The suspension balance model (SBM) for viscous Stokes flow has been well studied for the case of identical, monodisperse spherical particles in a channel, however, more work remains to be done to explore the bidisperse and polydisperse SBM. We present a simple extension of the SBM that allows for modeling of suspensions of particles of bidisperse size. The comparison with available experiments and direct simulations is found to be good. Additionally, we present a range of simulations to justify the assumptions made in the polydisperse suspension balance model for non-Brownian, neutrally buoyant particles that vary in size with a bidisperse distribution. The aim is to study the effects of moderate size variation on the rheology of the suspension and the distribution of the particles across the flow, especially in the near-wall regions. It is shown that, at the size ratios considered, bidispersity in the particle size does not significantly affect rheological parameters including the particle volume fraction and relative viscosity in the bulk of a Couette flow. The particle phase stresses are distributed between small and large particles in proportion to the relative volume fractions of each species. In bidisperse suspensions, the large particles in the wall layer develop a spatial structure and form chains in the streamwise direction.

In this paper, we present an in-depth analysis of pulsatile shear-thinning flows in two-dimensional channels. The characteristic viscosity was determined based on steady-state analysis of non-Newtonian flows and was used to nondimensionalize the flow system by introducing the non-Newtonian Womersley number. Numerical analyses on various Carreau fluids revealed the existence of master curves related to the amplitude and phase lag of the flows, where the shape of the master curve is determined by the degree of shear thinning. Such master curves imply that the competition between viscous and pulsatile time scales can be described appropriately by using the non-Newtonian Womersley number proposed in this paper. Furthermore, it is demonstrated that the flow dynamics can be predicted accurately using precomputed master curves, presenting a method for predicting shear-thinning pulsatile flow dynamics without explicit transient computations.

In this study we report an experimental investigation of droplet sliding under the influence of a laminar or turbulent airflow for water and glycerin droplets. The onset of sliding is described thanks to a critical Weber number, based on the mean airflow velocity impacting the droplet, depending upon the contact angle hysteresis and a drag coefficient (that also depends on the Reynolds number). A fairly good agreement is observed with our experiments and various data from the literature. The transitions between the various droplet shapes observed during sliding (oval, corner, and rivulet) are characterized in a phase diagram built on the droplet capillary and Bond numbers.

Depositing drops on a solid surface without entrapping bubbles is desirable for many spray coating and printing applications. Tian et al. [J. Fluid Mech. 946, A21 (2022)] reported that an electric field can be applied to eliminate air bubble entrapments for neutral drops. Herein we provide a complete physical picture of the entire process of a drop impacting onto the solid surface under an external electric field. The electrohydrodynamic behavior during the drop impact is divided into three stages: the deformation of the drop in the electric field prior to contact, the initial contact of the drop with the substrate, and the rich postcontact phenomena including spreading, receding, jetting, and fragmentation. The results show that under the increasingly stronger electric fields, the modest drop oscillation transforms into a vertically stretched spindle. As the drop approaches the substrate, the electric stress at the south pole increases rapidly, which sharpens the bottom surface into a conical shape. The cone angle is determined by both the impact velocity and the electric field strength. After the contact, the surface electric stress tends to pull the drop upward, breaking up the drop, forming several jetting modes, and reducing the maximum spreading radius. The various drop deposition modes are summarized in a phase diagram, which sheds light on identifying appropriate electric fields for high-quality drop depositions without air bubble entrapments or jettings.

The nonlinear effects induced on a nonspherical object exposed to an acoustic standing wave offer acoustic radiation force and torque, resulting in the dynamical motion of the object. Here, we study the translational and rotational motion of an oblate shaped particle exposed to standing bulk acoustic waves in a microchannel using numerical simulations. Acoustic pressure and velocity fields are obtained from a numerical model, and a perfectly matched layer boundary condition is used to simulate the particle dynamics. A systematic parametric study is carried out to understand the effects of initial orientation, aspect ratio, size, and initial location of the particle on the translational and rotational motion, by considering the acoustic streaming effects. In this paper, we reveal that the particle undergoes rotation to minimize the acoustic radiation torque potential when the minor axis of the particle is not in line with the acoustic pressure wave direction. We find that the direction of rotation changes from anticlockwise to clockwise beyond a critical aspect ratio of the particle. The location of maximum torque and consequently particle rotation shift closer to the pressure node with increased particle size for a constant aspect ratio. Our results show that a particle positioned closer to the pressure node rapidly rotates, attributed to a sharp increase in acoustic radiation torque acting on it owing to a higher torque potential. In this paper, we shed light on the dynamical motion of an oblate shaped particle exposed to acoustic standing waves which may be relevant in understanding the dynamics of an elongated micro-organism or biological cells.

Buoyant plumes often pulsate, or puff, at a characteristic frequency that depends on the Richardson number. In many engineering and natural applications, however, interactions between two or more plumes can substantially affect the puffing frequency. In this study, we use numerical simulations to investigate how the plume width, $W$, and the separation between two plumes, $S$, affect the puffing frequency. The plumes are formed by injecting helium into ambient air, and we perform the simulations in two spatial dimensions to identify scaling laws in the limits of large and small $S$. We find that the global dependence on $S$ closely matches that observed in reacting three-dimensional (3D) plumes, indicating that the plume dynamics are primarily connected to the presence of buoyant forces, regardless of the source of buoyancy. There is a critical value of $S$ at which the puffing frequency changes abruptly but, in contrast to 3D reacting plumes, this critical value is independent of $W$ for the present two-dimensional plumes. Ultimately, we find that the nonlinear decrease in puffing frequency with increasing spacing can be represented by a scaling law that depends only on $S/W$ and the inlet Richardson number. These results allow us to identify four regimes of puffing behavior, corresponding to merged, strongly interacting, weakly interacting, and noninteracting plumes.

We revisit from a dynamical point of view the classical problem of the deformation of a gas bubble suspended in an axisymmetric uniaxial straining flow. Thanks to a recently developed Linearized Arbitrary Lagrangian-Eulerian approach, we compute the steady equilibrium states and associated bubble shapes. Considering perturbations that respect the symmetries of the imposed carrying flow, we show that the bifurcation diagram is made of a stable and an unstable branch of steady states separated by a saddle-node bifurcation, the location of which is tracked throughout the parameter space. We characterize the most relevant global mode along each branch, namely, an oscillatory mode that becomes neutrally stable in the inviscid limit along the stable branch, and an unstable nonoscillating mode eventually leading to the breakup of the bubble along the unstable branch. Next, considering perturbations that break the symmetries of the carrying flow, we identify two additional unstable nonoscillating modes associated with the possible drift of the bubble centroid away from the stagnation point of the undisturbed flow. One of them corresponds merely to a translation of the bubble along the elongational direction of the flow. The other is counterintuitive, as it corresponds to a drift of the bubble in the symmetry plane of the undisturbed flow, where this flow is compressional. We confirm the existence and characteristics of this mode by computing analytically the corresponding leading-order disturbance in the inviscid limit, and show that the observed dynamics are made possible by a specific self-propulsion mechanism that we explain qualitatively.

We study numerically the effect of a soluble surfactant on the stability of two-phase flow in a finite-length microchannel. We calculate the steady base flow and its global eigenmodes for experimentally relevant choices of material, kinetic, and flow parameters. The results show that the system is unstable for capillary numbers above a critical value. The surfactant surface concentration takes values of the order of the maximum packing density over the whole interface, even for very small volume concentrations. The two streams drag the surfactant molecules toward the downstream end of the interface against the action of the Marangoni stress. The sharp reduction of the interfacial tension at that end enhances the interface deformation and considerably destabilizes the system, translating into a sharp reduction of the critical capillary number.

A highly efficient, easy-to-implement, long-ranged and nondestructive way to realize active pumping has been still a great challenge. Here, using molecular dynamics simulations, terahertz electric field (TEF) is employed to stimulate an active pump for water transportation by bias applied in a (6, 6) single-walled carbon nanotube under no external pressure gradient. An ultrafast conductivity (up to $\approx 9.5\mathrm{n}{\mathrm{s}}^{-1}$) through the pump around a characteristic frequency of 14 THz is found. The excellent pumping ability is attributed to the resonance coupling between the TEF and water molecules, in which water molecules can gain considerable energy continuously to break the binding of hydrogen bonds and the spatial symmetry. This proposed TEF-driven pump design will offer a guide in polar molecule transport through artificial or biological nanochannels, particularly in a controllable, noncontact and large-scale process.

We show that nonequilibrium and equilibrium measurements of slip are consistent, provided the hydrodynamic wall location associated with the equilibrium measurement is properly taken into account. The latter is a strong function of the fluid state and wall-fluid interaction and cannot be neglected as it typically has been. Our results are based on an alternative approach for calculating the hydrodynamic wall location which alleviates most of the difficulties associated with its calculation via a Green-Kubo integral that appear to have contributed to its neglect. Extensive molecular dynamics simulations are used to validate our approach including a model for calculating the slip length that does not involve a Green-Kubo integral.

Using numerical simulations, we show that the asymptotic states of two-dimensional (2D) Euler turbulence exhibit large-scale flow structures due to nonzero energy transfers among small wavenumber modes. These asymptotic states, which depend on the initial conditions, are out of equilibrium, and they are different from the predictions of Onsager and Kraichnan. We propose “hydrodynamic entropy” to quantify order in 2D Euler turbulence; we show that this entropy decreases with time, even though the system is isolated with no dissipation and no contact with a heat bath.

Large eddy simulations (LESs) are used to study the effects of veer (the height-dependent lateral deflection of wind velocity due to Coriolis acceleration) on the evolution of wind turbine wakes in the atmospheric boundary layer. Specifically, this work focuses on turbines that are yawed with respect to the mean incoming wind velocity, which produces laterally deflected wakes that have a curled (crescent-shaped) structure. These effects can be attributed to the introduction of streamwise mean vorticity and the formation of a counter-rotating vortex pair (CVP) on the top and bottom of the wake. In a truly neutral boundary layer (TNBL) in which wind veer effects are absent, these effects can be captured well with existing analytical wake models [Bastankhah et al., J. Fluid Mech. 933, A2 (2022)]. However, in the more realistic case of atmospheric boundary layers subjected to Coriolis acceleration, existing models need to be reexamined and generalized to include the effects of wind veer. To this end, the flow in a conventionally neutral atmospheric boundary layer (CNBL) interacting with a yawed wind turbine is investigated in this paper. Results indicate that in the presence of veer the CVP's top and bottom vortices exhibit considerable asymmetry. However, upon removing the veer component of vorticity, the resulting distribution is much more symmetric and agrees well with that observed in a TNBL. These results are used to develop a simple correction to predict the mean velocity distribution in the wake of a yawing turbine in a CNBL using analytical models. The correction includes the veer-induced sideways wake deformation, as proposed by Abkar et al. [Energies 11, 1838 (2018)]. The resulting model predictions are compared with mean velocity distributions from the LESs, and good agreement is obtained.

The problem of finding initial conditions that lead to self-similar motion of point vortices is formulated as a linear system. The linearity in the equations is used to check for the existence of similarity solutions with a given shape and, in particular, to numerically find self-similar vortex configurations with or without any prior knowledge of circulations. Algorithms for computing the one-parameter family of collapse and expansion configurations and the finitely many rigid-vortex configurations present in the family are also discussed. Typical families are shown to have vortices parametrized along closed curves, and the conditions for which they are not closed are investigated via several numerical examples.

The thinning of threads of low-viscosity fluids like water in air has been of interest for more than a century and is gaining new importance because of the emergence of applications involving the breakup of drops and jets of liquid metals which have viscosities comparable to but surface tensions and densities much larger than water. The dynamics of thinning and pinch-off is governed by the Ohnesorge number $\text{Oh}=\mu /\sqrt{\rho \gamma R}$, where $\mu , \rho , \gamma$, and $R$ stand for viscosity, density, surface tension, and nozzle or initial jet radius. When $\text{Oh}\ll 1$, the thread initially thins as if it were inviscid and its minimum radius ${\tilde{h}}_{\text{min}}$ obeys a universal scaling law ${\tilde{h}}_{\text{min}}=A{(\gamma /\rho )}^{1/3}{({\tilde{t}}_b-\tilde{t})}^{2/3}$, where ${\tilde{t}}_b$ is the time $\tilde{t}$ at which the thread breaks up and $A\doteq 0.717$. As the interface overturns prior to breakup when Oh is sufficiently small, it has proven challenging to observe in simulations and experiments the value of the prefactor $A$ predicted from theory and furthermore the transition of the dynamics as ${\tilde{h}}_{\text{min}}\to 0$ from the inviscid regime to a different scaling regime in which the effect of viscosity is no longer negligible. Here we employ high-accuracy simulation using a sharp-interface algorithm to show that for sufficiently small Oh, the value of $A$ predicted from computations agrees with the theoretical value to three decimal places and the inviscid power-law behavior can be observed over two to three decades in ${\tilde{h}}_{\text{min}}$ as ${\tilde{t}}_b-\tilde{t}\to 0$. Transition out of the inviscid regime and into a viscous one is also demonstrated from simulations.

In this study, we investigated the four-wave resonant and quasiresonant interactions in a special degenerated case, wherein bichromatic mother waves are generated to give birth to a daughter wave. One of the mother waves was counted twice to satisfy the four-wave resonant conditions. Particular attention is paid to the effect of finite water depth. Theoretical analyses based on the Zakharov equation and direct numerical simulations using a higher-order spectral (HOS) method were performed and compared. The present results revealed that both resonant and quasiresonant four-wave interactions were suppressed by the finite depth and eventually attenuated to zero for sufficiently shallow water. It is found that the corresponding critical depth depends on the crossing angle of the initial mother waves. For the two mother waves with a crossing angle $\theta ={25}^{\circ }$, four-wave resonance survives up to $k_{1}h\sim 0.57$, where $k_1$ denotes the wave number of the twice-counted mother wave and $h$ is the water depth. Furthermore, it is found that the four-wave resonant interactions for different values of $\theta$ survive up to a global threshold value of $k_{1}h\sim 0.4$. In addition, through three-dimensional (3D) Fourier analyses of the results by direct numerical simulations, it is found that the bound wave effects are enhanced, and more harmonics are generated as the water depth decreases.

Many microorganisms live and evolve in complex fluids. Examples include mammalian spermatozoa in cervical mucus, worms (e.g., C. elegans) in wet soil, and bacteria (e.g., H. pylori) in our stomach lining. Due to the presence of (bio)polymers and/or solids, such fluids often display nonlinear response to (shear) stresses including viscoelasticity and shear-rate-dependent viscosity. The successful interaction between these microorganisms and their fluid environment is critical to the function of many biological processes including human reproduction, ecosystem dynamics, and the spread of disease and infection. This interaction is often nonlinear and can lead to many unexpected behaviors. Here, I will discuss developments in characterizing, modeling, and understanding the swimming behavior of model microorganism in viscoelastic and shear-thinning fluids. Three main microorganisms will be explored: (i) the nematode C. elegans, an undulatory swimmer; (ii) the green algae C. reinhardtii, a puller swimmer; and (iii) the bacterium E. coli, a pusher swimmer. Investigation with artificial particles and swimmers will also be discussed; such studies are helpful in decoupling the biology from hydrodynamic effects. We will explore the interactions between these swimmers' gaits, geometry, and actuation and fluid rheological behavior using mostly experiments, and discuss these results relative to numerical and analytical predictions.

When an initially straight filament is immersed in a viscous fluid and rotated at one end, the fluid resists the rotational motion and causes a buildup of twist in the object. At a critical turning frequency, the object buckles due to the elastic stresses in the material. While this instability has been extensively studied over the past 25 years, these analyses have focused narrowly on filaments with circular cross sections near the onset of the instability. Here we explore the phase diagram for twirling filaments as a function of cross-sectional aspect ratio and rotational frequency. We find a large range of dynamic behaviors and even find that while filaments with circular cross sections transition directly from twirling to overwhirling, ribbonlike objects undergo a twirl-to-whirl transition, similar to what was originally predicted for rodlike objects. We show that the linear stability for rotating ribbons is equivalent to first order to that of cylindrical filaments. Hysteresis is also common, suggesting that there are multiple stable states in these systems. Finally, by comparing simulations using resistive force theory to immersed boundary methods, we identify the reason that these two methods have historically not agreed on the value of the critical turning frequency.

Capillary flows in corners and wedges are ubiquitous in technology and nature. Under certain conditions, the capillary flows are enhanced resulting in the rise of rivulets in the corners. These rivulets can affect the overall fluid movement in the aforementioned systems. In this work, we investigate the rivulet dynamics in a square capillary under forced wetting using two different forcing methods: immersion and pumping. In addition to the rivulet, we also study the bulk flow dynamics. In immersion, the descending tube forces the fluid movement everywhere downwards whereas, in pumping, the external pressure head pumping fluid into the tube drives the liquid upwards. Despite the fluid moving in opposite directions, we observe similarities between the two cases. In both cases, the fluid advances over a dry surface where the bulk flow moves at a constant speed. The rivulet undergoes two linear regimes during its evolution. It attains a constant speed once the forced wetting starts, where its length shortens with time. As the rivulet length approaches a threshold value, it abruptly enters another constant speed regime where its speed is comparable to the bulk flow suggesting a strong coupling between the bulk and the rivulet. We explain these observations using a model based on the fluid flow in a capillary.

This study reports on the vortex-induced lift production mechanisms in low Reynolds number flows over low aspect-ratio rectangular wings. We use a rigorous force-partitioning method which allows for the estimation of the pressure-induced aerodynamic loads due to distinct flow features or vortex structures in the flow around the wing. The specific focus of this work is on distinguishing the effect of spanwise- and cross-span-oriented vortex structures on pressure-induced lift production. We quantify the lift induced on the wing by these different vortices, and also estimate their influence within different regions of the flow-field around the wing and in the wake. By varying the aspect ratio and angle of attack of the wing, we show that for most cases, the spanwise-oriented vorticity contributes less to the total lift than cross-span-oriented vortices. Furthermore, the spanwise vorticity in the near wake is capable of producing net negative lift on the wing and this is explained by separating and quantifying the influence of vortex cores and regions of strain in the wake. The results demonstrate the utility of the force-partitioning method for dissecting the flow physics of vortex dominated flows.

Impurities such as ${\mathrm{H}}_2\mathrm{S}$ and ${\mathrm{SO}}_2$ play important roles in dissolution trapping mechanisms in geological sequestration of ${\mathrm{CO}}_2$. In this study, a pore-scale numerical investigation of the convective mixing process in geological storage is conducted using the lattice Boltzmann method. Tests with a different value of diffusivity ratio $R_D$ and buoyancy ratio of the impurities $R_{\beta }{R}_C$ are considered. Theoretical analysis demonstrates four distinct scenarios of initial diffusive density distribution, including the monotonic and nonmonotonic density distributions along the gravity direction. Numerical results show that the general phenomena of the mixing processes are quite different in different scenarios. In particular, when the density distribution is nonmonotonic, the intensity of the system's convective mixing will be weakened by the density stratification structure. At the same time, the time evolution of the dissolution flux is also affected by impurities correspondingly, leading to some differences from the pure-${\mathrm{CO}}_2$ system. In addition, the onset times of convection for different impure systems are also investigated. For a given Rayleigh number, the system is less prone to gravitational instability compared to that with only ${\mathrm{CO}}_2$, when $R_{\beta }{R}_C<0$ and the onset time will be prolonged correspondingly. In order to assess the strength of convection in an impure system, an effective Rayleigh number ${\mathrm{Ra}}_e$ is defined in this paper, where the influences of impurities are taking into account. According to the simulation results, the onset time $t_{\mathrm{on}}$ can be well fitted as $t_{\mathrm{on}}\sim {\text{Ra}}_e^{-2}$, which is consistent with the role of the Rayleigh number in a pure-${\mathrm{CO}}_2$ system.