It is shown that both normal and tangential heat-flux profiles in acceleration-driven Poiseuille flow of a granular gas can be qualitatively different from those in a molecular gas. Comparisons with a generalized Fourier's law confirm that the cross-thermal conductivity is responsible for the double-well-shaped profile of the tangential heat flux, and the net heat-flow rate can be directed along or against the external acceleration, depending on the value of the restitution coefficient and the Knudsen number $\left(\mathrm{Kn}\right)$. Collectively, the tensorial thermal conductivity and the inelasticity-induced clustering of particles can explain the anomalous behavior of shear-induced heat fluxes in a nonrarefied $(\mathrm{Kn}\to 0)$ granular gas. The importance of the heat-flux terms driven by the density gradient and the kinetic-stress gradient is discussed in the context of both molecular and granular gases.

This paper examines the streamwise-inhomogeneous nature of turbulence in a finite-size developing wind farm. While previous analysis involving Fourier spectra revealed an interesting dynamics showing a dominance of the large-scale motions on the order of ten rotor diameters in the energetics of fully developed wind farms [T. Chatterjee and Y. T. Peet, Phys. Rev. Fluids 3, 034601 (2018)], harmonic analysis methods do not capture the streamwise variability of spectra, especially important in strongly inhomogeneous flows such as a developing wind farm turbulence. The current study uses wavelet analysis of large eddy simulation data to investigate the turbulent spectra with respect to its spatial position along the wind farm. The analysis shows that the correlation length scales grow significantly past the first row of wind turbines, testifying to a strengthening of the large-scale motions by wind turbines. A vertical coherence of streamwise and vertical velocity fluctuations is also found to increase significantly past the first row of turbines, associated with the development of a global energy transfer mechanism between the outer layer and the wind turbine region. While this mechanism, known as a downdraft of kinetic energy, was previously discussed in the context of fully developed wind farms, the current study illustrates a signature of its origination after as early as the first row of wind turbines. Understanding of the mechanisms responsible for the reorganization of motions of different scales in wind farm flows is useful for designing efficient wind farm control strategies and mitigating the effects of the downstream wakes.

Passive droplet transport mechanisms, in which continuous external energy input is not required for motion, have received significant attention in recent years. Experimental studies of such mechanisms often ignore, or use careful treatments to minimize, contact angle hysteresis, which can impede droplet motion, or even arrest it completely. Here, we consider the effect of contact angle hysteresis on bendotaxis, a mechanism in which droplets spontaneously deform an elastic channel via capillary pressure and thereby move. We seek to understand when contact angle hysteresis prevents bendotaxis. We supplement a previous mathematical model of the dynamics of bendotaxis with a simple model of contact angle hysteresis, and show that this model predicts droplet trapping when hysteresis is sufficiently strong. By identifying the equilibrium configurations adopted by these trapped droplets and assessing their linear stability, we uncover a sensitive dependence of bendotaxis on contact angle hysteresis and develop criteria to describe when droplets will be trapped.

The membrane permeation of a fluid occurring near the wall is strongly influenced by lubrication because the generated pressure accelerates the fluid passing through the membrane. In the present study, the membrane permeation of a pure fluid driven by the lubrication pressure is modeled for a general wall-membrane geometry to understand the effect of permeability on the permeate flux in a range of wall-membrane gap widths that cannot be treated by the Reynolds lubrication equation. This lubrication effect (referred to as the non-Reynolds lubrication effect) is modeled by including a higher-order pressure component described by the wall-tangential derivative of the local Couette-Poiseuille velocity, and a permeate flux model with the non-Reynolds lubrication effect is developed. The permeation model is validated with a corrugated membrane placed in a two-dimensional parallel channel with a fixed aspect ratio (i.e., the average wall-membrane distance to the longitudinal membrane length) of 0.1. The permeation driven by the lubrication pressure between the membrane and wall is studied by varying the nondimensional permeability. At an infinitesimal permeability, the permeate flux model shows good agreement with the fully resolved numerical simulation owing to the comparable contribution of the Couette and Poiseuille components in the permeation model, whereas the permeation model exhibits a diverging trend at finite permeabilities because the Couette component in the model produces an excessive contribution to the lubrication pressure. However, by applying a simplified renormalization procedure to the Couette component into the lowest-order pressure component, the diverging trend is suppressed and the permeate flux in a finite permeability range is reproduced. The applicability of the renormalization-group permeation model is discussed in terms of the conditions of the wall-membrane gap and permeability range.

The current pandemic has spurred a great deal of debate about the use of cloth masks as effective alternatives to medical masks for the general public. Despite an abundance of experimental studies on the filtration of aerosols by cloth masks, there is currently a lack of analytical understanding to predict mask performance a priori. In this study, we establish a quantitative model for the pressure drop across woven heterogeneous cloth masks and their filtration efficiencies for aerosols with aerodynamic diameters less than 1 $\mu \mathrm{m}$. To compare the intrinsic filtration capabilities of diverse materials, we introduce a filtration quality factor. Finally, we present a decision map to illustrate the tradeoffs between filtration efficiency and breathability and to provide practical guidance on the purchase of cloth masks. For the most commonly used cotton, polyester, and polypropylene masks, the mechanical filtration capability is fairly independent of the material, but it exhibits a high sensitivity to the porosity and fiber diameter. Additionally, keys to a high-quality cloth mask include a homogeneous structure, micro- or even nanofibrous materials, and a suitable mass per unit area of the textile.

Mantle convection, the buoyancy-driven creeping flow of silicate rocks in the interior of terrestrial planets like Earth, Mars, Mercury, and Venus plays a fundamental role in the long-term thermal evolution of these bodies. Yet key parameters and initial conditions of the partial differential equations governing mantle convection are poorly constrained. This often requires a large sampling of the parameter space to determine which combinations can satisfy certain observational constraints. Traditionally, 1D models based on scaling laws used to parameterized convective heat transfer have been used to tackle the computational bottleneck of high-fidelity forward runs in two or three dimensions. However, these are limited in the amount of physics they can model (e.g., depth-dependent material properties) and predict only mean quantities such as the mean mantle temperature. A recent machine learning study has shown that feedforward neural networks (FNNs) trained using a large number of 2D simulations can overcome this limitation and reliably predict the evolution of entire 1D laterally averaged temperature profile in time for complex models. We now extend that approach to predict the full 2D temperature field, which contains more information in the form of convection structures such as hot plumes and cold downwellings. Using a data set of $10525$ 2D simulations of the thermal evolution of the mantle of a Mars-like planet, we show that deep learning techniques can produce reliable parameterized surrogates (i.e., surrogates that predict state variables such as temperature based only on parameters) of the underlying partial differential equations. We first use convolutional autoencoders to compress the size of each temperature field by a factor of 142 and then use FNNs and long-short-term memory networks (LSTMs) to predict the compressed fields. On average, the FNN predictions are $99.30\%$ and the LSTM predictions are $99.22\%$ accurate with respect to unseen simulations. Proper orthogonal decomposition (POD) of the LSTM and FNN predictions shows that despite a lower mean relative accuracy, LSTMs capture the flow dynamics better than FNNs. When summed, the POD coefficients from FNN predictions and from LSTM predictions amount to $96.51\%$ and $97.66\%$ relative to the coefficients of the original simulations, respectively.

We study the spatiotemporal evolution of an evaporating liquid film sheared by a gas considering both inertial and thermal instabilities, the latter arising from a combination of evaporation and Marangoni effects. The shearing gas is modeled by imposing a constant shear stress applied along the liquid's interface. Following in the footsteps of Joo et al. [S. W. Joo et al., J. Fluid Mech. 230, 117 (1991)], long-wave theory is used to derive a Benney-like equation governing the temporal evolution of the liquid interface under the effects of inertia, hydrostatic pressure, surface tension, thermocapillarity, evaporation, and gas shear. Linear stability theory is used to investigate the temporal and spatiotemporal characteristics of the flow, where it is found that the evaporation of the film promotes absolute instabilities and can cause convective-absolute transitions of the perturbations. It is also found that a strong enough counterflowing shearing gas can suppress the inertial instability, commonly known as the $H$ mode, affirming similar conclusions found by previous studies for a strongly confined isothermal film. Additionally, our temporal stability analysis indicates that the thinning of the film reduces the phase speed of thermal perturbations, due to the increasing dominance of viscosity. However, our spatiotemporal analysis shows that the thinning of the film actually results in the growth of additional modes with higher group velocities resulting in faster contamination of the flow field. Moreover, the interface evolution equation is solved numerically to (i) simulate the film's interface evolution subject to finite perturbations and (ii) compare to the results of the linear stability analysis. We find qualitative agreement between the temporal dynamics of the linear and nonlinear instabilities. Our subsequent numerical nonlinear spatiotemporal stability analysis demonstrates that for weaker thermal instabilities, the wave-front dynamics are imposed by the nonlinearly saturated wave packet, while for stronger thermal instabilities, the wave-front dynamics are dictated by the linear dispersion relationship. We also study the effects of the dimensionless parameters on the rupture location and the time it takes for the fluid film to rupture. Finally, the shear stress's effect on the rupture mechanics of the film is studied using self-similarity analysis, where we identify the fate of the evolution equation's solutions.

Immersed granular collapse is a common model case for the study of transient geophysical flows. This paper examines the effects of column size on granular collapses in water, with an emphasis on the granular flow mobility. Laboratory-scale experiments of underwater granular collapses with three different column sizes are carried out, together with their numerical simulations using the coupled lattice Boltzmann and discrete element method. Both experimental and numerical data show that, for an identical aspect ratio, a larger underwater granular collapse results in higher flow mobility and a longer runout distance normalized by the initial column length $L_i$ (increased by 18% on average as $L_i$ increases from 3 to 10 cm). Simulations show that as the column size increases, there is more potential energy being transferred into the kinetic energies of the fluid and the particles, and there is a positive relationship between the column size and the efficiency of energy conversion of the particle kinetic energies from vertical to horizontal directions, which contributes to a higher underwater granular flow mobility in larger cases. The reason is twofold. First, the fluid inertia scales disproportionately with the column size. A stronger eddy with high inertia is induced in the large case, which penetrates through the flowing layer of the granular phase and pushes the particles forward to reach a longer runout distance. Second, large underwater granular collapses are accompanied with more significant contact lubrication, which promotes basal slip and dissipates less energy during horizontal spreading.

Threads of colloidal dispersions can be formed in microfluidic channel systems and are often used for analytical purposes or to assemble macroscopic structures from colloidal particles. Here, we report a combined experimental and numerical study of thread formation in channel systems with varying geometry. In the reference flow-focusing configuration, the sheath flows impinge the core flow orthogonally while in four other channel configurations, the sheath flows impinge the core flow at different confluence angles, which are both positive and negative with respect to the reference sheath direction. Tomographic measurements of the thread development are made using optical coherence tomography (OCT) and are compared to numerically simulated 3D data. The numerical simulations performed with an immiscible fluid solver show good agreement with the experiments in terms of 3D thread shapes, wetted region morphologies, and velocity fields provided an ultralow interfacial tension is applied between the low viscosity (solvent) sheath flows and the high viscosity (dispersion) core flow. Such an ultralow interfacial tension is motivated by the so-called Korteweg stresses induced as a result of the concentration gradient between two miscible fluids in nonequilibrium state. These stresses mimic the effect of interfacial tension, and are often modeled as an effective interfacial tension (EIT), an approach chosen in the present work as well. The value of interfacial tension applied in the simulations was determined through an optimization procedure and compares well with a value deduced from a scaling analysis utilizing the downstream development of experimentally determined thread shape. The experimental and numerical results show that for channel configurations with modest deviations from orthogonal sheath flows, the effect on the thread is similar regardless of whether the sheath flows are co- or counterflowing the core flow. In fact, for these cases, the effect of co- and counterflowing sheath flows can be reproduced with orthogonal sheath flows, if the sheath channel width is increased. However, for channel configurations with larger deviations from orthogonal sheath flows, the effects on the thread are direction dependent. The one-to-one comparison and analysis of numerical and experimental results bring useful insights to understand the behavior of miscible systems involving high-viscosity contrast fluids. These key results provide the foundation to tune the flow-focusing for specific applications, for example in tailoring the assembly of nanostructured materials.

The dynamics of finite-density inertial particles subjected to Stokes drag is complex with no existing model to analytically predict their behavior in an arbitrary flow. While such a model has been recently introduced for heavy particles by Esmaily and Mani [Phys. Rev. Fluids 5, 084303 (2020)], it is yet to be extended to particles with a finite-density ratio. The present study generalizes that previous model to find a relationship for the Lyapunov exponent normalized by the particle relaxation time $\lambda$ as a function of the added-mass factor $\beta$ and a Lagrangian measure of the fluid velocity gradient tensor. This general expression is further simplified by considering a one-dimensional monoharmonic canonical flow that is of fundamental importance in investigating the behavior of particles in practice in a wide range of flows. The final result is a closed-form expression for $\lambda$ [Eq. (27)] that predicts, among others, a lower bound on clustering rate $(-1/2\le \lambda )$, the possibility of dispersion of neutrally buoyant particles in strong straining flows, the regimes at which clustering $(\lambda <0)$, dispersion $(\lambda >0)$, and trajectory crossing occurs (complex-valued $\lambda$ in straining and rotating regimes). A good agreement is observed between the prediction of this analysis and reference results, which are obtained from direct numerical computations.

We have studied vortex-induced vibrations (VIV) of a flexibly mounted cylinder with one degree of freedom for different angles that the direction of oscillations makes with the incoming flow, covering the entire range from a purely inline direction (α = 0°) to a purely crossflow (transverse) direction (α = 90°). Force and displacement measurements together with flow visualizations of the wake are used to characterize the response of the cylinder over a range of reduced velocities ($1<U^{*}<14$). It is shown that the two lock-in ranges that are observed in a purely inline VIV response of the cylinder persist to higher angles: The first lock-in range, which corresponds to a symmetric or alternating-symmetric wake, persists up to α = 40°, and the second one up to α = 50°. The response of the system follows that of a purely inline case both quantitatively and qualitatively up to α = 15°, a relatively large deviation from the pure inline direction. The lock-in range, which is typically observed in a purely crossflow VIV response, appears at angles as low as α = 25°. For α > 50°, this crossflow-induced VIV response is the only response that is observed. It is also shown that the symmetric and alternating-symmetric wakes that had been observed previously in a purely inline case are observed for angles up to α = 30° and α = 15°, respectively, indicating that their formation does not rely on a perfect alignment between the direction of oscillations and the flow direction. For larger angles, a skewed symmetric shedding is observed in which one of the two vortices that are shed simultaneously is larger than the other one.

In this work, we present general solutions for closely spaced corotating helical vortices using a filament approach. For these vortex structures, helical symmetry is broken, but solutions maintain a form of spatial periodicity. We show there exists a moving frame where vortex elements move along the structure without distorting it. These solutions can be used to characterize the evolution of the twin-tip vortices produced in the wake of a tip-splitting rotor blade. The resulting wake has a dual nature. Locally, the structure behaves much like an helical pair aligned with the locally tangent flow. However, as we move away from the vortex structure the induced flow is reminiscent of an “equivalent” helical vortex with thicker core.

Gallium based room temperature liquid metal alloys present an exciting opportunity for research due to their attractive material properties. These alloys can readily remain liquid at room temperature and exhibit unusual phenomena at the air-liquid interface due to oxidation of the gallium. We present a phenomenological study of droplet impacts on a solid substrate measuring the spread parameter ${\xi }_{max}=D_{max}/D_0$ as function of the Weber number, and by extension, the impact velocity, as well as the spread time of the droplets. In order to characterize the surface behavior, we utilized direct measurement of surface forces using a glass probe and a tensiometer, finding the effective surface tension to be ${\sigma }_{\mathrm{eff}}=628\pm 37\mathrm{mN}/\mathrm{m}$. Finally, we developed a model of spreading that scales the spread factor ${\xi }_{max}$ with the Weber number to the power of $\frac{1}{2}$.

Spectrograms provide an efficient way to analyze surface elevation signals of ship waves taken from a sensor fixed at a single point in space. Recent work based on a simplified model for the ship's disturbance suggests that matching the spectrogram heat-map patterns to a so-called dispersion curve has the potential for estimating of properties of a steadily moving ship, such as the ship's speed and closest distance to the sensor. Here we extend the theory behind the dispersion curve so that it can be applied to ships accelerating along arbitrary paths and demonstrate how acceleration affects the structure of the associated spectrograms. Examples are provided for a simple model of a ship accelerating/decelerating in a straight line or traveling in a circle with constant angular speed. We highlight a problem with nonuniqueness of the dispersion curve when comparing ships moving along different paths. Finally, we validate the new dispersion curve against experimental results of ship models accelerating in a finite depth basin. Our work will provide a basis for more comprehensive studies that extend the simplified model to take into account the shape of the hull in question.

We present experiments demonstrating that a small flag attached to the surface of an airfoil near the leading edge exhibits self-excited oscillations when the airfoil is set at a post-stall angle of attack. The limit cycle oscillations of the flag between the airfoil surface and the freestream have a dominant frequency and promote reattachment of the flow, producing a remarkable increase in the maximum lift coefficient and stall angle. Leading-edge vortex shedding and formation of a separation bubble are observed when the flag tip reaches around the maximum displacement. The instantaneous flow and the range of oscillation frequency have strong similarities to those of the active flow control methods for separation, yet this is a passive flow control method that relies on unsteady effects. The flag oscillations occur mostly in the first structural mode, while the higher modes reveal the three-dimensionality of the flag displacement field. The oscillation frequencies of the flag are in the same range of vortex shedding frequency of the baseline airfoil, suggesting that the wake resonance mechanism may be behind the observations of the enhanced lift at the post-stall angles of attack. There is virtually no effect of the compliant flag on the mean lift at small angles of attack.

The formation of deformed liquid marbles via impact of drops onto powder beds is analyzed using experimental and computational modeling approaches. Experimentally, particular attention is paid to determining a relationship between the maximum contact area of the spreading drops, which determines how much powder the drop's surface is able to harvest, and the drop's surface area when the powder (potentially) encapsulates and then immobilises (“freezes”) the surface of the drop to form a liquid marble. Comparisons between impacts on powder beds to those on rigid and impermeable superhydrophobic substrates show good agreement for a range of parameters and motivate the development of the first mathematical model for the process of liquid marble formation via drop impact. The model utilizes experimentally determined functions to capture encapsulation and freezing thresholds and accounts for the powder's influence on the drop via a surface viscous mechanism. Simulations in the volume-of-fluid framework qualitatively recover many features of the experiments and highlight physical effects that should be incorporated into future analyses.

In 1851, Stokes calculated the force exerted by a viscous fluid on an infinite cylinder in oscillating motion. Although the calculation was restricted to vanishingly small Reynolds numbers $\text{Re}$, most of the experimental tests performed up to now have been made with $\text{Re}>1$. Here we present a series of experiments involving a cylindrical pendulum oscillating in air at different pressures and with $\text{Re}<1$. We deduce the unsteady friction force from the measurement of the damping time of the oscillations. We compare our experimental results for the unsteady force (a) to Stokes' predictions for an infinite cylinder and (b) to predictions for finite-length cylinders, using an expression of the unsteady force derived from the works of Lawrence and Weinbaum and Loewenberg. The agreement is quite satisfactory and proves that macroscopic objects like a pendulum can be used as probes of the Stokesian flow regime.

We report on a series of fully resolved simulations of the flow around a rigid sphere translating steadily near a wall, either in a fluid at rest or in the presence of a uniform shear. Nonrotating and freely rotating spheres subject to a torque-free condition are both considered to evaluate the importance of spin-induced effects. The separation distance between the sphere and wall is varied from values at which the wall influence is weak down to gaps of half the sphere radius. The Reynolds number based on the sphere diameter and relative velocity with respect to the ambient fluid spans the range $0.1–250$, and the relative shear rate defined as the ratio of the shear-induced velocity variation across the sphere to the relative velocity is varied from $-0.5$ to $+0.5$, so that the sphere either leads the fluid or lags behind it. The wall-induced interaction mechanisms at play in the various flow regimes are analyzed qualitatively by examining the flow structure, especially the spanwise and streamwise vorticity distributions. Variations of the drag and lift forces at low-but-finite and moderate Reynolds number are compared with available analytical and semiempirical expressions, respectively. In more inertial regimes, empirical expressions for the two force components are derived based on the numerical data, yielding accurate fits valid over a wide range of Reynolds number and wall-sphere separations for both nonrotating and torque-free spheres.

The impact of droplets on dry and prewetted meshes was investigated using high-speed photography. The prewetting resulted from previous impacts. It was observed that an increase of the Weber number We resulted in a transition from no penetration of the mesh through an incomplete penetration to a complete penetration. It was found that both penetrations could be entirely suppressed by liquid trapped in the mesh (prewetted mesh), with the height $h$ of the sessile droplet being a key factor. The phase diagram in the $(\mathrm{We}, h)$ plane determining the expected type of impact has been determined. The transition Weber numbers for both types of penetration increased monotonically with $h$. A model for predicting the transition thresholds is proposed and compared with experimental results. It is suggested that the impact type is determined by the momentum exchange between the impacting droplet and the liquid trapped in the mesh.

Convection in the Sun occurs at Rayleigh numbers, $\mathrm{Ra}$, as high as ${10}^{22}$ and molecular Prandtl numbers, $\mathrm{Pr}$, as low as ${10}^{-6}$, under conditions that are far from satisfying the Oberbeck-Boussinesq (OB) idealization. The effects of these extreme circumstances on turbulent heat transport are unknown, and no comparable conditions exist on Earth. Our goal is to understand how these effects scale (since we cannot yet replicate the Sun's conditions faithfully). We study thermal convection by using direct numerical simulations, and determine the variation with respect to $\mathrm{Pr}$, to values as low as ${10}^{-4}$, of the turbulent Prandtl number, ${\mathrm{Pr}}_t$, which is the ratio of turbulent viscosity to thermal diffusivity. The simulations are primarily two-dimensional but we draw upon some three-dimensional results as well. We focus on non-Oberbeck-Boussinesq (NOB) conditions of a certain type, but also study OB convection for comparison. The OB simulations are performed in a rectangular box of aspect ratio 2 by varying $\mathrm{Pr}$ from $O\left(10\right)$ to ${10}^{-4}$ at fixed Grashof number $\mathrm{Gr}\equiv \mathrm{Ra}/\mathrm{Pr}={10}^9$. The NOB simulations are done in the same box by letting only the thermal diffusivity depend on the temperature. Here, the Rayleigh number is fixed at the top boundary while the mean $\mathrm{Pr}$ varies in the bulk from 0.07 to $5\times {10}^{-4}$. The three-dimensional simulations are performed in a box of aspect ratio 25 at a fixed Rayleigh number of ${10}^5$, and $0.005\le \mathrm{Pr}\le 7$. The principal finding is that ${\mathrm{Pr}}_t$ increases with decreasing $\mathrm{Pr}$ in both OB and NOB convection: ${\mathrm{Pr}}_t\sim {\mathrm{Pr}}^{-0.3}$ for OB convection and ${\mathrm{Pr}}_t\sim {\mathrm{Pr}}^{-1}$ for the NOB case. The ${\mathrm{Pr}}_t$ dependence for the NOB case especially suggests that convective flows in the astrophysical settings behave effectively as in high-Prandtl-number turbulence.