We study the reconnection of vortices in a quantum fluid with a roton minimum by numerically solving the Gross-Pitaevskii (GP) equations. A nonlocal interaction potential is introduced to mimic the experimental dispersion relation of superfluid ${}^4\mathrm{He}$. We begin by choosing a functional shape of the interaction potential that allows us to reproduce in an approximative way the so-called roton minimum observed in experiments, without leading to spurious local crystallization events. We then follow and track the phenomenon of reconnection, starting from a set of two perpendicular vortices. A precise and quantitative study of various quantities characterizing the evolution of this phenomenon is proposed: This includes the evolution of statistics of several hydrodynamical quantities of interest and the geometrical description of a observed helical wave packet that propagates along the vortex cores. Those geometrical properties are systematically compared to the predictions of the local induction approximation (LIA), showing similarities and differences. The introduction of the roton minimum in the model does not change the macroscopic properties of the reconnection event but the microscopic structure of the vortices differs. Structures are generated at the roton scale and helical waves are evidenced along the vortices. However, contrary to what is expected in classical viscous or inviscid incompressible flows, the numerical simulations do not evidence the generation of structures at smaller or larger scales than the typical atomic size.

This experimental work studies the impact large scale motions in a zero pressure gradient turbulent boundary layer have on the fluctuating streamwise wall shear stress component using a recently developed $1\times 1{\mathrm{mm}}^2$ floating element differential capacitive shear stress sensor. The sensing system allows for a flat band response with a bandwidth up to 1.8 kHz (based on a $\pm 3\text{−}\mathrm{dB}$ limit). The streamwise velocity is measured using single component hot-wire anemometry. The experimental setup is first verified to have a canonical zero pressure gradient turbulent boundary layer using the mean and fluctuating velocity profiles as well as fits for the mean wall shear stress with respect to the operating Reynolds number. Characteristics of the large scale structure are examined spatially using Taylor's frozen field hypothesis and the lag time of peak levels of correlation between the shear stress and velocity signals. The large scale motion inclination angle is determined to be ${16}^{\circ }$. The coherence between the signals demonstrate that low frequency motions dominate most of the boundary layer except nearest the wall. In addition, conditional sampling of velocity on shear stress provides conditional velocity statistics profiles which reveal information on the entire boundary layer during shear stress events, representing the qualitative features of the bursting-sweeping process.

We suggest longitudinal strips attached to an airfoil surface as a new stall control device. Their effects on the stall characteristics and flow modifications are experimentally investigated. The airfoil considered is SD7003 and the Reynolds numbers are $\mathrm{Re}=60000$ and 180 000 based on the chord length and freestream velocity. The drag and lift forces on the airfoil are measured by varying the angle of attack from $\alpha =0^{\circ }$ to 16° with and without strips. The optimal strip configuration is determined using a response surface method. Without strip, abrupt stalls occur at $\alpha ={11}^{\circ }$ and 12.5° for $\mathrm{Re}=60000$ and 180 000, respectively, whereas broad stalls occur without much changing the stall angles by optimal strips. The lift coefficient and lift-to-drag ratio are significantly increased by the strips at post-stall angles of attack. A corner vortex is generated at each corner of strip near the leading edge. Clockwise and counterclockwise streamwise vortices are generated at the left- and right-facing corners, respectively, and they slowly move away from the corners while travelling downstream. These vortices provide additional momentum to the airfoil suction surface, resulting in fully attached flow above the strips and reattachment of flow above grooved surface. The longitudinal strips presented here are different from other devices such as the vortex generator, trip wire, burst control plate, and zigzag tapes used for the separation control of low Reynolds number airfoil, in that the strips are installed nearly on the whole airfoil surface but with their heights lower than the boundary layer thickness, and produce positive control effects at post-stall angles of attack but little affect the aerodynamic performance at prestall angles of attack.

A model problem of low-Mach-number lean premixed reacting swirling flows with wall-separation zones in a contracting circular finite-length open chamber is studied. Assuming a complete reaction with high activation energy and chemical equilibrium behind the reaction zone, a nonlinear partial differential equation is derived for the solution of the flow stream function behind the reaction zone in terms of the specific total enthalpy for a reacting flow, the specific entropy, and the circulation functions prescribed at the chamber's inlet. Four types of solutions of the resulting ordinary differential equation for the columnar flow case describe the outlet state of the flow in a long chamber. The bifurcation diagrams of steady flows as the inlet swirl level is increased at fixed chamber contraction and reaction heat release are described. The approach is applied to an inlet solid-body rotation flow with constant profiles of the axial velocity, temperature, and mixture reactant mass fraction. The computed results provide theoretical predictions of the critical inlet swirl levels for the first appearance of wall-separation states and for the size of the separation zone as a function of the inlet swirl ratio, Mach number, chamber contraction, and heat release of the reaction. The methodology developed in this paper provides a theoretical feasibility for the development of the technology of swirl-assisted combustion where the reaction zone is supported and stabilized by a wall-separation zone.

The influence of interfacial elasticity on the rate of liquid drainage from gas-liquid interfaces is a subject that has encouraged prolific scientific work on coalescence and film stability. Elucidating this relationship is important for the design of surfactant mixtures where the amount of liquid content of the foam is critical for the aesthetics and/or effectiveness of the product. However, contradictory theoretical predictions exist with regard to how surface elasticity may influence thin-film dynamics. In this work, interferometric studies are performed to measure the liquid film entrainment between a bubble and an air-liquid interface in response to systematic variations of the surface elasticity. The surface elasticity is varied by adjusting the age of the interface or by adjusting the bulk concentration of a surface-active molecule known to form highly elastic surface layers. Surprisingly, the results indicate the absence of a strong relationship between the surface shear elasticity and the entrainment of liquid in foam films. In addition, qualitative differences are observed between the shapes of foam films with differences in interfacial shear viscosity, with no net effect on liquid entrainment under the conditions studied.

Drying of porous media very often occurs in the presence of significant temperature gradients because heat fluxes are imposed in many situations in order to decrease the drying time or to facilitate the moisture removal at a higher humidity of the surrounding gas phase. Here we consider the situation where the temperature increases with depth. We show from experiments with a micromodel that the temperature gradient induces the stabilization of the evaporation front within the model porous medium according to two different mechanisms occurring consecutively. The first mechanism occurs in the liquid phase and is explained by the dependence of surface tension upon temperature. This results in the preferential invasion of the warmer zones. The second mechanism occurs gas-sided due to the dependence of saturation vapor pressure upon temperature. We show that the time scales of both mechanisms are different leading to the temporary formation of distinctive phase patterns from which different periods of drying can be discriminated.

Motivated by the liquid metal coating on a divertor in a tokamak, we investigate the flow of a thin film of incompressible fluid on an inclined substrate subjected to a localized external pressure that oscillates parallel to the substrate. When the movement of the pressure occurs on a timescale significantly longer than the characteristic time for the thin film to equilibrate, the system is quasisteady. In the opposite extreme, where the pressure oscillates much faster than the response time of the free surface, a multiple-scale analysis shows that the free surface is exposed to an effective time-averaged pressure profile. Thus the oscillations can act to spread the momentum load of the applied pressure, resulting in smaller deformations of the liquid film. In the intermediate case, where the intrinsic and external timescales are similar, we find that there exists a critical speed of oscillations which maximizes the free-surface deflection and results in a possibly dangerous thinning of the film. Further local maxima in the free-surface deflection are caused by a fascinating nonlocal wave interaction mechanism.

The interaction of a small, solid particle with a nearby fluid droplet covered with a thin, permeable membrane is considered for linear ambient flows under conditions where viscous forces dominate. A bispherical-coordinate solution was developed to describe the relative motion along and normal to the line-of-centers between the particle and drop. The effect of the permeability of the drop membrane is relatively weak, except in near contact where the lubrication pressure in the narrow gap between the particle and drop surfaces can cause significant permeation of fluid across the membrane, as further described by a lubrication analysis. These results were then used in a trajectory analysis to predict particle collection rates by permeable drops in a dilute suspension undergoing uniaxial extensional (or compressional) flow. Even a small amount of permeation allows for a large increase in the particle collision rate with the drop interface. For example, the collision efficiency (collision rate divided by that in the absence of hydrodynamic interactions) is 0.17 for equisized particles and drops with a dimensionless permeability $k/a=0.0001$ (where $k$ is the membrane permeability per unit thickness, and $a$ is the reduced radius of the drop and particle). In contrast, it is identically zero (due to the singular lubrication resistance) for smooth, impermeable spheres in the absence of attractive molecular forces and fluid slip.

The stability of flows in layers of finite thickness $H$ is examined against small-scale three-dimensional (3D) perturbations and large-scale two-dimensional (2D) perturbations. The former provide an indication of a forward transfer of energy while the latter indicate an inverse transfer and the possibility of an inverse cascade. The analysis is performed using a Floquet-Bloch code that allows examination of the stability of modes with arbitrary large-scale separation. For thin layers, the 3D perturbations become unstable when the layer thickness $H$ becomes larger than $H>c_1{(\nu {\ell }_{{}_U}/U)}^{1/2}=c_1{\ell }_{{}_U}{\text{Re}}^{-1/2}$, where $U$ is the rms velocity of the flown, ${\ell }_{{}_U}$ is the correlation length scale of the flow, $\nu$ is the viscosity, and $\text{Re}={\ell }_{{}_U}U/\nu$ is the Reynolds number. At the same time, large-scale 2D perturbations also become unstable by an eddy viscosity mechanism when $\text{Re}>c_2$, where $c_1,c_2$ are order 1 nondimensional numbers. These relations define different regions in parameter space where 2D and 3D instabilities can (co)exist and this allows us to construct a stability diagram. Implications of these results for fully turbulent flows that display a change of direction of cascade as $H$ is varied are discussed.

We perform a three-dimensional, short-wavelength stability analysis on the numerically simulated two-dimensional, unsteady wake resulting from a uniform flow past a circular cylinder at Reynolds numbers in the range $50\le \text{Re}\le 300$; here, $\text{Re}=U_{\infty }D/\nu$ with $U_{\infty }$, $D$, and $\nu$ being the free-stream velocity, the diameter of the cylinder, and the kinematic viscosity of the fluid, respectively. For a given Re, inviscid local stability equations from the geometric optics approach are solved on all the closed fluid particle trajectories with the same period as the time period of the flow. For each of the six distinct closed trajectories, denoted orbits 1–6, the growth rate is plotted as a function of Re for purely transverse perturbations. The inviscid instability on orbits 1 and 2, which are symmetric counterparts of one another, is shown to undergo bifurcations at $\text{Re}\approx 50$ and $\text{Re}\approx 250$. The bifurcation at $\text{Re}\approx 250$ from an asynchronous to a synchronous instability is argued to be related to the emergence of mode-B secondary instability, which experimental, numerical, and theoretical studies have shown to occur at $\text{Re}\approx 260$. Incorporating finite-wave-number, finite-Reynolds-number effects in the local stability framework, and comparing the corrected local stability growth rates with the global stability growth rates further support our main conclusion: The bifurcation to three-dimensional short-wavelength synchronous instability on orbits 1 and 2 is a possible local mechanism for the emergence of mode-B secondary instability. The relevance (or lack thereof) of the local instabilities on the other orbits is also discussed.

We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on a two-range pseudopotential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short-range repulsive interaction between species in the classical single-range model, a competing mechanism between the short-range attractive and midrange repulsive interactions is imposed within each species. Besides extending the range of attainable surface tension as compared with the single-range model, the proposed scheme is also shown to achieve a positive disjoining pressure, independently of the viscosity ratio. The latter property is crucial for many microfluidic applications involving a collection of disperse droplets with a different viscosity from that of the continuum phase. As a preliminary application, the relative effective viscosity of a pressure-driven emulsion in a planar channel is computed.

Following the dimensional analysis approach carried out in previous studies, it is hypothesized that the small-scale fluctuations should only depend on the inner scales, analogous to the Prandtl's law of the wall for the mean flow. This allows us to examine the high-frequency regime of the streamwise energy spectra where a “law of the wall” in spectra would hold. Observations in high-Reynolds-number turbulent boundary layer data indicate that a conservative estimate for the start of this law of the wall is $f^{+}=0.005$ (which corresponds to 200 viscous time units) across a range of wall-normal positions and Reynolds numbers. This is sufficient to capture the energetic viscous-scaled motions such as the near-wall streaks, which have a timescale of approximately 100 viscous units. This spectral collapse is consistent with the observations in internal flows and external flows in other studies. Furthermore, the spectral collapse leads to a universal scaling (based on skin-friction velocity and kinematic viscosity) for the small-scale streamwise turbulence variance (consistent with the hypothesis) across the entire boundary layer. A logarithmic variation of this small-scale variance is observed farther away from the wall.

The equilibrium state of a flexible fiber settling in a viscous fluid is examined using a combination of macroscopic experiments, numerical simulations, and scaling arguments. We identify three regimes having different signatures on this equilibrium configuration of the elastic filament: weak and large deformation regimes wherein the drag is proportional to the settling velocity as expected in Stokes flow and an intermediate elastic reconfiguration regime where the filament deforms to adopt a shape with a smaller drag which is no longer linearly proportional to the velocity.

In this study, we investigated the shape evolution and bubble formation of acoustically levitated drops upon increasing the sound intensity. Here, a levitated liquid drop evolves progressively from an oblate spheroidal shape to a flattened film to a thin bowl-shaped film, eventually forming a closed bubble. Through systematic experiments, numerical simulation, and scaling analysis, we demonstrate that the buckled geometry of the liquid film can drastically enhance the suction effect of acoustic radiation pressure at its rim, forming a significant pressure gradient inside the film which causes an abrupt area expansion and bubble formation. Our results provide the mechanical origin responsible for the shape evolution and bubble formation of acoustically levitated drops, and highlight the role of buckled geometry in the levitation and manipulation of liquid films in an ultrasound field.

A rigid sphere entering a liquid bath does not always produce an entrained air cavity. Previous experimental work shows that cavity formation, or the lack thereof, is governed by fluid properties, wetting properties of the sphere, and impact velocity. In this study, wetting steel spheres are dropped into a water-surfactant mixture with and without passing through a bubble layer first. Surprisingly, in the case of a water-surfactant mixture without a bubble layer, the critical velocity for cavity formation becomes radius dependent. This occurs due to dynamic surface tension effects, with the local surface tension in the splash increasing during surface expansion and decreasing as surfactant molecules adsorb to the newly formed interface. The larger sphere radii take longer to submerge and hence allow more time for the surface tension to decrease back to the equilibrium value and decrease the critical velocity for cavity formation. When a soap bubble layer is present, subsurface cavities form at all impact velocities. Our analysis shows that the bubble layer wets the sphere prior to impact with a patchy coating of droplets and bubbles. The droplets alter the splash and create an aperture for air entrainment, which leads to cavity formation at wetted locations on the sphere surface. The water-surfactant entry behavior of these partially wetted spheres results in a progression of cavity formation regimes with increasing Weber number, similar to the cavity regimes of hydrophobic spheres entering water. Nonuniform droplet coatings create cavity asymmetries altering transitions between these regimes.

The problem of understanding the movement of red blood cells (RBCs) is at the heart of hemorheology. It has thus motivated an extensive body of experimental and numerical works, which showed that RBCs display a rich dynamical behavior in pure shear flow. However, a clear physical understanding of the coupling between cell orientation, membrane deformations, and membrane circulation is still not emerging, notably due to the lack of a comprehensive and tractable model to serve as the theoretical foundation for data analysis. Here, we propose a low-order model which, combined with detailed simulations and existing experimental data, demonstrates how membrane in-plane deformations and elasticity are the essential ingredients responsible for RBC dynamics at low shear stresses. Our approach demonstrates that out-of-plane deformations and fluid inertia are not necessary to explain the RBC dynamics and underlines the importance of the membrane stress-free shape. By reproducing all the details of known RBC dynamics in shear flow, our low-order model provides a single framework to understand the full dynamics of RBCs at low shear stresses.

The effect of insoluble surfactants on the dynamics of a drop immersed in another liquid has been numerically investigated. The interface is captured by means of the Level-Set method, and the evolution of the surfactant concentration $\mathrm{\Gamma }$ is solved along the deformable interface. The Marangoni stress resulting from tangential gradients of $\mathrm{\Gamma }$ has been implemented in the Ghost Fluid method, allowing one to compute the viscous-stress jump at the interface. The numerical model is first evaluated in the case of an oscillating droplet at mode 2. Numerical results accurately reproduce the shape-oscillation dynamics and demonstrate that the presence of surfactants has a strong impact on the damping rate. This effect, however, does not evolve monotonically with $\mathrm{\Gamma }$ but rather follows the evolution of the maximal value of the gradient of $\mathrm{\Gamma }$ that develops over the drop surface. The case of rising spherical droplets is next considered, where the distribution of surfactant at steady state results from the balance between tangential advection towards the rear of the droplet and the upward Marangoni flux. It is shown that the droplet velocity matches that of a solid particle, although a significant part of the interface is still surfactant free (around 30%). The gradient of $\mathrm{\Gamma }$ induced by the rising motion does not evolve monotonically with $\mathrm{\Gamma }$ as a result of the competition between Marangoni stress and the shear stress in the external boundary layer. Finally, the study of the case combining shape oscillations and rising motion shows that the rising motion does not influence the oscillation dynamics in the limit of low Weber number. The particular case of a droplet oscillating as a clean droplet (no change of eigenmodes) and rising as a fully contaminated droplet could be exhibited, in agreement with previous experimental observations.

Deformation of flexible vesicles suspended in a fluid medium due to an applied electric field can provide valuable insight into deformation dynamics at a very small scale. In an electric field, the response of the vesicle membrane is strongly influenced by the conductivity of surrounding fluid, vesicle size, and shape, and the magnitude of applied field. We studied the electrodeformation of vesicles immersed in a fluid media under a dc electric field. An immersed interface method is used to solve the electric field over the domain with conductive or nonconductive vesicles while an immersed boundary method is employed to solve fluid flow, fluid-solid interaction, membrane mechanics, and vesicle deformation. Initial force analysis on the membrane surface reveals almost linear influence of vesicle size, but the vesicle size does not affect the long-term deformation which is consistent with experimental evidence. Highly nonlinear effects of the applied field as well as the conductivity ratios inside and outside of the vesicle are observed. Results also point toward an early linear deformation regime followed by an equilibrium stage for the membranes. Modeling results suggest that electrodeforming vesicles can create unique external flows for different conductivity ratios. Moreover, significant influence of the initial aspect ratio of the vesicle on the force distribution is observed across a range of conductivity ratios.

We study a generalized Navier-Stokes model describing the coherent thin-film flows in semiconcentrated suspensions of ATP-driven microtubules or swimming cells that are enclosed by a moving ring-shaped container. Considering Stokes' second problem, which concerns the motion of an oscillating boundary, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. In the case of a freely suspended fluid-container system that is isolated from external forces or torques, active-fluid stresses can induce large fluctuations in the container's angular momentum if the confinement radius matches certain multiples of the intrinsic vortex size of the active suspension. This effect could be utilized to transform collective microscopic swimmer activity into macroscopic motion in optimally tuned geometries.

We study experimentally by means of atomic force microscopy (AFM) the jump-to-contact instability between two droplets in air, with radii ranging between 0.7 and $74\mu \mathrm{m}$. This instability which occurs at the nanoscale is responsible for droplet coalescence. The AFM experiments were conducted in contact and frequency-modulation modes where the interaction force and the frequency shift are monitored while the two droplet interfaces approach each other. The critical distance $d_{\min }$ at which the jump to contact takes place is determined by fitting the experimental curves by the theoretical expressions for the force and the frequency shift. The results point out the existence of two regimes. For submicrometer droplets, $d_{\min }$ scales as ${(H{R}_{\text{eq}}/\gamma )}^{1/3}$ where $R_{\text{eq}}$ is the equivalent droplet radius, $H$ the Hamaker constant, and $\gamma$ the surface tension of the liquid. For larger droplets, $d_{\min }$ no longer depends on the droplet size and scales as ${(H/\gamma )}^{1/2}$. This second scaling is the one that controls droplet coalescence in most situations.