We demonstrate through the use of a unique acoustically driven microfluidic extensional rheometry platform (ADMiER) that a single measurement – i.e. the time required for a liquid bridge filament comprising a microlitre semen sample to thin and break up under elastocapillary stresses – constitutes an appropriate proxy for quantifying the motile sperm concentration of the sample in place of computer-assisted sperm analysis (CASA) and haemocytometer measurements used in conventional semen assessment – without the need to separately resolve for individual dependencies on each sperm parameter. By benchmarking diagnostic test accuracy results of blind random bull semen samples ($n=35$) against OpenCASA measurements of these parameters, ADMiER is capable of predicting sperm quality to 93.7 % accuracy, 91.4 % sensitivity and 97.5 % specificity, with respect to commonly adopted veterinary industry minimum values for fertility. These results therefore highlight the potential diagnostic capability of the platform as a conceptual first step towards the development of a rapid, low-cost and portable alternative for veterinary male bovine fertility assessment.

The physics and mechanism of sheet/cloud cavitation in a convergent–divergent channel are investigated using synchronized dynamic surface pressure measurement and high-speed imaging in a water tunnel to probe the cavity shedding mechanism. Experiments are conducted at a fixed Reynolds number of Re = 7.8 × 105 for different values of the cavitation number σ between 1.20 and 0.65, ranging from intermittent inception cavitation, sheet cavitation to quasi-periodic cloud cavitation. Two distinct cloud cavitation regimes, i.e. the re-entrant jet and shockwave shedding mechanism, are observed, accompanied by complex flow phenomenon and dynamics, and are examined in detail. An increase in pressure fluctuation intensity at the numbers 3 and 4 transducer locations are captured during the transition from re-entrant jet to shockwave shedding mechanism. The spectral content analysis shows that, in cloud cavitation, several frequency peaks are identified with the dominant frequency caused by the large-scale cavity shedding process and the secondary frequency related to re-entrant jet/shockwave dynamics. Statistical analysis based on defined grey level profiles reveals that, in cloud cavitation, the double-peak behaviours of the probability density functions with negative skewness values are found to be owing to the interactions of the re-entrant jet/shockwave with cavities in the region of 0.25 ~ 0.65 mean cavity length (Lc). In addition, multi-scale proper orthogonal decomposition analysis with an emphasis on the flow structures in the region of 0.25 ~ 0.65 Lc reveals that, under the shockwave shedding mechanism, both the re-entrant jet and shockwave are captured and their interactions are responsible for the dynamics and statistics of cloud shedding process.

We revisit the laminar–turbulent transition of a fine-grained slurry in a large pipe. The combination of long measurement times in an industrial-scale facility and ultrasound imaging allows us to observe and address anomalous trends. Under turbulent conditions, the flow is homogeneous and steady. However, under laminar conditions, two types of long-time-scale transient behaviours are captured. In the first scenario, the system has been homogenized, following which the flow rate is reduced to laminar conditions. The flow rate continues to gradually drop, while particles settle and form a stationary bed. In the second scenario, the system has been shut down for a prolonged period and the flow rate is slowly increased. The flow rate continues to rise while particles are slowly resuspended from the gradually eroding bed. Near the laminar–turbulent transition point, two types of intermittent structures are responsible for resuspension. The equilibrium phase, with steady flow rate, coincides with complete resuspension. These two long-time-scale transients correspond to the phenomena of ‘slow settling’ and ‘self-equilibration’, respectively. While the former can lead to shutdowns, the latter generates a stable system. Being aware of these phenomena is of relevance while operating slurry pipelines near the favourable operating point of the laminar–turbulent transition.

The axially symmetric, swirl-free gas dynamics and interlinked motion of a cork stopper provoked by the opening of a champagne bottle are modelled rigorously and studied numerically. The experimental study by Liger-Belair et al. (Science Advances, 5(9), 2019) animated the present investigation. Inspection analysis justifies the inviscid treatment of the expanding jet of air enriched with dissolved carbonic acid gas initially pressurised in the bottle. Solving of the resulting Euler equations is facilitated by the open-source software Clawpack. Specific enhancements allow for resolving of the emerging supersonic pockets, associated with surprisingly complex shock structures, as well as the gas–stopper interaction with due accuracy. Our experimental effort provided modelling of the frictional behaviour, constitutive law and reversible (de-)compression of the cork material. Initially, the gas expands inside the bottleneck yet sealed by the stopper, and is hence accelerated by the gas but decelerated by dry sliding friction. Once the stopper has passed the bottle opening, the jet rapidly assumes locally supersonic speed, where a complex shock pattern is detected. Special attention is paid to the formation and dissolution of one or even two Mach discs between the opening and the released stopper. This simulated dynamics is found to be in fairly good agreement with recent experimental findings. It also provides a first insight into the generation of the typical popping sound.

This study aims to leverage the relationship between fluid dynamic loading and resulting structural deformation to infer the incident flow speed from measurements of time-dependent structure kinematics. Wind tunnel studies are performed on cantilevered cylinders and trees. Tip deflections of the wind-loaded structures are captured in time series data, and a physical model of the relationship between force and deflection is applied to calculate the instantaneous wind speed normalized with respect to a known reference wind speed. Wind speeds inferred from visual measurements showed consistent agreement with ground truth anemometer measurements for different cylinder and tree configurations. These results suggest an approach for non-intrusive, quantitative flow velocimetry that eliminates the need to directly visualize or instrument the flow itself.

The present paper simplifies the naturally formed dunes (riverbeds) as large-scale three-dimensional staggered wavy walls to investigate the features of the accompanying secondary flows and streamwise vortices via large-eddy simulation. A comparison between the swirling strength and the mean velocities suggests where a secondary flow induces upwash or downwash motions. Moreover, we propose a pseudo-convex wall mechanism to interpret the directionality of the secondary flow. The centrifugal instability criterion is then used to reveal the generation of the streamwise vortices. Based on these analytical results, we found that the streamwise vortices are generated in the separation and reattachment points on both characteristic longitudinal–vertical and horizontal cross-sections, which is related to the curvature effect of the turbulent shear layer. Furthermore, the maximum Görtler number characterized by the ratio of centrifugal to viscous effects suggests that, for fixed ratio of spanwise- to streamwise-wavelength cases, the strongest centrifugal instability occurring on the longitudinal–vertical cross-section gradually dominates with the increases in amplitude. A similar trend for the cases with varied spanwise wavelength can also be found. It is also found that the streamwise vortices are generated more readily via transverse flow around the crest near the separation and reattachment points when the ratio of spanwise- to streamwise-wavelength equals 1.

Locomoting organisms often carry loads such as captured prey or young. Load-carrying effects on high-Reynolds-number flight have been studied, but the fluid dynamics of load carrying by low-Reynolds-number microorganisms has not. We studied low-Reynolds-number load carrying using unicellular choanoflagellates, which wave a flagellum to swim and create a water current transporting bacterial prey to a food-capturing collar of microvilli. A regularized Stokeslet framework was used to model the hydrodynamics of a swimming choanoflagellate with bacterial prey on its collar. Both the model and microvideography of choanoflagellates showed that swimming speed decreases as number of prey being carried increases. Flux of water into the capture zone is reduced by bacteria on the collar, which redirect the water flow and occlude parts of the collar. Feeding efficiency (prey captured per work to produce the feeding current) is decreased more by large prey, prey in the plane of flagellar beating and prey near microvillar tips than by prey in other locations. Some choanoflagellates can attach themselves to surfaces. We found that the reduction in flux due to bacterial prey on the collars of these attached thecate cells was similar to the reduction in flux for swimmers.

Thwaites (Aeronaut. Q., vol. 1, 1949, pp. 245–280) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations (Alber, 9th Aerospace Sciences Meeting, 1971). The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

Bernoulli pads can create a significant normal force on an object without contact. The radial outflow which creates this force also imposes a significant shear force on the object. Better understanding this shear force can improve pad designs in order to mitigate material deformation and damage, or allow the pads to be used as shear-based cleaning implements. Here, we use computational fluid dynamics to explore the parameter space and show a power-law relationship between the fluid power at the pad inlet and the maximum shear stress. These simulations are validated by a particle tracking velocimetry experiment. A relationship between the maximum shear stress and the inlet Reynolds number is provided, and some implications of the observed scaling relationships are explored.

Fish often swim in crystallized group formations (schooling) and orient themselves against the incoming flow (rheotaxis). At the intersection of these two phenomena, we investigate the emergence of unique schooling patterns through passive hydrodynamic mechanisms in a fish pair, the simplest subsystem of a school. First, we develop a fluid dynamics-based mathematical model for the positions and orientations of two fish swimming against a flow in an infinite channel, modelling the effect of the self-propelling motion of each fish as a point-dipole. The resulting system of equations is studied to gain an understanding of the properties of the dynamical system, its equilibria and their stability. The system is found to have five types of equilibria, out of which only upstream swimming in in-line and staggered formations can be stable. A stable near-wall configuration is observed only in limiting cases. It is shown that the stability of these equilibria depends on the flow curvature and streamwise interfish distance, below critical values of which, the system may not have a stable equilibrium. The study reveals that simply through passive fluid dynamics, in the absence of any other feedback/sensing, we can justify rheotaxis and the existence of stable in-line and staggered schooling configurations.

Developed in this paper is a theoretical description of the fluid flow involved in contactless transport systems that operate using squeeze-film levitation. Regular perturbation methods are employed to solve the appropriate Reynolds equation that governs the viscous, compressible flow of air in the slender film separating the oscillator and the levitated object. The resulting reduced formulation allows efficient computation of the time-averaged levitation force and moment induced by fluid pressure, as well as the accompanying quasistatic thrust force that accounts additionally for shear stresses. Investigated, in particular, is the possibility of combining two distinct methods of thrust generation that have been experimentally demonstrated in previous studies – (i) inclination of the levitated body and (ii) generation of asymmetrical flexural deformations, such as travelling waves, on the oscillator surface – the latter of which is shown to allow a transition from the typically repulsive levitation force to one that is attractive. Computations reveal that systematic control of the inclination angle can provide significant performance benefits for squeeze-film transport systems. In the case of attractive levitation, the amount of improvement that can be obtained appears to correlate closely with the degree of lateral asymmetry exhibited by the flexural oscillations.

Rotorcraft can encounter highly unsteady flow when descending at a steep angle, leading to a flow condition called vortex ring state, which is associated with strong oscillatory airloads and substantial losses in mean rotor thrust. This study examines the aerodynamic coupling between closely arranged rotors in vertical flight and assesses the extent to which rotor–rotor interactions affect the rotor performance in this flight stage. Wind tunnel experiments were performed on a small-scale, dual-rotor set-up with adjustable rotor spacing, and the effect of rotor separation on thrust generation was quantified. Pairs of 4 in., 5 in. and 6 in. rotors ($3.0 \times 10^4< Re<8.1 \times 10^4$) were investigated, with load cell measurements showing significant thrust losses and concomitantly increased thrust oscillations as descent rate increased. Peak losses and fluctuations were consistently recorded at descent rates of 1.2–1.3 times the hover induced velocity for all rotor sizes and separations. While tests showed that the mean aerodynamic performance of dual-rotor systems is generally similar to that of single rotors, appreciable changes to the descent characteristics could be observed at low rotor separations. Particle image velocimetry flow visualization suggests considerable changes to the flow field as rotor separation decreases, where individual vortex ring systems merge into a single vortex ring structure.

Redox flow batteries (RFBs) are an emerging electrochemical technology envisioned towards storage of renewable energy. A promising sub-class of RFBs utilizes single-flow membraneless architectures in an effort to minimize system cost and complexity. To support multiple functions, including reactant separation and fast reactant transport to electrode surfaces, electrolyte flow must be carefully designed and optimized. In this work, we propose adding a secondary channel adjacent to a permeable battery electrode, solving for the flow field and analysing the effects on the reactant concentration boundary layer at the electrode. We find that an adjacent channel with gradually changing thickness leads to a desired nearly uniform flow through the electrode to the adjacent channel. Consequently, the thickness of the concentration boundary layer is significantly reduced, increasing reactant transport to the electrode surface to 140% of the rate of a battery with a constant width adjacent channel, and 350% of the rate with no adjacent channel. Overall, this theory provides insight into the important role of flow physics for this promising sub-class of flow batteries, and can pave the way to improved energy efficiency of such flow batteries.

Supersonic rectangular twin jets (SRTJ) are of interest for current and future generations of tactical aircraft. However, the adverse effects of screech-loop coupling have previously been documented to significantly increase the near-field (NF) pressure fluctuations. These high-amplitude pressure fluctuations have the potential to fatigue and damage nearby aft components of the aircraft. Previous studies have documented that the NF pressure fluctuation level depends on the coupling of the jets: in-phase coupling along the twin jets’ minor axes produces stronger NF pressure fluctuations than that of out-of-phase coupling. The objective of this work is to further investigate the effects of coupling modes on NF pressure fluctuations in SRTJ and to mitigate the adverse effects of coupling using active flow control. Localized arc filament plasma actuators are employed to alter the SRTJs’ coupling mode by leveraging natural flow instabilities with minimal power input. A NF microphone array is used for simultaneous coupling and NF pressure fluctuation measurements. Schlieren imaging and spectral proper orthogonal decomposition are used to assess the effects of control on the flow field. The effect of excitation at various frequencies and actuation patterns on coupling and NF pressure fluctuations in different flow regimes are explored and discussed.

In this study, we propose a novel cooling scheme that utilizes copper inverse opals (CIOs) for surface enhancement in a single-phase impingement jet cooling system. We perform computational fluid dynamics simulations to evaluate the cooling performance of the CIO jet coolers. Our modelling results indicate that the proposed CIO-coated cooler can significantly reduce the average temperature and improve the temperature uniformity across the entire chip surface. The average Nusselt number of the CIO-coated cooler can reach up to 2.8 times that of the flat surface jet cooler. However, the porous structure of the CIO-coated cooler increases the total pressure drop. To determine designs with high cooling performance and low energy consumption, we investigate two crucial design factors, namely the inlet velocity and the nozzle-to-CIO distance. Our analysis reveals that increasing the inlet velocity further enhances the heat transfer, but at the expense of high pressure drop. On the other hand, a larger nozzle-to-CIO distance results in a lower pressure drop but also reduces the heat transfer coefficient. The effects of nozzle-to-CIO distance are further understood by studying the flow resistance network. Furthermore, we present a reduced-order model that accurately captures the thermofluidic characteristics of the proposed design.

In several problems involving fluid flows, computational fluid dynamics (CFD) provides detailed quantitative information and allows the designer to successfully optimize the system by minimizing a cost function. Sometimes, however, one cannot improve the system with CFD alone, because a suitable cost function is not readily available; one notable example is diagnosis in medicine. The application considered here belongs to the field of rhinology; a correct air flow is key for the functioning of the human nose, yet the notion of a functionally normal nose is not available and a cost function cannot be written. An alternative and attractive pathway to diagnosis and surgery planning is offered by data-driven methods. In this work, we consider the machine learning study of nasal impairment caused by anatomic malformations, with the aim of understanding whether fluid dynamic features, available after a CFD analysis, are more effective than purely geometric features at the training of a neural network for regression. Our experiments are carried out on an extremely simplified anatomic model and a correspondingly simple CFD approach; nevertheless, they show that flow-based features perform better than geometry-based ones and allow the training of a neural network with fewer inputs, a crucial advantage in fields like medicine.

Ionic fluids subjected to externally applied electric fields experience Joule heating, which increases with the increased electric field and ionic conductivity of the medium. Temperature gradients induced by Joule heating can create buoyancy-driven flows produced by local density changes, as well as electrothermal transport due to the temperature-dependent variations in fluid permittivity and conductivity. This manuscript considers Joule heating-induced transport in microchannels by a pair of electrodes under alternating current electric fields. Resulting buoyancy-driven and alternating current electrothermal (ACET) flows are investigated theoretically, numerically and experimentally. Proper normalizations of the governing equations led to the ratio of the electrothermal and buoyancy velocities, as a new non-dimensional parameter, which enabled the construction of a phase diagram that can predict the dominance of ACET and buoyancy-driven flows as a function of the channel size and electric field. Numerical results were used to verify the phase diagram in various height microchannels for different ionic conductivity fluids and electric fields, while the numerical results were validated using the micro-particle-image velocimetry technique. The results show that ACET flow prevails when the channel dimensions are small, and the electric potentials are high, whereas buoyancy-driven flow becomes dominant for larger channel heights. The present study brings insights into Joule heating-induced transport phenomena in microfluidic devices and provides a pathway for the design and utilization of ACET-based devices by properly considering the co-occurring buoyancy-driven flow.

The most common method to characterize the electrical response of a nanofluidic system is through its steady-state current–voltage response. In Part 1, we demonstrated that this current–voltage response depends on the geometry, the layout of the surface charge and the effects of advection. We demonstrated that each configuration has a unique steady-state signature. Here, we will elucidate the behaviour of the time-transient response. Similar to the steady-state response, we will show that each configuration has its own unique time-transient signature when subjected to electroosmotic instability. We show that bipolar systems behave differently than unipolar systems. In unipolar systems, the instability appears only at one end of the system. In contrast, in bipolar systems the instability will either appear on both sides of the nanochannel or not at all. If it does appear on both sides, the instability will eventually vanish on one or both sides of the system. In Part 1, these phenomena were explained using steady-state considerations of the behaviour of the fluxes. Here, we will examine the time-transient behaviour to reveal the governing principles that are, on the one hand, not so different from unipolar systems and, on the other hand, remarkably different.

Hollow fibre membrane bioreactors provide a fast and efficient method for engineering functional tissue for use in medical treatments. Flow is utilised to overcome mass transport limitations by perfusing a nutrient-rich culture medium through the fibre lumen, which can then transport along the fibre lumen or across the porous membrane wall. Cells seeded at the outer membrane wall consume the nutrient and subsequently produce waste metabolites, which are transported away through an external extra-capillary space (ECS) along with excess nutrient. We present and investigate a two-dimensional axisymmetric model for fluid flow and solute transport through a single-fibre bioreactor configuration, with cells seeded to the external fibre wall. Fluid flow is modelled by steady lubrication and Darcy equations, which are coupled to the solute transport problem modelled by a system of advection–diffusion equations, supplemented with a reaction term to model the cell layer. Our model analysis reveals how spatially varying wall permeability distributions can be utilised to provide uniform nutrient delivery to a spatially uniform, homogeneous cell population. We also reveal how maximising the transmural pressure drop across the membrane wall is the dominant mechanism for waste removal rather than traditional experimental methods of flushing the ECS.

Benthic macroalgae (including brown macroalgae or kelp) constitute one of the largest contributors to coastal primary production, but their ability to store and sequester carbon remains uncertain. Here, we use a numerical model of the flow/kelp interactions to study how tidal currents interact with an idealised numerical model of a giant kelp (Macrocystis pyrifera) forest, intending to better understand the potential for kelp growth in nutrient-limited conditions and the export of important tracers such as dissolved organic carbon. We calibrate and test our model using observations of currents within and surrounding a kelp forest in Southern California. By varying the density of kelp in our model, we find that there is a kelp density that maximises the export of tracer released from the kelp forest. Since the tracer advection/diffusion equation is linear with respect to the tracer concentration, the same kelp density corresponds to the maximum uptake for a tracer with a constant far-field concentration. The density at which this maximum occurs coincides with the density typical of natural kelp forests, where kelp growth may be limited by the uptake of dissolved nutrients from the surrounding water. Additionally, the drag induced on the tidal currents by the kelp forest results in a mean circulation through the kelp forest and a mean displacement of the kelp forest canopy.