Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment.

We use three-dimensional direct numerical simulations of homogeneous isotropic turbulence in a cubic domain to investigate the dynamics of heavy, chiral, finite-size inertial particles and their effects on the flow. Using an immersed-boundary method and a complex collision model, four-way coupled simulations have been performed and the effects of particle-to-fluid density ratio, turbulence strength, and particle volume fraction have been analysed. We find that freely falling particles on the one hand add energy to the turbulent flow but, on the other hand, they also enhance the flow dissipation: depending on the combination of flow parameters, the former or the latter mechanism prevails, thus yielding enhanced or weakened turbulence. Furthermore, particle chirality entails a preferential angular velocity which induces a net vorticity in the fluid phase. As turbulence strengthens, the energy introduced by the falling particles becomes less relevant and stronger velocity fluctuations alter the solid phase dynamics, making the effect of chirality irrelevant for the large-scale features of the flow. Moreover, comparing the time-history of collision events for chiral particles and spheres (at the same volume fraction) suggests that the former tend to entangle, in contrast to the latter which rebound impulsively.

Studying liquid jet impacts on a liquid pool is crucial for various engineering and environmental applications. During jet impact, the free surface of the pool deforms and a cavity is generated. Simultaneously, the free surface of the cavity extends radially outward and forms a rim. Eventually the cavity collapses by means of gas inertia and surface tension. Our numerical investigation using an axisymmetric model in Basilisk C explores cavity collapse dynamics under different impact velocities and gas densities. We validate our model against theory and experiments across a previously unexplored parameter range. Our results show two distinct regimes in the cavity collapse mechanism. By considering forces pulling along the interface, we derive scaling arguments for the time of closure and maximum radius of the cavity, based on the Weber number. For jets with uniform constant velocity from tip to tail and ⩽ 150 the cavity closure is capillary dominated and happens below the surface (deep seal). In contrast, for ⩾ 180 the cavity closure happens above the surface (surface seal) and is dominated by the gas entrainment and the pressure gradient that it causes. Additionally, we monitor gas velocity and pressure throughout the impact process. This analysis reveals three critical moments of maximum gas velocity: before impact, at the instant of cavity collapse, and during droplet ejection following cavity collapse. Our results provide information for understanding pollutant transport during droplet impacts on large bodies of water, and other engineering applications, like additive manufacturing, lithography and needle-free injections.

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft's criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren ., ., vol. 871, 2019, pp. 831-864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g., miscible fluids) is finally discussed.

This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.

For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger , vol. 39, 2016, pp. 1-9). In this study, we numerically analyze the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by Péclet number . The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by Galileo number , and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number . We analyze how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters , , and . We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large , even collisions between the droplets can take place. Our study on the effect of further shows that with increasing , the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number , is proportional to /(/), where is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number , which is proportional to . The balance of attractive and repulsive effect leads to ~ , which agrees well with the transition curve between the regimes with and without collision.

A simple two-dimensional fluid-structure-interaction problem, involving viscous oscillatory flow in a channel separated by an elastic membrane from a fluid-filled slender cavity, is analyzed to shed light on the flow dynamics pertaining to syringomyelia, a neurological disorder characterized by the appearance of a large tubular cavity (syrinx) within the spinal cord. The focus is on configurations in which the velocity induced in the cavity, representing the syrinx, is comparable to that found in the channel, representing the subarachnoid space surrounding the spinal cord, both flows being coupled through a linear elastic equation describing the membrane deformation. An asymptotic analysis for small stroke lengths leads to closed-form expressions for the leading-order oscillatory flow, and also for the stationary flow associated with the first-order corrections, the latter involving a steady distribution of transmembrane pressure. The magnitude of the induced flow is found to depend strongly on the frequency, with the result that for channel flow rates of non-sinusoidal waveform, as those found in the spinal canal, higher harmonics can dominate the sloshing motion in the cavity, in agreement with previous observations. Under some conditions, the cycle-averaged transmembrane pressure, also showing a marked dependence on the frequency, changes sign on increasing the cavity transverse dimension (i.e. orthogonal to the cord axis), underscoring the importance of cavity size in connection with the underlying hydrodynamics. The analytic results presented here can be instrumental in guiding future numerical investigations, needed to clarify the pathogenesis of syringomyelia cavities.

To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh-Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation [Shemilt et al., ., 2022, vol. 944, A22] is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases.

When surface waves interact with ambient turbulence, the two affect each other mutually. Turbulent eddies get redirected, intensified and periodically stretched and compressed, while the waves suffer directional scattering. We study these mutual interactions experimentally in the water channel laboratory at the Norwegian University of Science and Technology (NTNU) Trondheim. Long groups of waves were propagated upstream on currents with identical mean flow but different turbulence properties, created by an active grid at the current inlet. The subsurface flow in the spanwise-vertical plane was measured with stereo particle-image velocimetry. Comparing the subsurface velocity fields before and after the passage of a wave group, a strong enhancement of streamwise vorticity is observed which increases rapidly towards the surface for z ≳ -0.3 (: vertical distance from still surface; : carrier wavenumber) in qualitative agreement with theory. Next, we measure the broadening of the directional wave spectrum at increasing propagation distance. The rate of directional diffusion is greatest for the turbulent case with the highest energy at the longest length scales whereas the highest total turbulent kinetic energy overall did not produce the most scattering. The variance of directional spectra is found to increase linearly as a function of propagation time.

Drop impact experiments allow to model a wide variety of natural processes, from raindrop impacts to planetary impact craters. In particular, interpreting the consequences of the planetary impacts requires an accurate description of the flow associated with the cratering process. In our experiments, we release a liquid drop above a deep liquid pool to investigate simultaneously the dynamics of the cavity and the velocity field produced around the air-liquid interface. Using particle image velocimetry, we analyse quantitatively the velocity field using a shifted Legendre polynomials decomposition. We show that the velocity field is more complex than considered in previous models, in relation to the non-hemispherical shape of the crater. In particular, the velocity field is dominated by the degrees 0 and 1, with contributions from the degree 2, and is independent of the Froude and the Weber number when these numbers are large enough. We then derive a semi-analytical model based on the Legendre polynomials expansion of an unsteady Bernoulli equation coupled with a kinematic boundary condition at the crater boundary. This model explains the experimental observations and can predict the time evolution of both the velocity field and the shape of the crater, including the initiation of the central jet.

We report flow measurements in rotating Rayleigh-Bénard convection in the rotationally-constrained geostrophic regime. We apply stereoscopic particle image velocimetry to measure the three components of velocity in a horizontal cross-section of a water-filled cylindrical convection vessel. At a constant, small Ekman number = 5 × 10 we vary the Rayleigh number between 10 and 4 × 10 to cover various subregimes observed in geostrophic convection. We also include one nonrotating experiment. The scaling of the velocity fluctuations (expressed as the Reynolds number ) is compared to theoretical relations expressing balances of viscous-Archimedean-Coriolis (VAC) and Coriolis-inertial-Archimedean (CIA) forces. Based on our results we cannot decide which balance is most applicable here; both scaling relations match equally well. A comparison of the current data with several other literature datasets indicates a convergence towards diffusion-free scaling of velocity as decreases. However, the use of confined domains leads at lower to prominent convection in the wall mode near the sidewall. Kinetic energy spectra point at an overall flow organisation into a quadrupolar vortex filling the cross-section. This quadrupolar vortex is a quasi-two-dimensional feature; it only manifests in energy spectra based on the horizontal velocity components. At larger the spectra reveal the development of a scaling range with exponent close to -5/3, the classical exponent for inertial-range scaling in three-dimensional turbulence. The steeper () scaling at low and development of a scaling range in the energy spectra are distinct indicators that a fully developed, diffusion-free turbulent bulk flow state is approached, sketching clear perspectives for further investigation.

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Linear stability analyses are performed to investigate the boundary layer instabilities developing in an incompressible flow around the whole leading-edge of swept ONERA-D and Joukowski airfoils of infinite span. The stability analyses conducted in our study are global in the chordwise direction and local in the spanwise direction. A neutral curve is drawn at a given leading-edge Reynolds number and several overlapping regions, called "lobes", are identified on a physical basis. A detailed study of the marginal modes reveals the presence of attachment-line and crossflow instabilities, as well as modes whose features do not fall within the standards of a specific type. Connected crossflow/Tollmien-Schlichting modes, that show a dominant spatial structure reminiscent of Tollmien-Schlichting waves but whose destabilization is linked to a crossflow mechanism, have been identified. The comparison of several neutral curves at different values reveals the greater stabilizing effect of the increase of on the crossflow instability compared to the attachment-line instability. The influence of the airfoil shape is also studied by comparing the neutral curves of the ONERA-D with the neutral curves of the Joukowski airfoil. These curves reveal similar characteristics with the presence of distinct lobes and their comparison at constant sweep angle shows that, under the conditions studied, the ONERA-D airfoil is more stable than the Joukowski airfoil, even for crossflow instabilities. The absolutely or convectively unstable nature of the flow in the spanwise direction is also tackled and our results suggest that the flow is only convectively unstable.

The fluid-structure interactions between flexible fibers and viscous flows play an essential role in various biological phenomena, medical problems, and industrial processes. Of particular interest is the case of particles freely transported in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations, and theoretical modeling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behavior through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler-Bernoulli rods whose hydrodynamics are described by local slender-body theory.

In this paper, we present a generic approach of a dynamical data-driven model order reduction technique for three-dimensional fluid-structure interaction problems. A low-order continuous linear differential system is identified from snapshot solutions of a high-fidelity solver. The reduced order model (ROM) uses different ingredients like proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and Tikhonov-based robust identification techniques. An interpolation method is used to predict the capsule dynamics for any value of the governing non-dimensional parameters that are not in the training database. Then a dynamical system is built from the predicted solution. Numerical evidence shows the ability of the reduced model to predict the time-evolution of the capsule deformation from its initial state, whatever the parameter values. Accuracy and stability properties of the resulting low-order dynamical system are analysed numerically. The numerical experiments show a very good agreement, measured in terms of modified Hausdorff distance between capsule solutions of the full-order and low-order models both in the case of confined and unconfined flows. This work is a first milestone to move towards real time simulation of fluid-structure problems, which can be extended to non-linear low-order systems to account for strong material and flow non-linearities. It is a valuable innovation tool for rapid design and for the development of innovative devices.

This paper investigates flow and transport in a slender wavy-walled vertical channel subject to a prescribed oscillatory pressure difference between its ends. When the ratio of the stroke length of the pulsatile flow to the channel wavelength is small, the resulting flow velocity is known to include a slow steady-streaming component resulting from the effect of the convective acceleration. Our study considers the additional effect of gravitational forces in configurations with a non-uniform density distribution. Specific attention is given to the slowly evolving buoyancy-modulated flow emerging after the deposition of a finite amount of solute whose density is different from that of the fluid contained in the channel, a relevant problem in connection with drug dispersion in intrathecal drug delivery (ITDD) processes, involving the injection of the drug into the cerebrospinal fluid that fills the spinal canal. It is shown that when the Richardson number is of order unity, the relevant limit in ITDD applications, the resulting buoyancy-induced velocities are comparable to those of steady streaming. As a consequence, the slow time-averaged Lagrangian motion of the fluid, involving the sum of the Stokes drift and the time-averaged Eulerian velocity, is intimately coupled with the transport of the solute, resulting in a slowly evolving problem that can be treated with two-time-scale methods. The asymptotic development leads to a time-averaged, nonlinear integro-differential transport equation that describes the slow dispersion of the solute, thereby circumventing the need to describe the small concentration fluctuations associated with the fast oscillatory motion. The ideas presented here can find application in developing reduced models for future quantitative analyses of drug dispersion in the spinal canal.

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.

We investigate the formation and stability of a pair of identical soft capsules in channel flow under mild inertia. We employ a combination of the lattice Boltzmann, finite element and immersed boundary methods to simulate the elastic particles in flow. Validation tests show excellent agreement with numerical results obtained by other research groups. Our results reveal new trajectory types that have not been observed for pairs of rigid particles. While particle softness increases the likelihood of a stable pair forming, the pair stability is determined by the lateral position of the particles. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.

We develop a model to predict the fragmentation limit of drops colliding off-centre. The prediction is excellent over a wide range of liquid properties and it can be used without adjusting any parameter. The so-called stretching separation is attributed to the extension of the merged drop above a critical aspect ratio of 3.25. The evolution of this aspect ratio is influenced by the liquid viscosity and can be interpreted via an energy balance. This approach is then adapted to drop-jet collisions, which we model as consecutive drop-drop collisions. The fragmentation criterion is similar to the one observed for drop-drop collisions, while the evolution of the stretched jet aspect ratio is modified to account for the different flow fields and geometry.

Phase-averaged and cycle-to-cycle analysis of key contributors to sound production in phonation is examined in a scaled-up vocal-fold model. Simultaneous temporally and spatially resolved pressure and velocity measurements permitted examination of each term in the streamwise integral momentum equation. The relative sizes of these terms were used to address the issue of whether transglottal pressure is a surrogate for vocal-fold drag, a quantity directly related to sound production. Further, time traces of transglottal pressure and volume flow rate provided insight into the role of cycle-to-cycle variations in voiced sound production which affect voice quality. Experiments were conducted using a 10× scaled-up model in a free-surface water tunnel. Two-dimensional vocal-fold models with semi-circular ends inside a square duct were driven with constant opening and closing speeds. The time from opening to closed, , was half the oscillation period. Time-resolved digital particle image velocimetry (DPIV) and pressure measurements along the duct centreline were made for 3650 ≤ ≤ 8100 and equivalent life frequencies from 52.5 to 97.5 Hz. Results showed that transglottal pressure does serve as a surrogate for the vocal-fold drag. However, smaller but non-negligible momentum flux and inertia terms, caused by the jet and vocal-fold motions, may also contribute to vocal-fold drag. Further, cycle-to-cycle variations including jet switching and modulation are inherent in flows of this type despite their high degrees of symmetry and repeatability. The origins of these variations and their potential role in sound production and voice quality are discussed.

The two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube and a concentric circular annulus. Here, we study peristaltic flow in a non-axisymmetric annular tube: in this case, the flow is three-dimensional, with motions in the azimuthal direction. This type of geometry is motivated by experimental observations of the pulsatile flow of cerebrospinal fluid along perivascular spaces surrounding arteries in the brain, which is at least partially driven by peristaltic pumping due to pulsations of the artery. These annular perivascular spaces are often eccentric and the outer boundary is seldom circular: their cross-sections can be well matched by a simple, adjustable model consisting of an inner circle (the outer wall of the artery) and an outer ellipse (the outer edge of the perivascular space), not necessarily concentric. We use this geometric model as a basis for numerical simulations of peristaltic flow: the adjustability of the model makes it suitable for other applications. We concentrate on the general effects of the non-axisymmetric configuration on the flow and do not attempt to specifically model perivascular pumping. We use a finite-element scheme to compute the flow in the annulus driven by a propagating sinusoidal radial displacement of the inner wall. Unlike the peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional: azimuthal pressure variations drive an oscillatory flow in and out of the narrower gaps, inducing an azimuthal wiggle in the streamlines. We examine the dependence of the flow on the elongation of the outer elliptical wall and the eccentricity of the configuration. We find that the time-averaged volumetric flow is always in the same direction as the peristaltic wave and decreases with increasing ellipticity or eccentricity. The additional shearing motion in the azimuthal direction will increase mixing and enhance Taylor dispersion in these flows, effects that might have practical applications.