We established an entropic lattice Boltzmann model to study surface tension effects on quasiequilibrium liquid plug rupture in two- and three-dimensional channels. The surface tension coefficient is supposed to be an increasing function of plug-gas density ratios, and the contact angle is not uniquely determined by surface tension. The influence of the surface tension coefficient on plug rupture is combined with the effects of viscosity and inertia. The plug is more likely to rupture at a greater Ohnesorge number (the ratio of viscous forces and the geometric mean of surface tension and inertial forces), which positively correlates to the plug's surface area-to-volume ratio and negatively to channel thickness. With the increasing of the initial plug length (at the fixed density ratio and surface tension), four patterns of plug rupture are observed in three-dimensional channels, four holes, two holes, one hole, and no hole (i.e., no rupture). There exists minimum initial plug length for a certain rupture pattern to appear. The four-hole rupture happens only in thick channels (the aspect ratio of channel thickness to width between 0.6 and 1.0). No two-hole rupture is available in square channels. Plug rupture in two-dimensional channels is similar to that in the three-dimensional, but simpler without the definition of the channel thickness and the four-hole rupture. The minimum plug lengths indicating two-dimensional rupture patterns quadratically decrease with the contact angle and slightly increase with surface tension. The results indicate not only the entropic lattice Blotzmann method's great potential in the study of multiphase fluid flows but also a clinical implication that increasing wetting ability of mucus plugs might be an effective practice in lung airway reopening. A final successful solution, however, depends on full understanding of all factors, especially the forces of surface tension, viscosity, and inertia.

We study size segregation in the limit of a single large particle (intruder) embedded within a flowing granular layer. Using discrete-element-method-based computations, we calculate and characterize the drag, lift, and buoyancy forces experienced by the intruder in two systems: (1) a simple shear flow without gravity and (2) gravity-driven flow down an inclined plane. In agreement with previous studies, the drag force in both systems is seen to follow Stokes' Law with a slightly different constant. However, in contrast with previous work, we report that lift force does not follow the Saffman relation; instead, its variation is captured effectively using a size-corrected Stokes' Law. The buoyancy forces calculated in our work scale in a manner that compares well with previous studies. The computed effective volumes of the intruders were found to be close to previously reported values, and the buoyancy force calculated using this effective volume was found to be significantly lower than our computed buoyancy force, suggesting contributions from other factors. Analysis of the relative velocity and stress in the neighborhood of the intruder shows that the lift force is caused by a net upward collisional stress arising from a higher relative inward velocity in the lower part of the intruder due to a positive slip velocity. The buoyancy force is higher than that predicted by Archimedean buoyancy due to large fluctuations in the pressure near the intruder. A continuum model for the segregation flux is presented based on the computed drag, lift, and buoyancy forces.

The coupling effect of physical and thermodynamic wall roughness is investigated using nonlinear parabolized stability equations. A patch of five sinusoidal physical and wall temperature variations, denoted here as roughness, is positioned upstream of the typical transition location of a zero-pressure gradient flat-plate boundary layer at $M=0.7$. Using only thermodynamic roughness on a flat plate, we note the stabilizing effect of cooling strips, whereas, the heating has a destabilizing effect on the stability of Tollmien-Schlichting waves. The combined effect of physical roughness patch superimposed on the thermodynamic roughness results in a synergetic coupling effect that delays the transition. The addition of sinusoidally varying wall temperature to physical roughness can stabilize the boundary layer through a spectral narrowing of the instability modes and the generation of off-peak frequencies. Thus, the physical roughness with cooling results in a more stable boundary layer compared to cooling alone, a finding that could help improve temperature-based active laminar flow control devices.

Constricted blood vessels in the circulatory system can severely impact the spatiotemporal organization of red blood cells (RBCs) causing various physiological complications. In laboratory-on-a-chip applications, constrictions are commonly used for cell sorting and plasma separation based on the formation of a cell-free layer (CFL) at the channel boundary. However, such devices usually employ a steady flow, although time-dependent and pulsatile flow conditions enhance many microfluidic operations and possess significant relevance for in vitro studies under physiologically relevant flow conditions. In this study we examine the CFL dynamics in a constricted microchannel under steady and time-dependent flow. Therefore, we develop an image-processing routine that allows us to resolve the spatiotemporal evolution of the CFL under time-dependent driving of the flow with arbitrary waveform. First, we perform a characterization of the CFL and the cell-free area (CFA) before and after the constriction under steady flow conditions. Second, we employ our method to study the effect of the hematocrit and the parameters of the flow modulations on the CFL and CFA using a sinusoidal pressure profile. Our results highlight the dominant effects of the RBC concentration and the amplitude of the applied pressure signal predominantly on the CFA dynamics. Moreover, we observe a dampening of the CFA amplitude with increasing hematocrit or decreasing pressure amplitude, and a peculiar phase shift of the CFA oscillations pre- and postconstriction. Complementary numerical simulations reveal how the time-dependent CFA dynamics are coupled with the dynamically changing flow field at the constriction. Due to the increasing demand for investigations and applications under time-dependent flow conditions, our study provides crucial insight into the flow behavior of complex fluids in unsteady microscale flows.

When releasing a droplet onto a distinct nonmiscible liquid layer, for positive spreading parameter $S$, a surface tension driven spreading arises. Here, for positive $S$, we report the reverse after the initial spreading phase: a secondary receding of the deposited volatile droplet. This behavior is found to result from the competition between two opposite effects: solutal and thermal Marangoni stresses, with the latter built from droplet's evaporation. To clarify the effects of evaporation-induced Marangoni, accurate infrared thermography tests are performed. These tests reveal a maximal temperature gradient at the droplet edge near the recession time. Also, universal scaling laws are proposed for the spreading dynamic of a law-viscous insoluble drop onto a more viscous oil, with droplet volume variation resulting from the evaporation and typical receding time. These predictions are successfully compared with experiments.

Liquid lens coalescence is an important mechanism involved in many industrial and scientific applications. It has been investigated both theoretically and experimentally, yet it is numerically very challenging to obtain consistent results over the wide ranges of surface tension and viscosity values that are necessary to capture the asymptotic temporal behavior in the viscous and inertial limits. We report results of massively parallel simulations based on the color gradient lattice Boltzmann method, which overcome these limitations, and investigate the scaling laws of both regimes. For the two-dimensional case we find good agreement with the similarity solution of the thin-sheet equation, where in the viscous regime the connecting bridge grows linearly with time and in the inertial regime proportionally to $t^{2/3}$. In three dimensions, the viscous growth of the bridge also exhibits a linear time dependence, while in the inertial regime the growth of both the bridge height and the bridge width is proportional to $t^{1/2}$.

This paper takes the perspective of a user of direct-numerical-simulation (DNS) data and quantifies the uncertainties in DNS statistics for plane channel flows. We focus on high-order statistics, such as skewness, kurtosis, and viscous dissipation, and quantify the uncertainties due to wall-normal numerics and grids while minimizing the sampling error and the discretization error in the wall-parallel directions. Two grid distributions and four discretization methods are considered, which are representative of the existing DNSs. Our results show that the available DNS data contain at least a 7% uncertainty in the computed mean viscous dissipation in the buffer layer. Moreover, since turbulence becomes more intermittent at higher Reynolds numbers, the flow will be less well-resolved at the higher Reynolds number if the same grid resolution in terms of the viscous units is employed. Specifically, our estimate shows that a grid that resolves 90% of the dissipation events at ${\text{Re}}_{\tau }=544$ resolves about 87% of the dissipation events at ${\text{Re}}_{\tau }=10000$.

This research computationally investigates the complex dynamic stall phenomena of a cross-flow turbine blade utilizing modal analysis to identify pertinent events within the cycle. The blade rotation perpendicular to the freestream generates a curved relative flow, a nonsinusoidal variation of relative flow speed and angle of attack, and the necessity of traveling through its own wake. These complexities have challenged traditional predictors of dynamic stall such as pitch rate, pitching moment, or relative angle of attack. To investigate these phenomena, aerodynamic loads and flow fields on the blade from large-eddy simulations are examined across two tip speed ratios. Proper orthogonal decomposition of the velocity fields is employed to analyze the spatiotemporal evolution of the dominant flow features. The modes' time development coefficients reveal a stronger representation of the flow at the higher rotation rate, capturing the trend of relative flow velocity magnitude and lift generation on the blade, along with critical events such as vortex formation and detachment. Additionally, mean power generation is enhanced by 40% by applying a nonconstant rotation rate (intracycle control or angular velocity control). The flow fields, supported by corresponding changes in the modal analysis, demonstrate that a delayed stall behavior is responsible for the additional power extraction. Finally, flow curvature, history effects, and induced flow are identified as significant factors that modify the dynamic stall onset and resulting force and moment curves as compared to nonrotating pitching or plunging foils.

Understanding the coupling between flow, hydrodynamic transport and dispersion of colloids of finite size in porous media is a long-standing challenge. This problem is relevant for a broad range of natural and engineered processes, including contaminant and colloidal transport, mixing of biochemical compounds, kinetics of reactions, and groundwater bioremediation, but also transport phenomena related to different systems like membranes or blood flow. While classical models for colloidal transport rely on macrodispersion theory and do not take into consideration the complex and heterogeneous structure of the porous host medium, recent studies take into consideration the detailed structure of the porous system and its impact on fluid velocity. However, the impact of confinement conditions, represented by the ratio of the radius of particles $a$ and pore-throat size $\lambda$, has been overlooked. Here, we use numerical simulations of fluid particle dynamics in resolved porous media to demonstrate that particle confinement affects the fluid macroscopic velocity field which in turn affects the particle transport itself. Our results show that even under small confinement conditions ($a/\lambda \sim 2$ %), fluid and transported particles are dynamically rerouted toward more permeable paths. This leads to the emergence of ephemeral laminar vortices at pore-throat entrances and affects the variance and mean fluid velocity.

The influence of stable and unstable stratification on the amplification of coherent structures in turbulent channel flows is investigated by computing the linear response to stochastic forcing near the turbulent mean flow. The velocity and thermal responses to momentum and thermal forcing are considered separately. It is found that, consistently with results of previous direct numerical simulations, the influence of the mean flow stratification on stochastic forcing amplifications is non-negligible only for streamwise-elongated large-scale structures. Unstable stratification is found to enhance the peak variance of the response, except for the velocity response to thermal forcing, and to increase the spanwise wavelength of the most amplified structures. Stable stratification induces opposite effects. The different spanwise wavelengths maximizing the different types of variance amplifications all converge to approximately six channels half-widths when approaching the linear instability threshold where large-scale coherent rolls become linearly unstable. We show that in the presence of even moderately unstable stratification, the profiles of turbulent buoyancy and momentum fluxes and of root-mean-square vertical velocity of all types of most amplified stochastic responses are nearly indistinguishable from those of the critical mode becoming unstable at the critical Richardson number. For all considered stratification levels, the two most energetic proper orthogonal decomposition modes are found to contribute to more than 90% of the variance of the response, except for the thermal response to thermal forcing. We conclude that the same mechanism underlies the onset of the instability of coherent large-scale rolls at the critical Richardson number and the amplification of coherent large-scale structures at subcritical Richardson numbers. The process leading to the onset of the instability of large-scale rolls is therefore gradual, and the increasing response variance associated to increasingly unstable mean flow stratification, as well as the increase of the optimal spanwise wavelength of the most amplified mechanically forced streaks, can be both interpreted as precursors of the linear instability of large-scale rolls.

Five sets of Navier-Stokes trefoil vortex knots in ${\left(2\pi \right)}^3$ domains show how the shape of their initial profiles, Gaussian/Lamb-Oseen or algebraic, and their widths influence their evolution, as defined by their enstrophy $Z\left(t\right)$, helicity $\mathcal{H}\left(t\right)$, and changes in their dissipation-scale structures. Significant differences develop even when all have the same three-fold symmetric trajectory, the same initial circulation and the same range of the viscosities $\nu$. The focus is upon how the dynamics of helicity density $h=\mathit{u}·\mathit{\omega }$ affects reconnection and the evolution of enstrophy. $h\lesssim 0$ patches on the vorticity isosurfaces show where and how reconnection forms. For the Lamb-Oseen profile, the tightest and most linearly unstable, there is only a brief spurt of enstrophy growth as thin braids form at these positions; before being dissipated as the post-reconnection helicity $\mathcal{H}$ grows significantly. For the algebraic cases: as $h<0$ vortex sheets form prior to reconnection, there is $\nu$-independent convergence of $\sqrt{\nu }Z\left(t\right)$ at a common $t_x$. For those with the broadest wings, enstrophy growth accelerates after reconnection, leading to approximately convergent dissipation rates $\epsilon =\nu Z\left(t\right)$. Maps of terms from the budget equations onto centerlines illustrate the divergent behavior. Lamb-Oseen briefly forms six locations of centerline convergence with local negative dips in the helicity dissipation ${\epsilon }_h$ and vortical-helicity flux $h_f$. These are the source of the following positive increase in the global $\mathcal{H}$ and suppression of enstrophy production. For the algebraic profiles there are only three locations of centerline convergence, each with spans of less localized ${\epsilon }_h<0$ that could be the seeds for the $h<0$ vortex sheets and whose interactions can explain the later accelerated growth of the enstrophy, approximate $\nu$-independent convergence of the energy dissipation rates $\epsilon$, and evidence for finite-time energy dissipation $\mathrm{\Delta }{E}_{\epsilon }$, despite the initial symmetries.

We study steady, fully developed, axisymmetric flows of soft, inelastic grains within a vertical circular pipe under the influence of gravity. We use extended kinetic theory to describe the collisional flow and include a region above the critical solid volume fraction near the center line that is the analog of an erodible bed. We calculate the profiles of velocity, shear stress, granular temperature, and particle concentration across the pipe for a variety of volume flow rates and pipe radii. We compare these with those measured in discrete element simulations by Barker et al. [J. Fluid Mech. 930, A21 (2022)] and see good agreement.

The dynamics of heat transfer in a model system of Rayleigh-Bénard (RB) convection reduced to its essentials, here dubbed Burgers-Rayleigh-Bénard (BRB), is studied. The system is spatially one-dimensional, the flow field is compressible, and its evolution is described by the Burgers equation forced by an active temperature field. The BRB dynamics shares remarkable similarities with realistic RB thermal convection in higher spatial dimensions: (1) it has a supercritical pitchfork instability for the onset of convection which depends solely on the Rayleigh number (Ra) and not on the Prandlt number (Pr), occurring at the critical value ${\mathrm{Ra}}_c={\left(2\pi \right)}^4$, (2) the convective regime is spatially organized in distinct boundary layers and bulk regions, and (3) the asymptotic high-$\mathrm{Ra}$ limit displays the Nusselt and Reynolds numbers scaling regime $\mathrm{Nu}=\sqrt{\mathrm{Ra}\mathrm{Pr}}/4$ for $\mathrm{Pr}\ll 1, \mathrm{Nu}=\sqrt{\mathrm{Ra}}/\left(4\sqrt{\pi }\right)$ for $\mathrm{Pr}\gg 1$, and $\mathrm{Re}=\sqrt{\mathrm{Ra}/\mathrm{Pr}}/\sqrt{12}$, thus making BRB the simplest wall-bounded convective system exhibiting the so-called ultimate regime of convection. These scaling laws, derived analytically through a matched asymptotic analysis are fully supported by the results of the accompanying numerical simulations. A major difference with realistic natural convection is the absence of turbulence. The BRB dynamics is stationary at any $\mathrm{Ra}$ number above the onset of convection. This feature results from a nonlinear saturation mechanism whose existence is grasped by means of a two-mode truncated equation system and via a stability analysis of the convective regime.

Realistic currents in seas and oceans are almost always changing in depth thus indicative on the presence of shear in the profile of the mean ambient flow. However, analysis methodologies interpreting directional wave data gathered by in situ measurement instruments such as buoys, pressure gauges, and acoustic Doppler current profilers (ADCPs) utilize potential irrotational flow theory which cannot account for the rotational shearing currents. The effects of shearing currents on the wave direction estimations were studied on numerically simulated ADCP data of waves propagating in a predetermined spread. The numerical data was generated employing the Rayleigh boundary-value problem (BVP) and a selected ambient current profile. The potential data processing led to significant errors in wave directional spread estimation for common shearing currents (up to $\approx {10}^{\circ }$ in mean wave direction for the presented example). This finding is of great importance because it addresses the influence of an ambient current profile on wave propagation direction. The obtained results suggest that there is an uncertainty with the confidence of any wave directional spread ever presented by in situ wave measurement devices. Here, we developed an approach for estimating directional wave spectra based on rotational flow physics by acquiring terms emanating from wave-shearing current interaction governing equations. This included a derivation of numerical transfer functions for the fluid's physical properties based on the Rayleigh BVP. Then, by applying classical cross- and auto-spectral analysis on time-series data sets, the directional spread function was numerically reconstructed. This derived data processing methodology was applied to the same numerically simulated ADCP data sets. It was found to be capable of reconstructing the spread with great accuracy ($0.4^{\circ }$ in mean wave direction for the presented example). This makes it a prominent methodology for estimating directional wave spectra in realistic oceanic conditions.

We report the mechanism and modeling for the formation of cavitylike structures on a planar interface subjected to a perturbed shock wave. The cavity is distinguished from bubbles and spikes formed in the standard Richtmyer-Meshkov instability (RMI). The two-dimensional direct numerical simulation is conducted at a range of shock Mach numbers and Atwood numbers. We elucidate the effects of the interfacial vorticity and the shock-induced vorticity on the cavity formation. The interfacial vorticity, which is important in the standard RMI, only has a minor influence on the cavity width in the linear stage. Alternatively, the cavity width is determined by the Mach-stem height when the shock accelerates the interface. A pair of vorticity patches connecting the Mach stem, as a part of the shock-induced vorticity, penetrate the interface to form the cavity via strong shear layers generated by slipstreams during shock propagation. Inspired by this mechanism, we develop a model of the Mach-stem height to estimate the cavity width in the linear stage at various Mach numbers.

We investigate the unbounded inertial flow of a Newtonian fluid past a fixed regular tetrahedron, the Platonic polyhedron with the lowest sphericity, in the range of Reynolds number $100\le \text{Re}\le 500$. Three angular positions of the tetrahedron are considered: a face facing the flow (TF), an edge facing the flow (TE), and a vertex facing the flow (TV). We analyze and determine the two well-known regime transitions: loss of symmetry of the wake structures and loss of stationarity of the flow as a function of the Reynolds number Re. In the steady regime, we show that the symmetry of the wake structure is closely related to the number of edges on the particle front surface. For the unsteady flows, we find a new symmetric double-hairpin vortex shedding regime in the edge facing the flow (TE) cases due to its unique angular position. The dominant frequency of this double-hairpin vortex shedding is twice that of the single-hairpin vortex shedding in the flow past a sphere, a cube, or a tetrahedron at other angular positions. Furthermore, we present a force analysis attempting to explain the wake transitions in connection to the drag and lift force evolution. Eventually, we provide the critical Reynolds numbers for the regime transitions from steady to unsteady flows, which are highly dependent on the angular position of the tetrahedron.

In this study, we investigate an unbounded Newtonian fluid flow past a stationary Platonic polyhedron. To reveal the effects of the particle angularity and angular position on the flow regime transitions, we select the three following different angular positions of the Platonic polyhedrons: a face facing the flow (F), an edge facing the flow (E), and a vertex facing the flow (V). We consider all five Platonic polyhedrons whose sphericity increases with the number of faces and a sphere as an asymptotic polyhedron of sphericity 1 featuring an infinite number of faces. Two well-known regime transitions are studied as a function of the particle sphericity, the particle angular position and the particle Reynolds number Re: the loss of symmetry in the particle wake region and the loss of stationarity of the flow. In the multiplanar symmetry regime, the flow symmetry in the particle wake region is highly related to the particle front surface. The number and orientation of particle front surface edges determine the wake vorticity pattern. With increasing Re, the steady flow past an angular particle transitions to a planar symmetry regime for all particle shapes and all particle angular positions. The plane of symmetry in the planar symmetry regime selects one of the axis in the multiplanar symmetry regime, and its direction may change in time and/or with Re. In the unsteady regime, we notice a wide variety of periodic hairpin vortex shedding modes. These vortex shedding modes are determined by the shape of the flow recirculation region, which itself is a reflection of the angularity and the angular position of the particle. Furthermore, we present an in-depth analysis of the hydrodynamic forces exerted on the Platonic polyhedrons at the vertex angular position (V) for a wide range of Reynolds numbers $100\le \text{Re}\le 500$. We attempt to understand and explain the significant variations in the flow regime transitions brought by the particle angularity and the particle angular position.

We explain the origins of yield stress, shear thinning, and normal stress differences in rigid fiber suspensions. We investigate the interplay between the hydrodynamic, noncontact attractive and repulsive, and interfiber contact interactions. The shear-thinning viscosity and finite yield stress obtained from the Immerse Boundary Method simulations are in quantitative agreement with experiential results from the literature. In this study, we show that attractive interactions result in yield stress and shear thinning rheology in the suspensions of rigid fibers. This is an important finding, given the ongoing discussion regarding the origin of the yield stress for suspensions of fibers. The ability of the proposed model to quantitatively predict the rheology is not limited to only shear thinning and yield stress but also extends to normal stresses.

We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing linear estimators using flow statistics from an initial training period and evaluating their performance during a subsequent testing period with data obtained from direct numerical simulation. We address cases where (i) no, (ii) limited, and (iii) full-field training data are available using estimators based on (i) resolvent modes, (ii) resolvent-based estimation, and (iii) spectral proper orthogonal decomposition modes. During training, we introduce blockwise inversion to accurately and efficiently compute the resolvent operator in an interpretable manner. During testing, we enable efficient streaming reconstructions by using a temporal sliding discrete Fourier transform to recursively update Fourier coefficients using incoming measurements. We use this framework to reconstruct with minimal time delay the turbulent velocity fluctuations in a minimal channel at ${\mathrm{Re}}_{\tau }\approx 186$ from sparse planar measurements. We evaluate reconstruction accuracy in the context of the extent of data required and thereby identify potential use cases for each estimator. The reconstructions capture large portions of the dynamics from relatively few measurement planes when the linear estimators are computed with sufficient fidelity. We also evaluate the efficiency of our reconstructions and show that the present framework has the potential to help enable real-time reconstructions of turbulent velocity fluctuations in an analogous experimental setting.

In this article, we investigate experimentally and numerically the time evolution of vortex rings generated by the translation of a rigid disk in a fluid initially at rest and submitted to an acceleration followed by a deceleration. The diameter of the disk and its motion in terms of stroke length and travel time are varied as control parameters. The startup vortex ring created in the near wake of the disk is characterized experimentally by PIV, and the measurements agree quantitatively with axisymmetric numerical simulations performed with the Basilisk flow solver. The maximum radius and circulation of the annular vortex and its dynamics are shown to follow different power laws with the control parameters. The modeling adapted from Wedemeyer's two-dimensional theoretical calculations [E. Wedemeyer, Ausbildung eines Wirbelpaares an den Kanten einer Platte, Ingenieur-Archiv 30, 187 (1961)] captures the observed scaling laws. Besides, after the disk stops, a secondary “stopping” vortex ring is generated, which is shown to affect the motion of the main vortex ring.