A vortical impulse theory is used to compute the thrust force of a plunging and pitching airfoil in forward flight at high Reynolds numbers within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick, which considered only two effects, the leading-edge suction and the projection in the flight direction of the pressure force on the airfoil. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains, in addition to the pressure force projection term, a new term that generalizes the leading-edge suction term in Garrick's theory. This term depends on Theodorsen function $C\left(k\right)$ and on a new complex function $C_1\left(k\right)$ of the reduced frequency $k$. The main qualitative difference with Garrick's theory is that the propulsive efficiency, or ratio of the mean thrust power and the mean input power required to drive the airfoil, tends to zero as the reduced frequency increases to infinity (as $k^{-1}$), in contrast to Garrick's propulsive efficiency that tends to a constant $\left(1/2\right)$. Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as $k\to \infty$ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining nondimensional parameters. The present analytical results are in good agreement, for small amplitude oscillations, with numerical results from unsteady panel methods, and with experimental data and numerical results from the Navier-Stokes equations, except for small reduced frequencies where viscous effects are obviously important.

Intraventricular pressure gradients were clinically demonstrated to represent one useful indicator of the left ventricle (LV) function during the development of heart failure. We analyze the fluid dynamics inside a model LV to improve the understanding of the development of hemodynamic forces (i.e., mean pressure gradient) in normal conditions and their modification in the presence of alterations of LV tissue motion. To this aim, the problem is solved numerically and the global force exchanged between blood flow and LV boundaries is computed by volume integration. We also introduce a simplified analytical model, based on global conservation laws, to estimate hemodynamic forces from the knowledge of LV tissue information commonly available in cardiac imaging. Numerical results show that the normal intraventricular gradients feature a deep brief suction at early diastolic filling and a persistent thrust during systolic ejection. In presence of abnormalities of the wall motion, the loss of time synchrony is more relevant than the loss of spatial uniformity in modifying the normal pressure gradient spatiotemporal pattern. The main findings are reproduced in the integral model, which represents a possible easy approach for integrating fluid dynamics evaluations in the clinical examination.

In this paper we propose equations of motion for the dynamics of liquid films of surfactant suspensions that consist of a general gradient dynamics framework based on an underlying energy functional. This extends the gradient dynamics approach to dissipative nonequilibrium thin-film systems with several variables and casts their dynamic equations into a form that reproduces Onsager's reciprocity relations. We first discuss the general form of gradient dynamics models for an arbitrary number of fields and discuss simple well-known examples with one or two fields. Next we develop the three-field gradient dynamics model for a thin liquid film covered by soluble surfactant and discuss how it automatically results in consistent convective (driven by pressure gradients, Marangoni forces, and Korteweg stresses), diffusive, adsorption or desorption, and evaporation fluxes. We then show that in the dilute limit, the model reduces to the well-known hydrodynamic form that includes Marangoni fluxes due to a linear equation of state. In this case the energy functional incorporates wetting energy, surface energy of the free interface (constant contribution plus an entropic term), and bulk mixing entropy. Subsequently, as an example, we show how various extensions of the energy functional result in consistent dynamical models that account for nonlinear equations of state, concentration-dependent wettability, and surfactant and film bulk decomposition phase transitions. We conclude with a discussion of further possible extensions towards systems with micelles, surfactant adsorption at the solid substrate, and bioactive behavior.

A study is made about the energy spectrum $E\left(k\right)$ of turbulence on the basis of high-resolution direct numerical simulations (DNSs) of forced incompressible turbulence in a periodic box using a Fourier spectral method with the number of grid points and the Taylor scale Reynolds number $R_{\lambda }$ up to $12{288}^3$ and approximately 2300, respectively. The DNS data show that there is a wave-number range (approximately $5\times {10}^{-3}<k\eta <2\times {10}^{-2}$) in which $E\left(k\right)$ fits approximately well to Kolmogorov's $k^{-5/3}$ scaling, where $\eta$ is the Kolmogorov length scale. However, a close inspection shows that the exponent is a little smaller than $-5/3$, and $E\left(k\right)$ in the range fits to $E\left(k\right)/\left[{\langle \epsilon \rangle }^{2/3}{k}^{-5/3}\right]=c{\left(kL\right)}^m$, where $\langle \epsilon \rangle$ is the mean energy dissipation rate per unit mass; $L$ is the integral length scale; and $m\approx -0.12$. The coefficient $c$ is independent of $k$, but has a $R_{\lambda }$ dependence, such as $c=C{R}_{\lambda }^{\zeta }$, where $C\approx 0.9$ and $\zeta \approx 0.14$.

We analyze the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity $\mathbf{\omega }$ equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number ${\mathrm{Re}}_{\mathrm{s}}$, for all aspect ratios considered. For the special case of a sphere we find $\omega /s=-1/2+0.0540{\mathrm{Re}}_{\mathrm{s}}^{3/2}$ where $s$ is the shear rate. The $O\left({\mathrm{Re}}_{\mathrm{s}}^{3/2}\right)$ correction differs from that derived by Lin et al. [J. Fluid Mech. 44, 1 (1970)], who obtained a numerical coefficient roughly three times larger.

Selective noise amplifiers are characterized by large linear amplification to external perturbations in a particular frequency range despite their global linear stability. Applying a stochastic forcing with increasing amplitude, the response undergoes a strong nonlinear saturation when compared to the linear estimation. Building upon our previous work, we introduce a predictive model that describes this nonlinear dynamics, and we apply it to a canonical example of selective noise amplifiers: the backward-facing step flow. Rewriting conveniently the stochastic forcing and response in the frequency domain, the model consists in a mean flow equation coupled to the linear response to forcing at each frequency. This coupling is attained by the Reynolds stress, which is constructed by the integral in frequency of the independent responses. We generalize the model for a response to a white noise forcing $\delta$-correlated in space and time restricting the flow dynamics to its most energetic patterns calculated from the optimal harmonic forcing and response of the flow. The model estimates accurately the response saturation when compared to direct numerical simulations, and it correctly approximates the structure of the response and the mean flow modification. It also shows that the response undergoes a selective process governed by the nonlinear gain, which promotes a response structure with an approximately single frequency and wavelength in the whole domain. These results suggest that the mean flow modification by the Reynolds stress is the key nonlinearity in the saturation process of the response to white noise.

We perform a linearized reduced-order modeling of the aeroacoustic sound sources in supersonic reacting mixing layers to explore their sensitivities to some of the flow parameters in radiating sound. Specifically, we investigate the role of outer modes as the effective flow compressibility is raised, when some of these are expected to dominate over the traditional Kelvin-Helmholtz (K-H) -type central mode. Although the outer modes are known to be of lesser importance in the near-field mixing, how these radiate to the far-field is uncertain, on which we focus. On keeping the flow compressibility fixed, the outer modes are realized via biasing the respective mean densities of the fast (oxidizer) or slow (fuel) side. Here the mean flows are laminar solutions of two-dimensional compressible boundary layers with an imposed composite (turbulent) spreading rate, which we show to significantly alter the growth of instability waves by saturating them earlier, similar to in nonlinear calculations, achieved here via solving the linear parabolized stability equations. As the flow parameters are varied, instability of the slow modes is shown to be more sensitive to heat release, potentially exceeding equivalent central modes, as these modes yield relatively compact sound sources with lesser spreading of the mixing layer, when compared to the corresponding fast modes. In contrast, the radiated sound seems to be relatively unaffected when the mixture equivalence ratio is varied, except for a lean mixture which is shown to yield a pronounced effect on the slow mode radiation by reducing its modal growth.

An asymptotic solution is derived for the motion of inertial particles exposed to Stokes drag in an unsteady random flow. This solution provides an estimate for the sum of Lyapunov exponents as a function of the Stokes number and Lagrangian strain- and rotation-rate autocovariance functions. The sum of exponents in a Lagrangian framework is the rate of contraction of clouds of particles, and in an Eulerian framework, it is the concentration-weighted divergence of the particle velocity field. Previous literature offers an estimate of the divergence of the particle velocity field, which is applicable only in the limit of small Stokes numbers [Robinson, Comm. Pure Appl. Math. 9, 69 (1956) and Maxey, J. Fluid Mech. 174, 441 (1987)] (R-M). In addition to reproducing R-M at this limit, our analysis provides a first-order correction to R-M at larger Stokes numbers. Our analysis is validated by a directly computed rate of contraction of clouds of particles from simulations of particles in homogeneous isotropic turbulence over a broad range of Stokes numbers. Our analysis and R-M predictions agree well with the direct computations at the limit of small Stokes numbers. At large Stokes numbers, in contrast to R-M, our model predictions remain bounded. In spite of an improvement over R-M, our analysis fails to predict the expansion of high Stokes clouds observed in the direct computations. Consistent with the general trend of particle segregation versus Stokes number, our analysis shows a maximum rate of contraction at an intermediate Stokes number of $O\left(1\right)$ and minimal rates of contraction at small and large Stokes numbers.

We analyze the response of a gas in a micro-slab, set at an initial pure-conduction state, to instantaneous thermal insulation of its boundaries. In line with ongoing efforts in generating gas flows at the microscale, thermal insulation is suggested as a means for flow excitation with no moving parts. The problem is analyzed in the entire range of gas rarefaction rates and for arbitrary initial temperature differences between the walls. Analytical solutions are obtained in the linearized limit of small temperature differences for large (collisionless) and small (continuum) Knudsen numbers. These solutions are supported by direct simulation Monte Carlo calculations, which are then used to investigate the nonlinear problem with large initial temperature differences. Followed by the system's initial state, boundary insulation results in a series of time-decaying waves, propagating across the slab, and transferring the system between its conductive and adiabatic equilibrium states. While larger initial temperature differences result in higher flow rates, it is found that nonlinear effects reduce the efficiency of flow excitation through boundaries insulation. At high Knudsen numbers, this is rationalized through the system's initial state, in which the gas uniform temperature is lower than the arithmetic mean of walls temperatures. At low Knudsen numbers, the dominant effect of molecular collisions causes thermal dissipation, which in turn results in kinetic energy losses. The analysis may be readily applied to calculate the gas response to arbitrary time variations of the boundary-imposed heat flux.

We investigate the dynamics of freely expanding liquid sheets prepared with fluids with different rheological properties: (i) Viscous fluids with a zero-shear viscosity ${\eta }_0$ in the range $1–1000\mathrm{mPa}\mathrm{s}$ and (ii) viscoelastic fluids whose linear viscoelastic behavior in the frequency range $0.1–100$ rad/s can be accounted for by a Maxwell fluid model, whose characteristic elastic modulus $G_0$, relaxation time $\tau$, and zero-shear viscosity ${\eta }_0=G_0\tau$, can be tuned over several orders of magnitude. The sheets are produced by a drop of fluid impacting a small cylindrical solid target. For viscoelastic fluids, we show that, when $\tau$ is shorter than the typical lifetime of the sheet ($\sim 10$ ms), the dynamics of the sheet is similar to that of Newtonian viscous liquids with equal zero-shear viscosity. In that case, for little viscous samples (${\eta }_0\lesssim 30$ mPa s), the maximal expansion of the sheet $d_{\max }$ is independent of ${\eta }_0$, whereas for more viscous samples, $d_{\max }$ decreases as ${\eta }_0$ increases. We provide a simple model for the dependence of the maximal expansion of the sheet with the viscosity that accounts well for our experimental data. By contrast, when $\tau$ is longer than the typical lifetime of the sheet, the behavior drastically differs. The sheet expansion is strongly enhanced as compared to that of viscous samples with comparable zero-shear viscosity, but is heterogeneous with the occurrence of cracks, revealing the elastic nature of the viscoelastic fluid.

Within the past decade, the separation of particles via continuous flow through microfluidic devices has been developed largely through an Edisonian approach whereby devices have been developed based on observation and intuition. This is particularly true in the development of vector chromatography at vanishingly small Reynolds number for non-Brownian particles. Note that this latter phenomenon has its origins in the irreversible forces that are at work in the device, since Stokes flow reversibility typically prohibits their function otherwise. We present a numerical simulation of the vector separation of non-Brownian particles of different sizes and deformabilities in the Stokes flow through channels whose lower surface is composed of slanted cavities. The simulations are designed to understand the physical principles behind the separation as well as to provide design criteria for devices for separating particles in a given size and flexibility range. The numerical simulations are Stokes flow boundary element simulations using techniques defined elsewhere in the literature, but including a close-range repulsive force between the particles and the slanted cavities. We demonstrate that over a range of repulsive force that is comparable to the roughness in the experimental devices, the separation data (particularly in particle size) are predicted quantitatively and are a very weak function of the range of the force. We then vary the geometric parameters of the simulated devices to demonstrate the sensitivity of the separation efficiency to these parameters, thus making design predictions as to which devices are appropriate for separating particles in different size, shape, and deformability ranges.

The comparison of the results of direct numerical simulations of isotropic turbulence of Newtonian and viscoelastic fluid provides evidence that viscoelasticity modifies qualitatively the behavior of the smallest scales: we observe a power law in the far dissipation range of the fluid kinetic energy spectrum and we show that it is a robust feature, roughly independent of the large scale dynamics. A detailed analysis of the energy transfer shows that at these scales energy is injected into the fluid flow through polymer relaxation. It is further shown that a part of the total energy is transferred among scales through an interaction of the velocity field with the polymer field.

Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface: hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly affects the global dynamics, due to variations in hydrodynamic interaction range. The array undergoes a transition from a traveling wave to either a steady chevron pattern or one punctuated by periodic phase defects. Within the transition between these regimes the system displays behavior reminiscent of chimera states.

When deposited on a plate moving quickly enough, any liquid can levitate as it does when it is volatile on a very hot solid (Leidenfrost effect). In the aerodynamic Leidenfrost situation, air gets inserted between the liquid and the moving solid, a situation that we analyze. We observe two types of entrainment. (i) The thickness of the air gap is found to increase with the plate speed, which is interpreted in the Landau-Levich-Derjaguin frame: Air is dynamically dragged along the surface and its thickness results from a balance between capillary and viscous effects. (ii) Air set in motion by the plate exerts a force on the levitating liquid. We discuss the magnitude of this aerodynamic force and show that it can be exploited to control the liquid and even to drive it against gravity.

We investigate the impact of nonideal diffusion on the structure of supercritical cryogenic binary mixing layers. This situation is typical of liquid fuel injection in high-pressure rocket engines. Nonideal diffusion has a dramatic impact in the neighborhood of chemical thermodynamic stability limits where the components become quasi-immiscible and ultimately form a nonmixing layer. Numerical simulations are performed for mixing layers of ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ at a pressure of 100 atm and temperature around 120–150 K near chemical thermodynamic stability limits.

We perform a thorough investigation of the drying dynamics of a charged colloidal dispersion drop in a confined geometry. We develop an original methodology based on Raman microspectroscopy to measure spatially resolved colloids concentration profiles during the drying of the drop. These measurements lead to estimates of the collective diffusion coefficient of the dispersion over a wide range of concentration. The collective diffusion coefficient is one order of magnitude higher than the Stokes-Einstein estimate, showing the importance of the electrostatic interactions for the relaxation of concentration gradients. At the same time, we also perform fluorescence imaging of tracers embedded within the dispersion during the drying of the drop, which reveals two distinct regimes. At early stages, concentration gradients along the drop lead to buoyancy-induced flows. Strikingly, these flows do not influence the colloidal concentration gradients that generate them, as the mass transport remains dominated by diffusion. At longer time scales, the tracer trajectories reveal the formation of a gel that dries quasihomogeneously. For such a gel, we show using linear poroelastic modeling that the drying dynamics is still described by the same transport equations as for the liquid dispersion. However, the collective diffusion coefficient follows a modified generalized Stokes-Einstein relation, as also demonstrated in the context of unidirectional consolidation by Style and Peppin [Style and Peppin, Crust formation in drying colloidal suspensions, Proc. R. Soc. A 467, 174 (2011)].

We report simultaneous measurements of the mean temperature profile $\theta \left(z\right)$ and temperature variance profile $\eta \left(z\right)$ near the lower conducting plate of a specially designed quasi-two-dimensional cell for turbulent Rayleigh-Bénard convection. The measured $\theta \left(z\right)$ is found to have a universal scaling form $\theta (z/\delta )$ with varying thermal boundary layer (BL) thickness $\delta$, and its functional form agrees well with the recently derived BL equation by Shishkina et al. [Phys. Rev. Lett. 114, 114302 (2015)]. The measured $\eta \left(z\right)$, on the other hand, is found to have a scaling form $\eta (z/\delta )$ only in the near-wall region with $z/\delta \lesssim 2$. Based on the experimental findings, we derive a BL equation for $\eta (z/\delta )$, which is in good agreement with the experimental results. These BL equations thus provide a common framework for understanding the effect of BL fluctuations.

The Lagrangian dynamics of semiflexible particles in homogeneous and isotropic turbulent flows is studied by means of analytically solvable stochastic models and direct numerical simulations. The stationary statistics of the bending angle shows a strong dependence on the dimension of the flow. In two-dimensional turbulence, particles are found in either a fully extended or a fully folded configuration; in three dimensions, the predominant configuration is the fully extended one. Such a sensitivity of the bending statistics on the dimensionality of the flow is peculiar to fluctuating flows and is not observed in laminar stretching flows.

The generalized Chapman-Enskog (GCE) method for rapid and slow thermochemical processes is employed to formulate a set of continuum breakdown parameters for chemically reacting flows. These GCE breakdown parameters are derived for one-temperature, two-temperature, and three-temperature models, through classification of the relevant thermochemical time scales relative to fast elastic collisional processes and slow flow processes associated with changes in macroscopic observables. Continuum breakdown mechanisms owing to multicomponent diffusion, thermal diffusion, normal and shear stresses, Fourier-type heat fluxes based on translational, rotational, and vibrational temperatures, bulk viscosity, and relaxation pressure are presented for chemically reacting flows. The GCE breakdown parameters, derived from rigorous kinetic theory, capture the proper physical mechanism leading to continuum breakdown. These breakdown parameters are used to analyze continuum breakdown in a Mach 24 reacting air flow over a sphere and continuum breakdown is observed in the shock and close to the sphere surface. The flow field near the sphere surface is found to be characterized by sharp species concentration gradients due to gas-phase and surface reactions. Chemical reactions thus lead indirectly to the distortion of the velocity distribution function (VDF), providing a pathway to continuum breakdown that is captured by the GCE specieswise diffusion breakdown parameter.