A surface of a thin viscoelastic film forms spinodal patterns when brought in contact proximity of another surface due to the dominance of destabilizing intermolecular interaction over the stabilizing elastic and surface tension forces. In this study, we theoretically explore such contact instabilities of a thin viscoelastic film, wherein the patterns generated on the surface of the film is developed with the help of a contactor decorated with periodic physical, chemical, and physicochemical features on the surface. The nonlinear analysis shown here considers the movement of the patterned contactor during the adhesion and debonding processes, which is unlike most of the previous works where the contactor is considered to be stationary. The simulations reveal that the amplitude and periodicity of the patterns decorated on the contactor together with the contactor speed can be the key parameters to stimulate pattern formation on the film surface alongside causing changeover of the various modes of debonding of the surfaces. In particular, the ratio of the elastic to viscous compliances of the film is found to play a critical role to stimulate the changeover of the modes from catastrophic to peeling or coalescence. The study uncovers that a higher wettability contrast across the patterned contactor leads to the catastrophic collapse of the patterns decorated on the film surface when the contactor debonds at a moderate speed. In comparison, a moderately high wettability contrast alongside a faster withdrawal speed of the contactor results in the gradual peeling of columns during the debonding cycle. Remarkably, a higher withdrawal speed of the contactor from the film-proximity can increase the aspect ratio of the patterns fabricated on the film surface to about fourfold during the peeling mode of debonding. The results show the importance of the usage of patterned contactors, their controlled movement, and extent of elastic to viscous compliance ratio of the film for the improvement of the aspect ratio of the patterns developed using the elastic contact lithography of the thin viscoelastic films. The simulations also reveal the possibilities of the fabrication of biomimetic micro- or nanostructures such as columns, holes, cavities, or a combination of these patterns with large-area ordering employing the patterned contactors. A few example cases are shown to highlight the capacity of the proposed methodology for the fabrication of higher aspect ratio hierarchical micro- or nanostructures.

We demonstrate experimentally that the long-range hydrodynamic interactions in an incompressible quasi-two-dimensional isotropic fluid result in an anisotropic viscous drag acting on elongated particles. The anisotropy of the drag is increasing with increasing ratio of the particle length to the hydrodynamic scale given by the Saffman-Delbrück length. The microrheology data for translational and rotational drags collected over three orders of magnitude of the effective particle length demonstrate the validity of the current theoretical approaches to the hydrodynamics in restricted geometry. The results also demonstrate crossovers between the hydrodynamical regimes determined by the characteristic length scales.

We consider dense, inclined flows of spheres in which the particles translate in layers, whose existence may be promoted by the presence of a rigid base and/or sidewalls. We imagine that in such flows a sphere of a layer is forced up the back of a sphere of the layer below, lifting a column of spheres above it, and then falls down the front of the lower sphere, until it bumps against the preceding sphere of the lower layer. We calculate the forces and rate of momentum transfer associated with this process of rub, lift, fall, and bump and determine a relation between the ratio of shear stress to normal stress and the rate of strain that may be integrated to obtain the velocity profile. The fall of a sphere and that of the column above it results in a linear increase in the magnitude of the velocity fluctuations with distance from the base of the flow. We compare the predictions of the model with measured profiles of velocity and granular temperature in several different dense, inclined flows.

This paper investigates the coupled motion between the dynamics of $N$ vessels coupled together in a one-dimensional array by springs and the motion of the inviscid fluid sloshing within each vessel. We develop a fully nonlinear model for the system relative to a moving frame such that the fluid in each vessel is governed by the Euler equations and the motion of each vessel is modeled by a forced spring equation. By considering a linearization of the model, the characteristic equation for the natural frequencies of the system is derived and analyzed for a variety of nondimensional parameter regimes. It is found that the problem can exhibit a variety of resonance situations from the $1\text{:}1$ resonance to $(N+1)$-fold $1\text{:}\cdots \text{:}1$ resonance, as well as more general $r\text{:}s\text{:}\cdots \text{:}t$ resonances for natural numbers $r,s,t$. This paper focuses in particular on determining the existence of regions of parameter space where the $(N+1)$-fold $1\text{:}\cdots \text{:}1$ resonance can be found.

Despite the large number of existing studies of viscous flows in rotating Hele-Shaw cells, most investigations analyze rotational motion with a constant angular velocity, under vanishing Reynolds number conditions in which inertial effects can be neglected. In this work, we examine the linear and weakly nonlinear dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell, considering the action of a time-dependent angular velocity, and taking into account the contribution of inertia. By using a generalized Darcy's law, we derive a second-order mode-coupling equation which describes the time evolution of the interfacial perturbation amplitudes. For arbitrary values of viscosity and density ratios, and for a range of values of a rotational Reynolds number, we investigate how the time-dependent angular velocity and inertia affect the important finger competition events that traditionally arise in rotating Hele-Shaw flows.

A detailed comparison is made of two different methods for simulating vibrational relaxation behind a strong shock wave in molecular oxygen. The first approach is phenomenological and makes a number of strong assumptions in using an overall vibrational energy relaxation equation. The second approach resolves all of the quantized vibrational energy states using temperature-dependent state-to-state transition rates. Comparisons with experimental measurements indicate that the state-resolved approach is more accurate. The assumptions made in the phenomenological model are assessed in detail by using the state-resolved approach. It is determined that all of the assumptions made in the simpler model are violated directly behind a strong shock wave. A parameter based on the effects of multi-quantum transitions is proposed for predicting when the more detailed modeling approach must be used in compressed non-reacting flows and is found to be effective.

Recent findings [X. Wu et al., Proc. Natl. Acad. Sci. USA 114, E5292 (2017)] reinforce earlier assertions [e.g., R. Falco, Philos. Trans. R. Soc. London A 336, 103 (1991)] that the sublayer pocket motions play a distinctly important role in near-wall dynamics. In the present study, smoke visualization and axial velocity measurements are combined in order to establish the scaling behavior of pocket events in the viscous sublayer of the turbulent boundary layer. In doing so, an identical analysis methodology is employed over an extensive range of friction Reynolds numbers $388\le {\delta }^{+}\le 2.2\times {10}^5$. Both the pocket width $W$ and time interval between pocket events $T$ increase logarithmically with Reynolds number when normalized by viscous units. Normalization of $W$ and $T$ by the Taylor microscales evaluated at a wall-normal location of about 100 viscous units, however, appears to successfully remove this Reynolds-number dependence. The present results are discussed in the context of motion formation owing to the three dimensionalization of the near-wall vorticity field and, concomitantly, the recurring perturbation of the viscous sublayer.

The classic problem reported by Taylor [Philos. Mag. 46, 671 (1923)] on the viscous decay of a planar vortex grid is here extended in three ways. First we present solutions for the vortex grid modulated in the direction normal to the grid. Second, we find a solution for viscous decay of vortices on a disk and its modulation along the axial direction. Finally, we provide solutions for the viscous decay of vortices on a cylindrical surface and its modulation along the radial direction. The exponentially decaying vortices in these modulated vortex systems represent exact unsteady three-dimensional solutions of the Navier-Stokes equations.

Outflow of granular materials from silos is a remarkably complex physical phenomenon that has been extensively studied with simple objects like monodisperse hard disks in two dimensions (2D) and hard spheres in 2D and 3D. For those materials, empirical equations were found that describe the discharge characteristics. Softness adds qualitatively new features to the dynamics and to the character of the flow. We report a study of the outflow of soft, practically frictionless hydrogel spheres from a quasi-2D bin. Prominent features are intermittent clogs, peculiar flow fields in the container, and a pronounced dependence of the flow rate and clogging statistics on the container fill height. The latter is a consequence of the ineffectiveness of Janssen's law: the pressure at the bottom of a bin containing hydrogel spheres grows linearly with the fill height.

Droplet-based microfluidics turned out to be an efficient and adjustable platform for digital analysis, encapsulation of cells, drug formulation, and polymerase chain reaction. Typically, for most biomedical applications, the handling of complex, non-Newtonian fluids is involved, e.g., synovial and salivary fluids, collagen, and gel scaffolds. In this study, we investigate the problem of droplet formation occurring in a microfluidic T-shaped junction, when the continuous phase is made of shear thinning liquids. At first, we review in detail the breakup process, providing extensive, side-by-side comparisons between Newtonian and non-Newtonian liquids over unexplored ranges of flow conditions and viscous responses. The non-Newtonian liquid carrying the droplets is made of Xanthan solutions, a stiff, rodlike polysaccharide displaying a marked shear thinning rheology. By defining an effective Capillary number, a simple yet effective methodology is used to account for the shear-dependent viscous response occurring at the breakup. The droplet size can be predicted over a wide range of flow conditions simply by knowing the rheology of the bulk continuous phase. Experimental results are complemented with numerical simulations of purely shear thinning fluids using lattice Boltzmann models. The good agreement between the experimental and numerical data confirm the validity of the proposed rescaling with the effective Capillary number.

Acoustic streaming designates the ability to drive quasisteady flows by acoustic propagation in dissipative fluids and results from an acoustohydrodynamics coupling. It is a noninvasive way of putting a fluid into motion using the volumetric acoustic force and can be used for different applications such as mixing purposes. We present an experimental investigation of a kind of square flow driven by acoustic streaming, with the use of beam reflections, in a water tank. Time-resolved experiments using particle image velocimetry have been performed to investigate the velocity field in the reference plane of the experiments for six powers: 0.5, 1, 2, 4, 6, and 8 W. The evolution of the flow regime from almost steady to strongly unsteady states is characterized using different tools: the plot of time-averaged and instantaneous velocity fields, the calculation of presence density maps for vortex positions and for the maximal velocity and vorticity crest lines, and the use of spatiotemporal maps of the waving observed on the jets created by acoustic streaming. A transition is observed between two regimes at moderate and high acoustic forcing.

We scrutinize the statistical characteristics of liquid films flowing over an inclined planar surface based on film height and velocity measurements that are recovered simultaneously by application of planar laser-induced fluorescence (PLIF) and particle tracking velocimetry (PTV), respectively. Our experiments are complemented by direct numerical simulations (DNSs) of liquid films simulated for different conditions so as to expand the parameter space of our investigation. Our statistical analysis builds upon a Reynolds-like decomposition of the time-varying flow rate that was presented in our previous research effort on falling films in [Charogiannis et al., Phys. Rev. Fluids 2, 014002 (2017)], and which reveals that the dimensionless ratio of the unsteady term to the mean flow rate increases linearly with the product of the coefficients of variation of the film height and bulk velocity, as well as with the ratio of the Nusselt height to the mean film height, both at the same upstream PLIF/PTV measurement location. Based on relations that are derived to describe these results, a methodology for predicting the mass-transfer capability (through the mean and standard deviation of the bulk flow speed) of these flows is developed in terms of the mean and standard deviation of the film thickness and the mean flow rate, which are considerably easier to obtain experimentally than velocity profiles. The errors associated with these predictions are estimated at $\approx 1.5$% and 8% respectively in the experiments and at $<1$% and $<2$% respectively in the DNSs. Beyond the generation of these relations for the prediction of important film flow characteristics based on simple flow information, the data provided can be used to design improved heat- and mass-transfer equipment reactors or other process operation units which exploit film flows, but also to develop and validate multiphase flow models in other physical and technological settings.

We present a minimal system for generating flow at low Reynolds number by oscillating a pair of rigid rods in silicone oil. Experiments show that oscillating them in phase produces no net flow, but a phase difference alone can generate rich flow fields. Tracer particles follow complex trajectory patterns consisting of small orbital movements every cycle and then drifting or swirling in larger regions after many cycles. Observations are consistent with simulations performed using the method of regularized Stokeslets, which reveal complex three-dimensional flow structures emerging from simple oscillatory actuation. Our findings reveal the basic underlying flow structure around oscillatory protrusions such as hairs and legs as commonly featured on living and nonliving bodies.

We present a detailed series of experiments using spatially resolved flow velocimetry to examine the flow of Newtonian fluids through rectangular channels with one wavy surface of wave number $k$. The glass channels are fabricated by the method of selective laser-induced etching, which allows them to be made with a high (quasi-2D) aspect ratio (width/depth, $w/2d=5)$ and with an accurate wave profile of small relative amplitude $\left(A/d=0.05,A<k\right)$. Following the prior theoretical work for plane Couette flow over a wavy surface [Charru and Hinch, J. Fluid Mech. 414, 195 (2000)], we examine the influence of two dimensionless parameters (the normalized channel half-depth $\alpha =kd$ and the viscous length scale $\theta )$ on the penetration depth $\mathcal{P}$ of the perturbations that the wavy surface induces to the Poiseuille base flow. The asymptotic analysis by Charru and Hinch predicted three regimes of behavior classified as “shallow viscous” $\left(\mathcal{P}\approx \alpha \right)$, “deep viscous” $\left(\mathcal{P}\approx 1\right)$, and “inviscid” $\left(\mathcal{P}\sim \theta \right)$. All three regimes are here verified experimentally. Minor differences in details of the “phase diagram” for the flow regimes in $\alpha \text{−}\theta$ parameter space observed between Poiseuille and plane Couette flow are attributed to the contrasting boundary conditions in the different flow configurations. Our experimental results also compare favorably to results from linear theory for a Poiseuille base flow and thus establish a detailed experimental complement to the theory.

Film flow along an inclined, solid substrate featuring periodic rectangular trenches may either completely wet the trench floor (Wenzel state) or get pinned on the entrance and exit corners of the trench (Cassie state) or assume other configurations in between these two extremes. Such intermediate configurations are examined in the present study. They are bounded by a second gas-liquid interface inside the trench, which adheres to its walls forming two three-phase contact lines, and encloses a different amount of air under different physical conditions. The Galerkin finite-element method is used to solve the Navier-Stokes equations in a physical domain, which is adaptively remeshed. Multiple steady solutions, connected by turning points and transcritical bifurcations as well as isolated solution branches, are revealed by pseudo-arc-length continuation. Two possible configurations of a single air inclusion inside the trench are examined: the inclusion either surrounds the upstream convex corner or is attached to the upstream trench wall. The penetration of the liquid inside the trench is enhanced primarily by increasing either the wettability of the substrate or capillary over viscous forces or by decreasing the flow rate. Flow hysteresis may occur when the liquid wetting of the upstream wall decreases abruptly, leading to drastically different flow patterns for the same parameter values. The interplay of inertia, viscous, gravity, and capillary forces along with substrate wettability determines the volume of the air encapsulated in the trench and the extent of deformation of the outer free surface.

We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of high-resolution direct numerical simulations in a unique setting: a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers $\text{Pr}$ that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including $\text{Pr}=0.021$ for liquid mercury or gallium and $\text{Pr}=0.005$ for liquid sodium. In this parameter range of RBC, inertial effects cause a dominating turbulent momentum transport that is in line with highly intermittent fluid turbulence both in the bulk and in the boundary layers and thus should be able to trigger a transition to the fully turbulent boundary layers of the ultimate regime of convection for higher Rayleigh number. Second, we predict the ranges of Rayleigh numbers for which the viscous boundary layer will transition to turbulence and the flow as a whole will cross over into the ultimate regime. These transition ranges are obtained by extrapolation from our simulation data. The extrapolation methods are based on the large-scale properties of the velocity profile. Two of the three methods predict similar ranges for the transition to ultimate convection when their uncertainties are taken into account. All three extrapolation methods indicate that the range of critical Rayleigh numbers ${\text{Ra}}_c$ is shifted to smaller magnitudes as the Prandtl number becomes smaller.

Analytical expressions are derived for the first-order correction to the effective slip length of a weakly shear-thinning Carreau-Yasuda fluid in both longitudinal and transverse semi-infinite shear flow over a unidirectional superhydrophobic surface of flat no-shear slots. The formulas, which are derived using suitably generalized forms of the standard reciprocal theorem for Stokes flow, are given by explicit integrals which require only numerical quadrature for their evaluation. For both longitudinal and transverse flow we find that for a given no-shear fraction of the superhydrophobic surface and a given power-law index characterizing the Carreau-Yasuda fluid, there is a critical imposed strain rate of the shear at which the enhancement of effective slip is maximal. The theoretical results are qualitatively consistent with recent numerical work by other authors for the transverse case.

We examine the spatial field of orientations of slender fibers that are advected by a two-dimensional fluid flow. The orientation field of these passive directors are important in a wide range of industrial and geophysical flows. We introduce emergent scar lines as the dominant coherent structures in the orientation field of passive directors in chaotic flows. Previous work has identified the existence of scar lines where the orientation rotates by $\pi$ over short distances, but the lines that were identified disappeared as time progressed. As a result, earlier work focused on topological singularities in the orientation field, which we find to play a negligible role at long times. We use the standard map as a simple time-periodic two-dimensional flow that produces Lagrangian chaos. This class of flows produces persistent patterns in passive scalar advection and we find that a different kind of persistent pattern develops in the passive director orientation field. We identify the mechanism by which emergent scar lines grow to dominate these patterns at long times in complex flows. Emergent scar lines form where the recent stretching of the fluid element is perpendicular to earlier stretching. Thus these scar lines can be labeled by their age, defined as the time since their stretching reached a maximum.

We investigated the transient relaxation of a discontinuous shear thickening (DST) suspension of cornstarch in water. We performed two types of relaxation experiments starting from a steady shear in a parallel-plate rheometer, followed either by stopping the top plate rotation and measuring the transient torque relaxation or by removing the torque on the plate and measuring the transient rotation of the tool. We found that at low effective weight fraction ${\varphi }_{\mathrm{eff}}<58.8\pm 0.4\%$, the suspensions exhibited a relaxation behavior consistent with a generalized Newtonian fluid in which the relaxation is determined by the steady-state relationship between shear stress and shear rate. However, for larger weight fraction $58.8\%<{\varphi }_{\mathrm{eff}}<61.0\%$, near the liquid-solid transition ${\varphi }_c=61.0\pm 0.7\%$, we found relaxation behaviors qualitatively and quantitatively different from the generalized Newtonian model. The regime where the relaxation was inconsistent with the generalized Newtonian model was the same where we found positive normal stress during relaxation, and in some cases we found an oscillatory response, suggestive of a solidlike structure consisting of a system-spanning contact network of particles. This regime also corresponds to the same packing fraction range where we consistently found discontinuous shear thickening in rate-controlled, steady-state measurements. The relaxation time in this range scales with the inverse of the critical shear rate at the onset of shear thickening, which may correspond to a contact relaxation time for nearby particles in the structure to flow away from each other. In this range, the relaxation time was the same in both stress- and rate-controlled relaxation experiments, indicating the relaxation time is more intrinsic than an effective viscosity in this range and is needed in addition to the steady-state viscosity function to describe transient flows. The discrepancy between the measured relaxation times and the generalized Newtonian prediction was found to be as large as four orders of magnitude, and extrapolations diverge in the limit as ${\varphi }_{\mathrm{eff}}\to {\varphi }_c$ as the generalized Newtonian prediction approaches 0. This quantitative discrepancy indicates the relaxation is not controlled by the dissipative terms in the constitutive relation. At the highest weight fractions, the relaxation time scales were measured to be on the order of $\sim 1$ s. The fact that this time scale is resolvable by the naked eye may be important to understanding some of the dynamic phenomenon commonly observed in cornstarch and water suspensions. We also showed that using the critical shear rate ${\dot{\gamma }}_c$ at the onset of shear thickening to characterize the effective weight fraction ${\varphi }_{\mathrm{eff}}$ can more precisely characterize material properties near the critical point ${\varphi }_c$, allowing us to resolve this transition so close to ${\varphi }_c$. This conversion to ${\varphi }_{\mathrm{eff}}$ can also be used to compare experiments done in other laboratories or under different temperature and humidity conditions on a consistent ${\varphi }_{\mathrm{eff}}$ scale at our reference temperature and humidity environment.

On low-adhesion surfaces, coalescing droplets can spontaneously jump off, known as coalescence-induced droplet jumping. It is observed on a variety of synthetic and natural superhydrophobic surfaces, and gives rise to a range of applications, such as self-cleaning condensers, anti-icing coatings, and thermal diodes. Through three-dimensional simulations, this paper demonstrates the fluid dynamics of droplet jumping upon binary unequal-sized-droplet coalescence. Parametric studies show the influence of droplet mismatch, viscosity, and contact angle on jumping velocities, where liftoff regimes are defined on the basis of Ohnesorge number and droplet size ratio. Because of the strong asymmetric flow behavior, the well-known small conversion efficiency for equal-sized-droplet jumping, where around $6\%$ of the released surface energy is convertible into translational kinetic energy, is further reduced for unequal-sized-droplet jumping. The findings offer insights into their fluid dynamics and give a starting point for further modeling of dropwise condensation on superhydrophobic surfaces.