We address the problem of steady laminar flow of a shear-thinning fluid in a rectangular duct, which is encountered in many systems, particularly in microfluidic and biomedical devices. However, an exact solution for the flow of non-Newtonian fluids that considers a realistic shear-thinning rheological behavior is not available in the literature. In this paper, an accurate solution for the case of Carreau fluid is obtained and investigated numerically. The numerical solution allows us to analyze the effects of the fluid rheology and the aspect ratio of the rectangular duct on the velocity field and pressure gradient that drives the flow. The relationship between the pressure gradient and the Carreau number is found to follow the rheological curve of the shear-thinning fluid. The analysis shows that the fluid rheology and the aspect ratio have independent contributions to the integral flow characteristics. Moreover, separate consideration of these contributions allows us to arrive at universal scaling and general formulas for the pressure gradient and friction factor for various rheological parameters of the fluid and aspect ratios of rectangular ducts.

Turbulent convection at rough surfaces covers a large variety of heat transfer processes in nature and engineering. However, in particular the transport of heat near the rough surface is still not well understood. We present measurements of the near-wall temperature field in turbulent Rayleigh-Bénard convection with rough walls, and for reference also with smooth walls. The measurements have been undertaken in a large-scale convection experiment, the “Barrel of Ilmenau.” Our experiments covered Rayleigh numbers in a domain $5.4\times {10}^9<\text{Ra}<9.6\times {10}^{11}$ and two different aspect ratios $\mathrm{\Gamma }=1.1$ and 2.9. The working medium was air with a Prandtl number $\text{Pr}=0.7$. Using very tiny micro-thermistors of $150\mu \mathrm{m}$ diameter and $350\mu \mathrm{m}$ length, we conducted highly resolved measurements of the temperature field near the heated bottom plate. Our measurements show that, as was already observed in high Prandtl number fluids, the ratio between the thickness of the thermal boundary layer ${\delta }_{\text{th}}=H/\left(2\text{Nu}\right)$ and the roughness height $h$ plays a crucial role for the near-wall temperature field, and thus for the convective heat transport. If ${\delta }_{\text{th}}/h>1$, the temperature field at the rough surface does not differ from that at the smooth one. If this ratio falls below ${\delta }_{\text{th}}/h=1$, both the mean temperature field and the temperature fluctuations start to change and to differ from that at the smooth surface. These variations are virtually independent of the Rayleigh number in the parameter domain we investigated.

A liquid film coating a cylindrical substrate is unstable to interfacial disturbances governed by Rayleigh-plateau instability. These initial disturbances grow in time and, beyond saturation, develop into a train of droplets of equal amplitude that move downstream at the same velocity. The traveling wave profiles, formed by a thermoviscous fluid as it flows down the exterior of a nonisothermal vertical cylinder, are computed as a function of various parameters. Further, this study investigates the stability behavior of these traveling waves. An unstable film leads to the formation of an axially asymmetric pattern. The influence of the thermoviscous nature of the fluid, along with the Biot number, Marangoni number, and Bond number, has been investigated. Linear stability analysis is performed by perturbing the axisymmetric traveling wave solution in the azimuthal direction. It is shown that while a gravity mode exists at small wave numbers, a thermocapillary mode exists at large wave numbers. The streamline patterns are shown to be consistent with the presence of the thermocapillary mode. The nonlinear analysis shows that the chosen pattern of instability does not correspond to the largest growth rate but is governed by the wavelength conforming to the periodic confinement in the azimuthal direction. An interesting pattern evolves in the presence of more than one such conforming wavelength.

Observations from various missions to Jupiter and Saturn showed that temperature of heavy-ion plasma contained in expanding discs around planets is increasing with radial distance. Magnetospheres of Jovian planets are successfully heating ions in a plasma fluid and magnetic field system. Turbulent fluctuations were suggested as a plasma heating mechanism. Suitability of turbulence to heat heavy-ion dense plasma and the source of turbulent fluctuations in Jupiter's magnetosphere is investigated. Relation between ion velocity variations and magnetic field fluctuations is derived from magnetohydrodynamic principles. This is then used to obtain turbulent power density contained in plasma fluid and magnetic field. Energy cascade in magnetohydrodynamic and kinetic subranges in different mediums is demonstrated. Measurements from magnetometer instrument on Juno mission to Jupiter are used to observe turbulent fluctuations in the magnetic field and to infer dynamics in plasma fluid. Extensive radial map of turbulent power density in Jupiter's magnetosphere inside and outside of the plasma disk is presented.

Control over emulsion stability and phase separation is important for industries such as oil and gas, where it is critical to remove all the oil content from oily wastewater before discharging it into the environment or, conversely, to remove small droplets of water from oil prior to upgrading. Prior work has qualitatively shown that it may be possible for crude oil emulsions to be highly stable at rest and then rapidly destabilized by shearing interactions between droplets due to a phenomenon that we coin shear-triggered coalescence in this paper. In this paper, we provide quantitative evidence of this phenomenon using a cantilevered-capillary force apparatus to precisely manipulate two liquid droplets within another immiscible liquid (i.e., mineral oil in water or water in mineral oil). We first show that droplets in surfactant solutions clearly do not exhibit shear-triggered coalescence because they have the same probability of coalescing when a head-on collision of the droplets is compared to a shearing collision. In contrast, we show that when droplets have spherical Janus microparticles adsorbed onto the interface, the droplets undergoing shearing collisions coalesce faster than those undergoing a head-on collision. Similarly, we show that when rod-shaped nanoparticles (cellulose nanocrystals) are adsorbed onto the interface, with an intermediate salt concentration in the suspending phase, that shear-triggered coalescence occurs in dramatic fashion. We offer mechanistic explanations for why shear-triggered coalescence is possible in these two cases, but is not observed in other cases such as with disklike microparticles, non-Janus spherical microparticles, or rodlike nanoparticles without electrostatic screening or with strong electrostatic screening.

Liquid nanofilms are ubiquitous in nature and technology, and their equilibrium and out-of-equilibrium dynamics are key to a multitude of phenomena and processes. We numerically study the evolution and rupture of viscous nanometric films, incorporating the effects of surface tension, van der Waals forces, thermal fluctuations, and viscous shear. We show that thermal fluctuations create perturbations that can trigger film rupture, but they do not significantly affect the growth rate of the perturbations. The film rupture time can be predicted from a linear stability analysis of the governing thin film equation, by considering the most unstable wavelength and the thermal roughness. Furthermore, applying a sufficiently large unidirectional shear can stabilize large perturbations, creating a finite-amplitude traveling wave instead of film rupture. In three dimensions, unidirectional shear does not inhibit rupture, as perturbations are not suppressed in the direction perpendicular to the applied shear. However, if the direction of shear varies in time, then the growth of large perturbations is prevented in all directions, and rupture can be impeded.

We show that, in the transitional regime of pulsatile pipe flow, at moderate-to-high amplitudes $0.5\lesssim A\lesssim 1$, the first long-lived turbulent structures are localized and take the form of the puffs and slugs observed in statistically steady pipe flow. We perform direct numerical simulations at many pulsation frequencies (Wo), amplitudes, and Reynolds number (Re) and observe different dynamics of puffs and slugs. At certain flow parameters we find, using a causal analysis, that puffs actively make use of linear instabilities in the laminar Sexl-Womersley (SW) profile to survive the pulsation. Using all these lessons learned, we extend a low-order model by Barkley et al. [Nature (London) 526, 550 (2015)] to reproduce these dynamics. We find a good agreement between the extended model and our numerical results in a broad parametric space of pulsation amplitudes $0.5\lesssim A\lesssim 1$, frequencies $\mathrm{Wo}\gtrsim 5$ and $2100\le \mathrm{Re}\le 3000$. With the help of our numerical results, causal analysis and model, we determine that turbulence production has two sources at these flow parameters: the mean shear as in statistically steady pipe flow and the instabilities of the instantaneous pulsatile mean profile.

For a flowing soap film with added surfactants, theoretically there exists symmetric elastic waves due to the elasticity of the soap film that originates from the surface tension change with the film surface area change. However, the symmetric elastic waves remain elusive from experimental observations due to the lack of approaches to stimulate such waves. Here, we propose a focused laser heating method to study the properties of liquid films under symmetric disturbances. The thermocapillary flows caused by the laser-induced Marangoni effect lead to symmetric disturbances in the film thickness without causing antisymmetric disturbances in the film shape. Thus, on flowing soap films with low surfactant concentrations, i.e., with appreciable elasticities, the laser-induced disturbances in the film thickness are propagated by the symmetric elastic waves, and the envelope of the wave fronts forms a shock wave starting from the laser heating point. Interestingly, on flowing soap films with high surfactant concentrations, i.e., vanishingly small elasticities, the laser-induced disturbances in the film thickness remain unchanged and flow with the film without propagating, similar to “laser engraving” on free liquid films.

Electrowetting is a technique that reversibly or irreversibly alters the wetting properties of a droplet on a hydrophobic substrate by applying an electrical field. In this paper, we studied electrowetting dynamics of sessile droplets on a hydrophobic substrate surrounded by viscous liquids. Through this study, we answered the following unanswered questions: the drop's transient response immediately after the actuation, the drop's retraction and resultant dynamics, and the effect of multiple wave actuation on the droplet transition. An overall energy balance approach is extended for analyzing the transient wetting dynamics of droplets from the initial position to the new equilibrium position in viscous media with appropriate governing parameters. The governing nondimensional parameters are the electrowetting number ($\eta$), the Roshko number ($\mathrm{Ro}$), the Ohnesorge number ($\mathrm{Oh}$), and the viscosity ratio (${\mu }_r$) between the droplet and the surrounding medium. This theoretical study, in corroboration with the experimental study, describes the transient evolution of the drop motion from the initial position to the new equilibrium position and predicts the shift from in-phase to out-of-phase drop response for the applied waves.

The flow past a clean spherical bubble translating steadily parallel to a no-slip wall in a stagnant fluid is studied numerically over a wide range of moderate-to-high Reynolds numbers. We focus on situations where the distance separating the bubble from the wall is smaller than the size of the bubble to explore the competition between viscous and inertial effects in the gap. More precisely, the range of the wall distance considered is $1.1\le L_{\text{R}}\le 2$ ($L_{\text{R}}$ being the distance from the bubble center to the wall normalized by the bubble radius), and that of the Reynolds number is $50\le \text{Re}\le 1000$ ($\text{Re}$ being based on the bubble diameter and the slip velocity). In contrast to predictions based on potential flow theory, the numerical results reveal that, when the gap is smaller than a critical value that depends on the Reynolds number, the transverse force starts to decrease with decreasing separation and may finally reverse, changing from attractive to repulsive. This effect is found to be due to the strong shear generated in the gap, which, combined with the local transverse gradient of the streamwise velocity, results in a system of two counterrotating streamwise vortices and, consequently, a shear-induced lift pointing away from the wall. Computational results together with available high-Reynolds-number theory provide empirical expressions for the drag and transverse forces in the steady-state limit. Then the competition between the various transverse forces on a bubble bouncing close to the wall is examined, based on previously measured data for bubble trajectory. The central role of the history effects due to the misalignment between the wake and the instantaneous angle of the bubble path is confirmed. Computational results also reveal that, depending on the initial separation, a freely moving bubble may either reach a stable equilibrium position close to the wall or depart from the wall up to infinity.

Viscoplastic fluids flow through a microfluidic channel having a built-in two-part cylinder inside, while the upstream and downstream parts of the cylinder bear the surface potential of the same sign but of different magnitudes. We consider the Herschel-Bulkley model in describing the rheology of the viscoplastic fluids considered in this analysis. Consistent with the finite element method, the modeling framework employed here considers the prevailing effect of fluid rheology, and geometrical configuration−modulated electroosmotic forcing while solving the transport equations governing the mixing dynamics. We demonstrate that electroosmotic forcing, induced from the topology-modulated electrical double-layer effect, upon interacting with the prevalent viscous force in the field, leads to the flow reversal in the region closer to the built-in cylinder, which in turn, gives rise to the formation of vortices therein. As seen, the shear-thinning nature of the viscoplastic fluid results in an enhancement of the recirculation velocity strength, albeit the inevitable yield stress of the fluid sparsely influences the onset of flow recirculation. By showing the impact of the geometrical parameter of the cylinder and viscoplastic effect (signifying the effect of yield stress) on the recirculation strength, we show that the developed vortices in the pathway promote mixing of the constituent fluids nontrivially. Also, the characteristic time for shear-induced binary aggregation that illustrates the underlying mixing of fluids containing biomolecules, such as proteins and DNAs, is calculated based on the maximum strain rate. It is seen that cylinder radius and flow behavior index strongly affect the shear-induced binary aggregation kinetics and the associated probability density distribution of particles, while the yield stress has a negligible impact on the same.

When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. Contrary to this intuition, due to thermal Marangoni contraction, the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. We describe and quantify this self-propulsion of the volatile drop. It arises due to spontaneous symmetry breaking of thermal Marangoni convection, which is induced by the nonuniform evaporation of the droplet. Using infrared imaging, we reveal the characteristic interfacial flow patterns associated with Marangoni convection in the evaporating drop. A scaling relation describes the correlation between the moving velocity of the drop and the apparent contact angle, both of which increase with the substrate temperature.

We present a length-scale-based rheology for dense sheared particle suspensions as they transition from inertial- to viscous-dominated. We derive a length-scale ratio using straightforward physics-based considerations for a particle subjected to pressure and drag forces. In doing so, we demonstrate that an appropriately chosen length-scale ratio intrinsically provides a consistent relationship between normal stress and system proximity to its “jammed” or solidlike state, even as a system transitions between inertial and viscous states, captured by a variable Stokes number.

We analyze the linear stability of viscoelastic channel flows, with velocity profiles that are asymmetric about the channel centerline, belonging to the one-parameter Couette-Poiseuille family (CPF). These flows are driven by a combination of an imposed pressure gradient and (tangential) wall motion. A particular member of this family, corresponding to a zero net volumetric flux, may be experimentally realized in a shallow lid-driven cavity flow configuration, as well as in the narrow-gap limit of the Taylor-Couette geometry with an obstruction at a fixed azimuthal angle (a narrow gap Taylor-Dean flow). Recent work by Khalid et al. [Phys. Rev. Lett. 127, 134502 (2021)] has shown, using the Oldroyd-B model, that plane Poiseuille flow with a symmetric velocity profile becomes unstable, even in the absence of inertia, to an elastic “center mode” with phase speed close to the base-state maximum. In contrast, viscoelastic plane Couette flow is linearly stable. The objective of this study is to determine parameter regimes where viscoelastic CPF, whose members include the two limiting flows above, is unstable in the inertialess limit. The dimensionless groups that govern stability are the Weissenberg number $W=\lambda U_{\text{avg}}/L$, the parameter $\alpha$ characterizing the relative importance of Couette ($\alpha =0$) and Poiseuille flow ($\alpha =1$) components, and the ratio of solvent to solution viscosities $\beta ={\mu }_s/\mu$. Here, $\lambda$ is the polymer relaxation time, $L$ the channel half-width and $U_{\text{avg}}$ the average speed; $\beta \in [0,1]$, and $\alpha \in (-\infty ,\infty )$ with $\alpha \to \pm \infty$ representing the unidirectional flow in a shallow lid-driven cavity. We show that, similar to plane Poiseuille flow, an elastic center-mode instability does indeed exist for the aforesaid family in the limit of ultra-dilute polymer solutions ($\beta \gtrsim 0.99$); the instability relies on the existence of a base-state maximum, implying its absence for CPF members with $\alpha \in (-0.5,0.25)$. Our results point to the potential relevance of the center-mode instability to viscoelastic Taylor-Dean flows and other curvilinear shear flow configurations.

Unstable or optimally growing perturbations of turbulent flows are often representative of the energy-containing coherent structures populating the flow, as for streaks in a turbulent channel. Within this framework, this work aims at studying the modal and nonmodal stability of stably stratified turbulent channel flow, assessing the influence of stratification while changing the friction Richardson number, ${\text{Ri}}_{\tau }$, at fixed friction Reynolds number, ${\text{Re}}_{\tau }$. When increasing the stratification of the flow, the energy gain for streamwise-independent perturbations at the outer peak increases by two orders of magnitude, and the spanwise wavenumber for which the energy gain peaks reaches values comparable to those reported in the direct numerical simulations of Garcia-Villalba and Del Alamo. At the same time, the value of the optimal gain for the inner peak slightly changes, corroborating the observations made through direct numerical simulation (DNS) about the fact that the wall cycle is not altered by the presence of stratification. Moreover, for nonzero values of the streamwise and spanwise wavenumbers, $\alpha$ and $\beta$, the energy gain curve has two peaks, one for shorter target times and $\alpha >\beta$, leading to a center-channel temperature peak, and another occurring for $\alpha <\beta$ at larger target times. In the former case, energy production is mostly linked to velocity production, whereas, in the latter case, the strongest term is that of temperature production, indicating that this mechanism is driven by the increase of the potential energy rather than the kinetic one, and it is intimately linked to the presence of stratification. For strong stratification, the optimal energy gain considerably extends towards higher values of $\alpha$, leading to energy amplifications reaching three orders of magnitudes for values of $\alpha$ up to 2. The associated optimal perturbations are characterized by temperature patches at the center channel, phase lagged by $\pi /2$ with the wall-normal velocity, similarly to gravity waves recovered in the DNS for sufficiently large stratification. However, for large values of $\beta$, we observe an increasing asymmetry in the optimal perturbations, probably due to the shielding effect of the core of the channel, as also observed in the DNS of Garcia-Villalba and Del Alamo.

Although continuum theories have been proven quite robust to describe confined fluid flow at molecular length scales, molecular dynamics (MD) simulations reveal mechanistic insights into the interfacial dissipation processes. Most MD simulations of confined fluids have used setups in which the lateral box size is not much larger than the gap height, thus breaking thin-film assumptions usually employed in continuum simulations. Here we explicitly probe the long-wavelength hydrodynamic correlations in confined simple fluids with MD and compare to gap-averaged continuum theories as typically applied in, e.g., lubrication. Relaxation times obtained from equilibrium fluctuations interpolate between the theoretical limits from bulk hydrodynamics and continuum formulations with increasing wavelength. We show how to exploit this characteristic transition to measure viscosity and slip length in confined systems simultaneously from equilibrium MD simulations. Moreover, the gap-averaged theory describes a geometry-induced dispersion relation that leads to overdamped sound relaxation at large wavelengths, which is confirmed by our MD simulations. Our results add to the understanding of transport processes under strong confinement and might be of technological relevance for the design of nanofluidic devices.

We present an experimental study of the aerodynamic forces on a thick and cambered airfoil at a high Reynolds number (Re) ($3.6\times {10}^6$), which is of direct relevance for wind turbine design. Unlike thin airfoils at low chord-based Reynolds numbers, no consistent description currently exists for the stall process on such airfoils. We consider two chordwise rows of instantaneous wall pressure measurements, taken simultaneously at two spanwise locations over a range of angles of attack. We show that around maximum lift conditions, a strong asymmetry is observed in the statistics of the normal force on each chord. In this range of angles of attacks, the pressure fluctuations are largest in the adverse pressure gradient region, and the fluctuation peak along the chord is systematically located directly upstream of the mean steady separation point, indicating intermittent flow separation. Moreover, the fluctuations are characterized by bistability in both space and time: For each spanwise location, large excursions of the local wall pressure between two different levels can be observed in time (jumps), and these excursions are highly anticorrelated between the two spanwise locations (spatial switches). The characteristic timescale for the switches is found to be well correlated with the amplitudes of the fluctuations. Application of proper orthogonal decomposition (POD) analysis to each row of sensors confirms that the flow separation is an inherently local, three-dimensional, and unsteady process that occurs in a continuous manner when the angle of attack increases. The correlation between the dominant POD mode amplitudes is found to be a good indicator of bistability. For all angles of attack, most of the fluctuations can be captured with the two most energetic POD modes. This suggests that force fluctuations near the maximal lift could be modelled by a low-order approach for monitoring and control purposes.

Many microswimmers propel themselves by rotating microcylindrical organelles such as flagella or cilia. These cylindrical organelles almost never live in free space, yet their motions in a confining geometry can be counterintuitive. For example, one of the intriguing yet classical results in this regard is that a rotating cylinder next to a plane wall does not generate any net force in Newtonian fluids and therefore does not translate. In this work we employ analytical and numerical tools to investigate the motions of microcylinders under prescribed torques in a confining geometry. We show that a cylinder pair can form four nontrivial hydrodynamic bound states depending on the relative position within the confinement. Our analysis shows that the distinct states are the results of competing effects of the hydrodynamic interactions within the cylinder pair and between the active cylinders and the confinement.

A vortex-induced vibration (VIV) test of a tensioned flexible pipe in oscillatory sheared flow was performed in an ocean basin. The model was $28.41\text{mm}$ in diameter and $3.88\text{m}$ in length. The test was performed on a rotating test rig to simulate oscillatory sheared flow conditions. One end of the test pipe is fixed, and one end is forced to harmonically oscillate to simulate oscillatory sheared flows with various combinations of amplitudes and periods, Keulegan-Carpenter (KC) numbers from 25 to 160, and five kinds of reduced velocities $V_r$ from 6 to 14. Fiber Bragg grating strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. The VIV response in the cross-flow direction is investigated. The results show that VIV under oscillatory sheared flow exhibits amplitude modulation and hysteresis phenomena. Compared with oscillatory uniform flow-induced VIV, the Strouhal number is smaller in oscillatory sheared flow-induced VIVs. The VIV developing process in oscillatory sheared flow is analyzed, and critical KC is proposed to describe the occurrence of modulated VIV under oscillatory sheared flow.