Dynamics Of Shear Flows Research Articles

Shear flow dynamics in vibrated granular materials: Analysis of viscosity transitions and non-Newtonian behaviors

In a continuous fluid, the presence of a velocity gradient perpendicular to the flow creates shear stress and shear rate between adjacent layers. The fluid's viscosity can be constant, depending only on temperature (Newtonian fluid), or vary with shear rate (non-Newtonian fluid). However, the viscosity characteristics of shear flows in discrete media, such as vibrated granular materials, remain insufficiently understood. This study experimentally investigated shear flows in vibrated granular media, exploring the relationship between shear stress, shear rate, and the impact of vibration conditions and particle number on granular viscosity. The findings indicate that the viscosity of sheared granular material transitions between dilatant and pseudoplastic non-Newtonian states with increasing vibration strength, shifts from pseudoplastic non-Newtonian fluid to Newtonian fluid with increasing vibration frequency, and remains consistently pseudoplastic non-Newtonian with increasing particle number. Two continuous non-Newtonian fluid models were utilized for comparison with our experimental results. Additionally, ascending curves of granular viscosity against granular temperature reveal gas-like flow characteristics in the sheared granular material, albeit with an abnormal descending viscosity–temperature relationship. These are attributed to volume expansion and oblique collisions in the vibrated granular medium. This study uncovers distinct viscosity properties in a discrete medium under shear flows, markedly different from those in continuous fluids, and highlights potential new applications for granular materials.

The role of shear flow collapse and enhanced turbulence spreading in edge cooling approaching the density limit

Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction fG=n¯/nG=n¯/(Ip/πa2) increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized E×B shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.

Numerical simulation of an extensible capsule using regularized Stokes kernels and overset finite differences

In this paper, we present a novel numerical scheme for simulating deformable and extensible capsules suspended in a Stokesian fluid. The main feature of our scheme is a partition-of-unity (POU) based representation of the surface that enables asymptotically faster computations compared to spherical-harmonics based representations. We use a boundary integral equation formulation to represent and discretize hydrodynamic interactions. The boundary integrals are weakly singular. We use the quadrature scheme based on the regularized Stokes kernels by Tlupova and Beale 2019 (given in [34]). We also use partition-of unity based finite differences that are required for the computation of interfacial forces. Given an N-point surface discretization, our numerical scheme has fourth-order accuracy and O(N) asymptotic complexity, which is an improvement over the O(N2log⁡N) complexity of a spherical harmonics based spectral scheme that uses product-rule quadratures by Veerapaneni et al. 2011 [36]. We use GPU acceleration and demonstrate the ability of our code to simulate the complex shapes with high resolution. We study capsules that resist shear and tension and their dynamics in shear and Poiseuille flows. We demonstrate the convergence of the scheme and compare with the state of the art.

Time-delayed characteristics of turbulence in pulsatile pipe flow

Direct numerical simulations are performed to study temporal variations of the wall shear stresses and flow dynamics in the turbulent pulsatile pipe flow. The mechanisms, responsible for the paradoxical phenomenon for which the amplitude of the oscillating wall shear stress in the turbulent flow is smaller than that in the laminar flow for the same pulsation conditions, are investigated. It is shown that the delayed response of turbulence in the buffer layer generates a large magnitude of the radial gradient of the Reynolds shear stress near the wall, which counteracts the effect of the oscillating pressure gradient on the change of the streamwise velocity and hence reduces the amplitude of the wall shear stress. Such a delayed response consists of two processes: the delayed development of near-wall streaks and the subsequent energy redistribution from the streamwise velocity fluctuation to the other two co-existing components. This is a dynamical manifestation of the viscoelasticity of turbulent eddies. As the frequency is reduced, the variation of the friction Reynolds number results in a phase-wise variation of the time scale and intensity of the turbulence response, causing the hysteresis of the wall shear stress. Such a phase asymmetry is amplified by the increase of the pulsation amplitude. An examination of the energy spectra reveals that the near-wall streaks are stretched in the streamwise direction during the acceleration phase, and then break up into small-scale structures in the deceleration phase, accompanied by the enhanced dissipation that transforms the turbulent kinetic energy into heat.

Variation of Shear Stresses and Flow Dynamics in Stented Patient Specific Carotid Bifurcation Model using Numerical Investigation

The carotid artery is a clinically important site in the human circulatory system as the consequences of its disease results in adverse outcomes like ischemic strokes, or death for too prolonged ischemia. Understanding the hemodynamics of this artery and its bifurcation are important. A method of treating the stenosis of this artery is Carotid Angioplasty and Stenting (CAS). This procedure results in a heavily modified hemodynamics or state of flow. To understand and predict this flow field modification Computational Fluid Dynamics (CFD) is an important computational tool. Further, the presence of a stent would affect hemodynamics. The aim of this work is to study these effects in patient-specific cases. The reconstructed patient-specific models will form the basis of the construction of the post-stenting carotid bifurcation models. A transient analysis was carried out to estimate the time-varying parameters in the fluid domains over a cardiac cycle as well as to gauge time average values over a cardiac cycle. Results are obtained for hemodynamic parameters, like wall shear stress, velocity, pressure, vorticity, and helicity, in both the prepared stenosed and stented geometries. It is seen that the stenting procedure leads to the renewal of the CCA to ICA flow path. But simultaneously the region in which the stent is present becomes a region of low TAWSS and contains areas of high OSI. These areas of low TAWSS and high OSI within the stented portions of the carotid bifurcations are indications for regions of possible restenosis. Therefore, the investigation demonstrates the likely region for future plaque growth. Further, the effects of widening of the lumen are also noted in comparison to the pre-stent cases

Reduced model for droplet dynamics in shear flows at finite capillary numbers

Droplet deformation at finite capillary numbers is accurately studied in shear flows via Immersed Boundary - Lattice Boltzmann (IB-LB) simulations. A reduced model is introduced to capture nonlinear effects in droplet deformation and orientation.

Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel

The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau–Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.

Ordered and disordered dynamics in inertialess stratified three-layer shear flows

Three-layer stratified shear flows provide an excellent opportunity to study the interaction between fluid-fluid interfaces. In this paper we explore this coupling by studying a pair of nonlinear evolution equations derived in the limit of strong surface tension. The addition of a third fluid, hence a second interface, destabilizes the linearized system, and we use a numerical approach to simulate the resulting disturbance growth. A range of nonlinear phenomena are subsequently observed which include stable traveling waves, droplet formation of the middle fluid, quasi-periodicity, and coarsening phenomena, as shown in the key image.

Plastic strain rate quantified from dislocation dynamics in dusty plasma shear flows.

Dynamics of dislocations and defects are investigated in 2D dusty plasma experiments with two counterpropagating flows. It is experimentally demonstrated that the Orowan equation is able to accurately determine the plastic strain rate from the motion of dislocations, well agreeing with the shear rate defined from the drift velocity gradient. For a higher shear rate, the studied system is in the liquidlike flow state, as a result, the determined shear rate from the Orowan equation deviates from its definition. The obtained probability distribution function of dislocations from the experiments clearly shows that the dislocation motion can be divided into the local and gliding ones. All findings above are further verified by the corresponding Langevin dynamical simulations with various levels of shear rates. The dislocation and defect analysis results from these simulations clearly indicate that the defect and dislocation dynamics in the sheared dusty plasmas clearly exhibit two stages as the shear rate increases.

Similar but Distinct Roles of Membrane and Interior Fluid Viscosities in Capsule Dynamics in Shear Flows.

The dynamics of biological capsules and red blood cells in shear flows has been studied extensively with experimental, analytical, and numerical methods. In particular, the effects of various parameters, including the shear rate or shear stress, membrane elasticity, capsule shape, and interior fluid viscosity, have been investigated carefully. The role of the membrane viscosity for capsule deformation dynamics has not been examined adequately. In previous studies, the so-called energy dissipation ratio has been used to account for the membrane viscosity effect by increasing the interior viscosity; however, the applicability and accuracy of this treatment have not been evaluated carefully. In this study, using the recently developed finite-difference scheme for immersed boundary simulations of viscoelastic membranes, we conduct comprehensive numerical simulations of the deformation processes of an originally spherical capsule in shear flows with various combinations of membrane and interior fluid viscosities. Our results show that the membrane and interior fluid viscosity have similar however different effects on the capsule deformation dynamics. While the capsule deformation decreases with both membrane and interior fluid viscosities, a typical decrease-then-increase variation is observed for the inclination angle as the membrane viscosity increases, instead of the monotonic decrease in the inclination angle with the interior fluid viscosity increase. Also, although both large membrane and interior fluid viscosity values can introduce oscillations in the capsule deformation and inclination, larger aptitudes and slow decay processes are noticed at larger membrane viscosities. The variations of other dynamic parameters of the capsule, including the circumference, average membrane velocity, and rotation frequency, are also analyzed, and an intuitive mechanism is proposed to relate the membrane velocity and rotation frequency to the capsule deformation and inclination angle. The simple mechanism is then applied to explain the spoon-like variation patterns for membrane velocity and rotation frequency observed in our results. Furthermore, we examine the validity of the energy dissipation ratio approach based on the mathematical functional dependence. Our results and analysis show that the dissipation ratio is a system and process dependent variable and it cannot be treated as a constant even for the same capsule. This research is valuable for a better understanding of the complex capsule dynamics in flows and also suggests that the membrane viscosity needs to be considered explicitly for accurate and reliable results in future studies.

The dynamics of stratified horizontal shear flows at low Péclet number

Abstract

On the statistical evolution of viscous vortex-gas free shear layers

The temporal vortex-gas free shear layer is a Hamiltonian system of N-point vortices in a singly-periodic domain relevant to the (large-scale) development of plane (3D Navier–Stokes) turbulent shear layers. It has been shown (Suryanarayanan et al., 2014) that there are three distinct temporal regimes in its evolution, including an intermediate self-similar regime (RII) with a universal constant spreading rate, and a final state of relative equilibrium. Here, we study the evolution of vortex-gas free shear layers affected by viscosity as simulated by the addition of a random walk component to the motion of the vortices (Chorin, 1973). We show that while the momentum thickness of the layer, θ, scales as t1∕2 in the first and final regimes for the viscous system, it grows as t1 in the intermediate Regime II (observed here for momentum thickness Reynolds numbers Reθ from 50 to over 5000 across different simulations), with the same universal growth rate dθ∕dtΔU=0.0166±0.0002 as in the inviscid case. This suggests that the non-equilibrium universality of Regime II is robust to small perturbations of the Hamiltonian, and that this result could have general consequences for systems with long-range interactions. We further find that, even under conditions where the viscous shear stress is not negligible, the Reynolds shear stress adjusts itself in such a way that their sum is a constant in Regime II and equal to the value of the latter in the inviscid case. The implications of this observation on the dynamics of turbulent shear flows are elaborated.

Critical velocity shear flow for triggering L-H transition and its parametric dependence in the HL-2A tokamak

The dynamics of shear flows and turbulence in the pedestal region during the L-H transition have been studied in the HL-2A tokamak. It has been shown that ion diamagnetic shear flow plays a key role in triggering the L-H transition. A critical velocity shear has been found for the L-H transition. Statistical results indicate that the velocity shear threshold is independent of the plasma density and the total heating power.

Regime transitions and energetics of sustained stratified shear flows

We describe the long-term dynamics of sustained stratified shear flows in the laboratory. The stratified inclined duct (SID) experiment sets up a two-layer exchange flow in an inclined duct connecting two reservoirs containing salt solutions of different densities. This flow is primarily characterised by two non-dimensional parameters: the tilt angle of the duct with respect to the horizontal, (a few degrees at most), and the Reynolds number , an input parameter based on the density difference driving the flow. The flow can be sustained with constant forcing over arbitrarily long times and exhibits a wealth of dynamical behaviours representative of geophysically relevant sustained stratified shear flows. Varying and leads to four qualitatively different regimes: laminar flow; mostly laminar flow with finite-amplitude, travelling Holmboe waves; spatio-temporally intermittent turbulence with substantial interfacial mixing; and sustained, vigorous interfacial turbulence (Meyer & Linden, J. Fluid Mech., vol. 753, 2014, pp. 242–253). We seek to explain the scaling of the transitions between flow regimes in the two-dimensional plane of input parameters . We improve upon previous studies of this problem by providing a firm physical basis and non-dimensional scaling laws that are mutually consistent and in good agreement with the empirical transition curves we inferred from 360 experiments spanning and . To do so, we employ state-of-the-art simultaneous volumetric measurements of the density field and the three-component velocity field, and analyse these experimental data using time- and volume-averaged potential and kinetic energy budgets. We show that regime transitions are caused by an increase in the non-dimensional time- and volume-averaged kinetic energy dissipation within the duct, which scales with at high enough angles. As the power input scaling with is increased above zero, the two-dimensional, parallel-flow dissipation (power output) increases to close the budget through an increase in the magnitude of the exchange flow, incidentally triggering Holmboe waves above a certain threshold in interfacial shear. However, once the hydraulic limit of two-layer exchange flows is reached, two-dimensional dissipation plateaus and three-dimensional dissipation at small scales (turbulence) takes over, at first intermittently, and then steadily, in order to close the budget and follow the scaling. This general understanding of regime transitions and energetics in the SID experiment may serve as a basis for the study of more complex sustained stratified shear flows found in the natural environment.

Slender body theory for particles with non-circular cross-sections with application to particle dynamics in shear flows

This paper presents a theory to obtain the force per unit length acting on a slender filament with a non-circular cross-section moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has$O(1/\ln (2A))+O(\unicode[STIX]{x1D6FC}/\ln ^{2}(2A))$contributions driven by the relative motion of the particle and the local fluid velocity and an$O(\unicode[STIX]{x1D6FC}/(\ln (2A)A))$contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ($A=l/a_{0}$) is defined as the ratio of the particle size ($l$) to the cross-sectional dimension ($a_{0}$) and$\unicode[STIX]{x1D6FC}$is the amplitude of the non-circular perturbation. Using thought experiments, we show that two-lobed and three-lobed cross-sections affect the response to relative motion and velocity gradients, respectively. A two-dimensional Stokes flow calculation is used to extend the perturbation analysis to cross-sections that deviate significantly from a circle (i.e.$\unicode[STIX]{x1D6FC}\sim O(1)$). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasi-periodically if they have two-lobed cross-section, and rotate chaotically and translate diffusively if they have a combination of two- and three-lobed cross-sections. Finally, we show the remarkable ability of our theory to accurately predict the motion of rings, retaining great accuracy for moderate aspect ratios (${\sim}10$) and cross-sections that deviate significantly from a circle, thereby making our theory a computationally inexpensive alternative to other Stokes flow solvers.

Regime transitions and energetics of sustained stratified shear flows

We describe the long-term dynamics of sustained stratified shear flows in the laboratory. The stratified inclined duct (SID) experiment sets up a two-layer exchange flow in an inclined duct connecting two reservoirs containing salt solutions of different densities. This flow is primarily characterised by two non-dimensional parameters: the tilt angle of the duct with respect to the horizontal, $\unicode[STIX]{x1D703}$ (a few degrees at most), and the Reynolds number $Re$, an input parameter based on the density difference driving the flow. The flow can be sustained with constant forcing over arbitrarily long times and exhibits a wealth of dynamical behaviours representative of geophysically relevant sustained stratified shear flows. Varying $\unicode[STIX]{x1D703}$ and $Re$ leads to four qualitatively different regimes: laminar flow; mostly laminar flow with finite-amplitude, travelling Holmboe waves; spatio-temporally intermittent turbulence with substantial interfacial mixing; and sustained, vigorous interfacial turbulence (Meyer & Linden, J. Fluid Mech., vol. 753, 2014, pp. 242–253). We seek to explain the scaling of the transitions between flow regimes in the two-dimensional plane of input parameters $(\unicode[STIX]{x1D703},Re)$. We improve upon previous studies of this problem by providing a firm physical basis and non-dimensional scaling laws that are mutually consistent and in good agreement with the empirical transition curves we inferred from 360 experiments spanning $\unicode[STIX]{x1D703}\in [-1^{\circ },6^{\circ }]$ and $Re\in [300,5000]$. To do so, we employ state-of-the-art simultaneous volumetric measurements of the density field and the three-component velocity field, and analyse these experimental data using time- and volume-averaged potential and kinetic energy budgets. We show that regime transitions are caused by an increase in the non-dimensional time- and volume-averaged kinetic energy dissipation within the duct, which scales with $\unicode[STIX]{x1D703}Re$ at high enough angles. As the power input scaling with $\unicode[STIX]{x1D703}Re$ is increased above zero, the two-dimensional, parallel-flow dissipation (power output) increases to close the budget through an increase in the magnitude of the exchange flow, incidentally triggering Holmboe waves above a certain threshold in interfacial shear. However, once the hydraulic limit of two-layer exchange flows is reached, two-dimensional dissipation plateaus and three-dimensional dissipation at small scales (turbulence) takes over, at first intermittently, and then steadily, in order to close the budget and follow the $\unicode[STIX]{x1D703}Re$ scaling. This general understanding of regime transitions and energetics in the SID experiment may serve as a basis for the study of more complex sustained stratified shear flows found in the natural environment.

Rheology of bacterial suspensions under confinement

As a paradigmatic model of active fluids, bacterial suspensions show intriguing rheological responses drastically different from their counterpart colloidal suspensions. Although the flow of bulk bacterial suspensions has been extensively studied, the rheology of bacterial suspensions under confinement has not been experimentally explored. Here, using a microfluidic viscometer, we systematically measure the rheology of dilute Escherichia coli suspensions under different degrees of confinement. Our study reveals a strong confinement effect: the viscosity of bacterial suspensions decreases substantially when the confinement scale is comparable or smaller than the run length of bacteria. Moreover, we also investigate the microscopic dynamics of bacterial suspensions including velocity profiles, bacterial density distributions, and single bacterial dynamics in shear flows. These measurements allow us to construct a simple heuristic model based on the boundary layer of upstream swimming bacteria near confining walls, which qualitatively explains our experimental observations. Our study sheds light on the influence of the boundary layer of collective bacterial motions on the flow of confined bacterial suspensions. Our results provide a benchmark for testing different rheological models of active fluids and are useful for understanding the transport of microorganisms in confined geometries.

Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals.

We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict it to a shear flow and spatially homogeneous situation. We analyse the dynamics focusing on the effect of the flow. We show that in the co-rotational case one has gradient dynamics, up to a periodic eigenframe rotation, while in the non-co-rotational case we identify the short- and long-time regimes of the dynamics. We express these in terms of the physical variables and compare with the predictions of other models of liquid crystal dynamics.

Customised bifurcating networks for mapping polymer dynamics in shear flows

Understanding the effect of varying shear stresses on individual polymer dynamics is important for applications such as polymer flooding, polymer induced drag reduction, or the design of DNA separation devices. In all cases, the individual polymer response to varying shear flows needs to be understood. A biomimetic design rule was recently proposed for bifurcating networks of rectangular channels of constant depth. These customised microfluidic geometries represent an elegant option to investigate, in a single device, multiple well-controlled shear stresses. Here, we present the first experimental realisation of such customised microfluidic networks, consisting of a series of rectangular microchannels with varying cross-sections, and we demonstrate their potential for testing polymer dynamics. We used microfluidic geometries optimised for both Newtonian and power-law fluids of constant or increasing average wall shear stress. The experimental model systems were tested using particle tracking velocimetry to confirm the theoretically predicted flow fields for shear-thinning xanthan gum solutions and a Newtonian fluid. Then, λ-DNA molecules were used as an example of shear sensitive polymers to test the effect of distinct shear stress distributions on their extension. By observing the conformation of individual molecules in consecutive channels, we demonstrate the effect of the varying imposed stresses. The results obtained are in good agreement with previous studies of λ-DNA extension under shear flow, validating the bifurcating network design. The customised microfluidic networks can thus be used as platforms for the investigation of individual polymer dynamics, in a large range of well-controlled local and cumulative shear stresses, using a single experiment.

Effect of non-Maxwellian electrons on shear flow modified ion acoustic solitons

Dynamics of shear flow modified ion acoustic wave is investigated assuming electrons to follow q-nonextensive and Cairns distribution functions. A modified linear dispersion relation and electrostatic KdV solitons are analyzed. Results are illustrated considering solar wind and F-region ionospheric plasmas. Effects of non-Maxwellian distribution of electrons on the amplitude and the width of solitons are pointed out in the presence of field-aligned inhomogeneous flow.