit distinct characteristics as compared with those of passive particles because the internal particles are in a state of spontaneous motion. Although there have been many studies of microswimmer suspensions, not many have carefully considered the hydrodynamics. Hydrodynamics becomes particularly important when discussing non-dilute suspensions, because the lubrication flow generates a large force when the swimmers are in close proximity. This paper focuses on hydrodynamics and describes the transport phenomena of microswimmer suspensions, such as migration, collective motion, diffusion and rheology. The paper is structured to progressively scale up from a single microswimmer to collective motion to a macroscale continuum. At each scale, the discussion also evolves from dilute to concentrated suspensions. We first introduce natural swimming microorganisms, artificial microswimmers and mathematical models, as well as the fundamentals of fluid mechanics relevant to microswimmers. We then describe the migration of microswimmers by taxis, where microswimmers respond passively or actively to their hydrodynamic environment. Microswimmers exhibit collective motions, the mechanism of which is discussed in terms of hydrodynamics. The spreading of microswimmers is often diffusive, and the diffusion coefficient is much larger than for passive particles. Similarly, the mass diffusivity in microswimmer suspensions is higher due to their swimming activity. We explain these macroscopic diffusion properties. The viscosity of microswimmer suspensions can be higher or lower depending on the characteristics and orientation of the microswimmers. We describe the rheological properties of microswimmer suspensions in shear flow and Poiseuille flow. Finally, current issues and future research perspectives are discussed.

An experimental study was conducted to investigate the impingement of a vortex ring onto a porous wall by laser-induced fluorescence and particle image velocimetry. The effects of different Reynolds numbers (${{Re}}_{\it\Gamma } = 700$ and $1800$) and hole diameters ($d_{h}^{*} = 0.067$, $0.10$, $0.133$ and $0.20$) on the flow characteristics were examined at a constant porosity ($\phi = 0.75$). To characterise fluid transport through a porous wall, we recall the model proposed by Naaktgeboren, Krueger & Lage (2012, J. Fluid Mech., vol. 707, 260–286), which shows rough agreement with the experimental results due to the absence of vortex ring characteristics. This highlights the need for a more accurate model to correlate the losses in kinetic energy ($\Delta E^{*}$) and impulse ($\Delta I^{*}$) resulting from the vortex ring–porous wall interaction. Starting from Lamb’s vortex ring model and considering the flow transition from the upstream laminar state to the downstream turbulent state caused by the porous wall disturbance, a new model is derived theoretically: $\Delta E^{*} = 1 - k(1 - \Delta I^{*})^2$, where $k$ is a parameter dependent on the dimensionless core radius $\varepsilon$, with $k = 1$ when no flow state change occurs. This new model effectively correlates $\Delta E^{*}$ and $\Delta I^{*}$ across more than 70 cases from current and previous experiments, capturing the dominant flow physics of the vortex ring–porous wall interaction.

To address the global climate crisis, it is urgent to achieve carbon neutrality by the mid-21st century, balancing carbon emissions and carbon absorption from the atmosphere. This study examines the current advancements in biological methods for capturing carbon dioxide (CO2) in response to global climate change, emphasizing the importance of sequestering CO2 through biological carbon capture and utilization. First, we present an overview of typical carbon capture methods, including geological and oceanic carbon storage. We then highlight the significance of utilizing photosynthetic organisms, such as plants, algae and microorganisms, for carbon capture and sequestration. We also analyze the role of photosynthesis in carbon capture and explore the potential of microbial carbon capture, examining the impact of environmental factors on capture efficiency. Additionally, we discuss the development of symbiotic approaches to enhance carbon fixation capacity. Finally, this review provides key insights into the challenges and future directions in advancing the field of biological carbon capture to achieve carbon neutrality.

Submerged flexible aquatic vegetation exists widely in nature and achieves multiple functions mainly through fluid–structure interactions (FSIs). In this paper, the evolution of large-scale vortices above the vegetation canopy and its effect on flow and vegetation dynamics in a two-dimensional (2-D) laminar flow are investigated using numerical simulations under different bending rigidity $\gamma$ and gap distance d. According to the variation of large-scale vortex size and intensity, the evolution process is divided into four distinct zones in the streamwise direction, namely the ‘developing’ zone, ‘transition’ zone, ‘dissipation’ zone and ‘interaction’ zone, and different evolution sequences are further classified. In the ‘developing’ zone, the size and intensity of the large-scale vortex gradually increase along the array, while they decrease in the ‘dissipation’ zone. The supplement of vegetation oscillating vortices to large-scale vortices is the key to the enhancement of the latter. The most obvious dissipation of large-scale vortices occurs in the ‘transition’ zone, where the position of the large-scale vortex is significantly uplifted. The effects of $\gamma$ and d on the evolution of the large-scale vortex are discussed. In general, the features of vegetation swaying vary synchronously with those of large-scale vortices. The flow above the canopy is dominated by large-scale vortices, and the development of flow characteristics such as time-averaged velocity profile and Reynolds stress are closely related to the evolution of large-scale vortices. The flow inside the canopy, however, is mainly affected by the vortex shed by the vegetation oscillation, which leads to the emergence of negative time-averaged velocity and negative Reynolds stress.