Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput plot, indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work [Sanaei, Richardson, Witelski, and Cummings, J. Fluid Mech. 795, 36 (2016)] used a highly simplified membrane model to investigate how the pleating effect and membrane geometry affect this performance differential. In this work, we extend this line of investigation and use asymptotic methods to couple an outer problem for the flow within the pleated structure to an inner problem that accounts for the pore structure within the membrane. We use our model to formulate and address questions of optimal membrane design for a given filtration application.

Direct numerical simulations two-way coupled with inertial particles are used to investigate the particle distribution and two-way coupling mechanisms in turbulent open channel flow. In particular, the relationship between low- and high-inertia particles and the distinct large-scale motions (LSMs) and very-large-scale motions (VLSMs) which are characteristic of high-Reynolds-number, wall-bounded turbulence are examined. To do this, two methods of spatial filtering are applied to isolate the effects of LSMs versus VLSMs and separately analyze their interactions with inertial particles. One method of filtering the VLSMs from the flow is via artificial domain truncation, which alters the mean particle concentration profile and particle clustering due to the absence of VLSMs. The second method uses on-the-fly low- and high-pass filtering on the velocity field seen by the particles, so that as the simulation progresses the particles can only couple with certain scales of the flow. The results show that turbophoretic drift of particles toward the wall and the resulting increase in near-wall concentration is underpredicted without VLSMs, whereas the small-scale clustering and two-way coupling effects are mainly determined by particle coupling with LSMs. In the inner layer, the elongated streamwise anisotropic particle clustering can be reproduced by coupling solely with LSMs for low Stokes number. However, we do not observe a similar particle clustering behavior in the outer layer as seen in the full simulation by coupling particles with either LSMs or VLSMs at high Stokes numbers. This indicates that the organized particle structures are formed by the joint action of LSMs and VLSMs, especially for high-Stokes-number particles in the outer layer. The implications of these scale interactions are discussed in the context of large eddy simulation (LES) of one- and two-way coupled flows.

We study the fractal scaling of iso-level sets of a passive scalar mixed by three-dimensional homogeneous and isotropic turbulence at high Reynolds numbers. The scalar field is maintained by a linear mean scalar gradient, and the Schmidt number is unity. A fractal box-counting dimension $D_F$ can be obtained for iso-levels below about three standard deviations of the scalar fluctuation on either side of its mean value. The dimension varies systematically with the iso-level, with a maximum of about $8/3$ for the iso-level at the mean scalar value; this maximum dimension also follows as an upper bound from the geometric measure theory. We interpret this result to mean that mixing in turbulence is incomplete. A unique box-counting dimension for all iso-levels results when we consider the spatial support of the steep cliffs of the scalar conditioned on local strain rate; that unique dimension, independent of the iso-level set, is about $4/3$.

The fragmentation of liquid sheets produces a collection of droplets. The size distribution of the droplets has a considerable impact on the coating efficiency of sprays and the transport of contaminants. Although many processes commonly used particulate suspensions, the influence of the particles on the spreading dynamics of the sheet and its subsequent fragmentation has so far been considered negligible. In this paper, we consider experimentally a transient suspension sheet that expands radially. We characterize the influence of the particles on the dynamics of the liquid sheet and the fragmentation process. We highlight that the presence of particles modifies the thickness and reduces the stability of the liquid sheet. Our study suggests that particles can significantly modify the dynamics of liquid films through capillary effects, even for volume fractions much smaller than the maximum packing.

An impinging liquid jet impacts a target plate, forming a hydraulic jump that can exhibit a steady polygonal geometry under a range of conditions. Experiments are conducted to determine the effect of weir geometry and flow history on mode selection and the geometry of these polygonal jumps. Modal transitions occur at different flow rates in upscale and downscale flow sweeps, leading to hysteresis and the coexistence of multiple modes at a given flow rate, illustrating the importance of flow history. The characteristic ratio $A/PH$ or normalized jump geometry, where $A$ is the upstream area of the jump, $P$ is the perimeter, and $H$ is the downstream height, is unaffected by the flow history or experimental protocol but has a slight dependence on the weir height $h_w$ and weir radius $r_w$ provided the ratio of the weir radius to nozzle radius $r_n$ is large, $r_w/r_n\ge 28$. The collapse of the geometry suggests surface tension plays a critical role in the formation of polygonal jumps. All of our data, approximately 1800 observations, collapse upon plotting the scaled perimeter $P/H$ with the downstream Weber number We, and we show the critical wavelength is approximately constant $\lambda /H$ for any given experiment, suggesting the mode selection mechanism is related to Plateau-Rayleigh breakup.

A portion of vulnerable stenosis can be deformed periodically under pulsatile blood-flow condition. The deformable stenosis consists of fibrous cap covering a lipid pool, which is analogous to a capsule containing oily liquid or soft gel. The deformation increases mechanical stress acting on the fibrous cap. The magnitude of the stress determines likelihood of rupture, which causes sudden cardiac death or stroke. Previous studies tried to measure the stress by using intravascular imaging or numerical simulation. However, the methods have limitations of invasiveness and long process time in calculating the stress, respectively. In this study, the main determinants for the fibrous cap deformation and the normal stress acting on the fibrous caps are experimentally examined using deformable stenosis models. Particle image velocimetry is employed to measure flow induced forces acting on the fibrous caps. The deformable stenosis models are deformed to increase geometrical slope when inlet flow rate is increased. Deformation extent and mean normal stress acting on the fibrous caps are proportional to the square of the inlet flow rate and inversely proportional to the fibrous cap thickness. The periodic deformation of stenotic shape induces fluctuations of jet angle at the throat of the stenosis. Temporal variation of the jet angle is inversely proportional to the fibrous cap thickness of the deformable stenosis models. The variations of the jet angle for rigid stenosis models are negligibly small. The present results reveal the potential use of flow rate and variation of jet angle to approximate normal stress on the fibrous caps and to distinguish deformable stenosis from rigid stenosis. The flow rate and the jet angle can be measured directly by using noninvasive imaging devices in hospital.

The steady motion and deformation of a lipid-bilayer vesicle translating through a circular tube in low Reynolds number pressure-driven flow are investigated numerically using an axisymmetric boundary element method. This fluid-structure interaction problem is determined by three dimensionless parameters: reduced volume (a measure of the vesicle asphericity), geometric confinement (the ratio of the vesicle effective radius to the tube radius), and capillary number (the ratio of viscous to bending forces). The physical constraints of a vesicle—fixed surface area and enclosed volume when it is confined in a tube—determine critical confinement beyond which it cannot pass through without rupturing its membrane. The simulated results are presented in a wide range of reduced volumes [0.6, 0.98] for different degrees of confinement; the reduced volume of 0.6 mimics red blood cells. We draw a phase diagram of vesicle shapes and propose a shape transition line separating the parachutelike shape region from the bulletlike one in the reduced volume versus confinement phase space. We show that the shape transition marks a change in the behavior of vesicle mobility, especially for highly deflated vesicles. Most importantly, high-resolution simulations make it possible for us to examine the hydrodynamic interaction between the wall boundary and the vesicle surface at conditions of very high confinement, thus providing the limiting behavior of several quantities of interest, such as the thickness of lubrication film, vesicle mobility and its length, and the extra pressure drop due to the presence of the vesicle. This extra pressure drop holds implications for the rheology of dilute vesicle suspensions. Furthermore, we present various correlations and discuss a number of practical applications. The results of this work may serve as a benchmark for future studies and help devise tube-flow experiments.

We study numerically the fluid forces acting on aggregates formed by a collation of cubic particles as a model of marine aggregates in the ocean. The flow around the aggregates and the resulting stresses on the surface of the aggregates are computed in the limit of zero Reynolds number using a boundary integral method, resulting in an accurate evaluation of the flow around fractal objects. We compare a single- and double-layer integral method to compute the velocity, and we determine that the single-layer approach is more suitable to capturing the flow around aggregates. We then characterize the drag of translation flows, the torque of rotational flows, and the straining force of extensional flows acting on aggregates as a function of their size and mode of formation. We determine that the force and torque are best characterized using the gyration radius of the aggregates, and the straining force is better characterized by the maximal radius.

Inertial and kinetic-Alfvén wave turbulences have a priori little in common: indeed, the first one concerns rotating hydrodynamics in the limit of a small Rossby number (with ${\mathit{\Omega }}_0$ the rotating rate) while the second describes high frequency plasmas in the limit of a strong uniform magnetic field ${\mathbf{B}}_{\mathbf{0}}$. In this paper we show analytically that, in the limit of local interactions in the perpendicular direction to ${\mathit{\Omega }}_0$, the inertial wave turbulence equation converges towards the same nonlinear diffusion equation as for kinetic-Alfvén waves when the same limit is taken; the only difference resides in the constants in front of the equations. Therefore, both systems share the same physical properties for the stationary phase with an energy spectrum in $k_{\perp }^{-5/2}$; it is preceded by a self-similar solution of the second kind during the nonstationary phase with a spectrum proportional to $k_{\perp }^{-8/3}$ which propagates explosively towards small scales. It is suggested that the proximity between these two problems may be used to better understand inertial or kinetic-Alfvén wave turbulence.

This work reports a numerical study of mixing in temperature- or density-stratified fluids induced by the motion of a monodispersed swarm of bubbles in a thin gap. Simulations are run for void fractions between $3.35\%$ and $13.4\%$. The strength of stratification is varied by changing the Froude number between 4.5 and 12.74. The confinement prevents turbulence production, and mixing occurs primarily due to transport of colder liquid into the hotter layers by the bubble wake. Bubbles move in a zigzag motion attributed to the periodic vortex shedding in their wake. We report the formation of horizontal clusters and establish a direct correlation between the size of clusters and the rise velocity of the bubbles. We report an increase in the buoyancy flux across the isopycnals as the void fraction increases. The fraction of energy production due to the buoyancy flux increases with the strength of stratification, giving rise to a higher mixing efficiency. At the same time, cross isopycnal diffusion is higher at weaker stratification strengths.

Instability and transition in an elementary porous medium are investigated via global linear stability analysis and numerical simulation. The porous medium is presented by a representative elementary volume which consists of a staggered array of square cylinders. The stability analysis indicates the first critical Reynolds number at ${\mathrm{Re}}_{cr}\approx 84$. Two unstable modes are captured from the linear stability analysis: a two-dimensional oscillatory mode and a three-dimensional stationary mode. A series of analyses based on direct and adjoint methods is conducted on both the unstable modes. The energy analysis shows that lift-up and converging-flow effects are both responsible for the unstable modes. In the numerical simulation, the averaged fluctuation profiles exhibit spatial distributions similar to those of the perturbation kinetic energy from the three-dimensional mode, which confirms the prediction from the stability analysis. In addition, we observe stationary counterrotating streamwise vortices beginning at the subcritical Reynolds number, which is a consequence of lift-up instability.

We investigate experimentally the different shapes taken by a water drop freezing during its impact on a cold surface. We show that these shapes are formed by a water film that remains on top of the first formed ice layer. The capillary hydrodynamics of this water film dewetting on its own ice, coupled with its vertical solidification, is thus quantitatively characterized, allowing us to understand and predict the formation of the emerging patterns. Finally, this experiment enables us to study the contact angle dynamics, giving deep insight into the wetting of water on ice.

The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The amplification of the magnetic field is reduced due to stronger alignment between the velocity field, magnetic field, and electric current density. Furthermore, we confirm that the amplification decreases due to a weaker stretching of the magnetic field lines. The enhancement in diffusion relative to the field line stretching is quantified by a decrease in the computed local value of the magnetic Reynolds number. Using the Minkowski functionals, we quantify the shape of the magnetic structures produced by the dynamo as magnetic filaments and ribbons in both kinematic and saturated dynamos and derive the scalings of the typical length, width, and thickness of the magnetic structures with the magnetic Reynolds number. We show that all three of these magnetic length scales increase as the dynamo saturates. The magnetic intermittency, strong in the kinematic dynamo (where the magnetic field strength grows exponentially), persists in the statistically steady state, but intense magnetic filaments and ribbons are more volume-filling.

The Navier-Stokes equations are greatly simplified when the Reynolds number, Re, tends to zero and inertial effects become negligible. A plethora of relevant, real-world flows occur at small but nonzero Re, and these flows are generally well approximated by the simplified Stokes equations. However, the simplification to Stokes equations means important qualitative features that are inertial in origin may be lost. One approach to capture inertial effects such as lift, for small Re, without wholly having to consider the full Navier-Stokes equations, is to consider a complimentary problem using an asymptotic expansion in Re; here inertial corrections are represented by the $O\left(\text{Re}\right)$ terms. Research in this direction has mainly employed analytic approaches and thus relied on simple, symmetric shapes of any objects in the fluid, such as spheres. Here we extend this work and present a numerical approach to compute the analytic expressions for weak, inertial lift on arbitrarily shaped objects moving in a fluid near a wall. Specifically, we use the Method of Regularized Stokeslets to solve two, distinct Stokes equations systems that arise in the complimentary problem. We compute the lift on these objects due to pure translation, pure rotation, and coupled translation and rotation, for various orientations and distances from the wall. The method is validated by comparing to previous analytical results for a sphere and then used to compute inertial lift on two adjacent spheres (dimer), as well as prolate and oblate spheroids.

Energy transport in the spectral space is analyzed to study the mechanism underlying the Taylor–Görtler-like (TGL) vortices that appear as two layers of streamwise-elongated roll cells in a turbulent channel flow subjected to fast streamwise system rotation. The transport equation of the velocity-spectrum tensor in a rotating frame is derived to study the budget balance of energy spectra at different length scales. Two new terms, namely, the rotation-induced redistribution term and rotation-induced wall-normal diffusion term, are defined to reflect the effect of the imposed system rotation on the energy transport process. By analyzing the data obtained from direct numerical simulation, it is discovered that four key processes are responsible for sustaining the motion of the TGL vortices. The first process corresponds to the energy production at the characteristic length scales of the TGL vortices that drains energy from the mean flow to the TGL vortices. The second process is the rotation-induced energy redistribution from the streamwise velocity fluctuations to the wall-normal and spanwise velocity fluctuations that form the vortex structures on a cross-stream plane. The third process is the energy diffusion from the near-wall region to the channel center, which is enhanced due to the occurrence of the TGL vortices and, in turn, feeds energy to the vortices. The last process is the inverse interscale energy transfer, through which the large-scale TGL vortices absorb energy from small-scale eddies.

As pioneered by Donzis and Maqui [J. Fluid Mech. 797, 181 (2016)] and Khurshid and Donzis [Phys. Fluids 31, 015103 (2019)], the compressible isotropic turbulence in thermal nonequilibrium is drawing attention in the fluid dynamics community. In the present study, the vibrational rate and the dissipation or production of vibrational energy fluctuation of compressible isotropic turbulence with solenoidal forcing in vibrational nonequilibrium are investigated using numerical simulations. The turbulent Mach number (${\text{M}}_t$) is set to be 0.44 and 1.09, and the Taylor Reynolds number (${\text{Re}}_{\lambda }$) equals 98.58 approximately. The focus is on the effect of the normalized vibrational relaxation time ($K_{\tau }$) and characteristic temperature (${\theta }_v$) on statistical features of the vibrational rate and the dissipation or production components of vibrational energy fluctuation. When $K_{\tau }$ is small $(\lesssim 1.0)$, the average of normalized vibrational rate conditioned on the normalized dilatation is positive in the compression region and negative in the expansion region, enhanced with increase of compression and expansion level, respectively. It indicates that, on average, the energy transfers from translational-rotational to vibrational modes in the compression region and in the inverse direction in the expansion region. The conditional average of the normalized vibrational rate reduces with increase of $K_{\tau }$, and is insensitive to ${\theta }_v$. The joint probability density functions (PDFs) and conditional PDFs of the normalized vibrational rate are also analyzed, to reveal the effect of compression and expansion motions on the internal energy exchange between the translational-rotational and vibrational modes. The dissipation or production of vibrational energy fluctuation can result from effects of dilatation, thermal diffusion, and vibrational relaxation. The dissipation component due to thermal diffusion always weakens the vibrational energy fluctuation in both compression and expansion regions for the weakly and highly compressible turbulence, but its effect is insignificant compared to the other two components. For the weakly compressible turbulence, the dissipation or production of vibrational energy fluctuation mainly comes from effects of dilatation and vibrational relaxation when $K_{\tau }$ is small $(\lesssim 1.0)$, and the vibrational relaxation component loses its significance with increasing of $K_{\tau }$. For the highly compressible turbulence, both the dilatation and vibrational relaxation effects play an important role in the dissipation and production of vibrational energy fluctuation, and their effects are significantly different from that of the weakly compressible turbulence. The conditional average, joint PDFs, and conditional PDFs of each dissipation or production component are calculated and analyzed in detail to reveal their effects on the vibrational energy fluctuation in different compression and expansion regions. Furthermore, the bulk viscosity effect on the compression or expansion motion in flow field, the vibrational rate, and the dissipation or production components of vibrational energy fluctuation is discussed briefly.

In this paper, we aim at characterizing the spin-up process and the permanent regime of a rotating flow with free surface. The motion is created by the quasi-impulsive rotation of a disk located at the bottom of a cylindrical tank partially filled with a Newtonian water-glycerol mixture at a fixed initial aspect ratio (height to radius) of 0.25. Two experimental setups with different radius sizes and two numerical codes with distinct formulations are used, allowing for numerous comparisons and cross validations. Time-dependent surface height profiles and azimuthal velocity profiles are accurately measured with a laser line sensor and Laser Doppler Velocimetry, respectively. These measurements are compared to numerical results showing an overall excellent agreement and whenever a discrepancy exists, explanations are given. The spin-up and permanent regime for two typical flow cases are detailed: (i) one for which the angular speed moderately deforms the free surface and (ii) one at higher angular speed for which the disk becomes partially dewetted. The shape of the free surface in the permanent regime for intermediate rotation speeds is also reported. The flow parameters are chosen in such a way that large deformations of the free surface are achieved, yet remaining under the threshold of appearance of rotating polygonal patterns. This enables us to characterize realistic base flows on which this instability may develop.

We revisit the issue of Lagrangian irreversibility in the context of recent results [H. Xu et al., Proc. Natl. Acad. Sci. USA 111, 7558 (2014)] on flight-crash events in turbulent flows and show how extreme events in the Eulerian dissipation statistics are related to the statistics of power fluctuations for tracer trajectories. Surprisingly, we find that particle trajectories in intense dissipation zones are dominated by energy gains sharper than energy losses, contrary to flight crashes, through a pressure-gradient driven take-off phenomenon. Our conclusions are rationalized by analyzing data from simulations of three-dimensional intermittent turbulence, as well as from nonintermittent decimated flows. Lagrangian irreversibility is found to persist even in the latter case, wherein fluctuations of the dissipation rate are shown to be relatively mild and to follow probability distribution functions with exponential tails.

Particles at a liquid interface can interact through capillarity, and depending on their size, shape, or surface chemistry, it may lead to their aggregation. Yet the two-dimensional structures thus created can be eroded by strong enough flows or as described in this paper via their own motion along a deformed interface. Here we experimentally highlight an unexpectedly high resistance of such a granular raft to erosion, which cannot be explained by the usual linear calculation of the capillary interaction. To clarify this result, we develop a model experiment in which two particles are horizontally moved along the liquid interface at a chosen velocity until they separate. We deduce again a cohesive force that exceeds the capillary attraction expected by one or two orders of magnitude. A precise description of the geometry of the contact line around a sphere and of its vertical position seems to account rather well for the experimental results.

Soft plates immersed in fluids appear in many biological processes, including swimming, flying, and breathing. The plate deforms in response to fluid flows, yet fluid stresses are in turn influenced by the plate's deformation. We present a mathematical model examining the flow of a viscous fluid in a narrow slit formed by two rectangular elastic plates, and demonstrate a strongly nonlinear flow response. The volumetric flow rate first increases linearly with pressure; however, the bending of the plates causes the corners to approach. This in turn reduces the flow rate. In some cases, the corners meet and the slit no longer permits flow. Our model, which is based on low-Reynolds-number hydrodynamics and linear plate theory, yields insights into two competing effects: While the plate bending generally reduces the slit aperture, it also causes the two plates to move apart, thus increasing the gap. Relations to biomedical flows are outlined and potential applications to flow control in man-made systems are considered.