Dimensionless Shear Rate Research Articles

Porous structures impact on particle dynamics of non-Brownian and noncolloidal suspensions

This study aims to provide valuable insights into the impact of porous structures on particle dynamics in non-Brownian, non-colloidal suspension flows at very low Reynolds numbers. Two experimental approaches, Particle Image Velocimetry (PIV) with refractive index matching and Optical Flow Tracking Velocimetry (OFTV) were employed to analyze very dilute suspensions over various porous media models. The study considered three different porous structures with permeabilities ranging from 0.7 to 0.9 and three different thicknesses ranging from 0.2 cm to 0.5 cm, while the suspension bulk volume fraction was maintained at 3 %. In the PIV analysis, we observed that decreasing the porous permeability resulted in the maximum velocity location within the free flow region moving closer towards the interface between the flow and the porous media. We further quantified the effect of the porous structure on the suspension by characterizing interface properties, such as dimensionless slip velocity, shear rate, and slip length. These interface properties were found to be influenced by both the thickness and permeability of the porous media. Next, we analyzed particle migration due to the presence of porous structures using OFTV for very dilute suspensions of 1 %, 2 %, and 3 %, considering a porous medium with known physical properties and thickness. The study revealed two local concentration maxima: one within the free flow region on top of the rod arrays used to create the porous structure and a second along the rods' centerline inside the porous media model.

Two types of quaking and shear unjamming: State diagram for soft granular particles in quasistatic shear

Understanding intermittency, a ubiquitous behavior in flows of packed grains, is pivotal for establishing the rheology of granular matter. A straightforward explanation has been missing despite the long development of theories at various levels of abstraction. Here, we propose the use of a Stribeck-Hertz model that starts with the classic Coulomb friction but takes into account the interparticle , i.e., the reduction of friction coefficient with sliding speed as is commonly observed. Our numerical experiments reveal a state diagram that covers a wide range of packing fractions and show that incorporating the tribology enables the occurrence of quaking intermittency in the midrange of a dimensionless shear rate, consistent with prior experimental observations. Further study of the discontinuities in the evolution of the mean contact number leads to our discovery of two types of quaking that are distinguished by the abrupt or of neighboring contacts and reveal different pathways of microstructural change underlying these discrete events. In contrast to the prevailing paradigm in which shear is believed to promote jamming at intermediate densities, our study demonstrates that shear can also unjam a granular system, and this occurrence depends on the shear rate. Published by the American Physical Society 2024

Drag, lift and torque correlations for axi-symmetric rod-like non-spherical particles in locally linear shear flows

This paper derives new correlations to predict the drag, lift and torque coefficients of axi-symmetric non-spherical rod-like particles for several fluid flow regimes and velocity profiles. The fluid velocity profiles considered are locally uniform flow and locally linear shear flow. The novel correlations for the drag, lift and torque coefficients depend on the particle Reynolds number Rep, the orientation of the particle with respect to the main fluid direction θ, the aspect ratio of the rod-like particle α, and the dimensionless local shear rate G̃. The effect of the linear shear flow on the hydrodynamic forces is modeled as an additional component for the resultant of forces acting on a particle in a locally uniform flow, hence the independent expressions for the drag, lift and torque coefficients of axi-symmetric particles in a locally uniform flow are also provided in this work. The data provided to fit the coefficient in the new correlation are generated using available analytical expressions in the viscous regime, and performing direct numerical simulations (DNS) of the flow past the axi-symmetric particles at finite particle Reynolds number. The DNS are performed using the direct-forcing immersed boundary method. The coefficients in the proposed drag, lift and torque correlations are determined with a high degree of accuracy, where the mean error in the prediction lies below 2% for the locally uniform flow correlations, and bwlow 1.67%, 5.35%, 6.78% for the correlation accounting for the change in the drag, lift, and torque coefficients in case of a linear shear flow, respectively. The proposed correlations for the drag, lift and torque coefficients can be used in large-scale simulations performed in the Eulerian-Lagrangian framework with locally uniform and non-uniform flows.

Large-amplitude oscillatory shear flow from general rigid bead-rod theory

Oscillatory shear flow, performed at small-amplitude, interrogates polymeric liquids in their equilibrium states. The fluid responds in sinusoidal shear stress waves whose amplitude and phase lead depend on the dimensionless frequency (called the Deborah number). By contrast, this same flow field, performed at large-amplitude, probes departures from the equilibrium state, and the fluid responds with shear stress in the form of a Fourier series, whose component amplitudes and phase leads depend on both the dimensionless frequency (called the Deborah number) and the dimensionless shear rate amplitude (called the Weissenberg number). The physics of these departures from equilibrium in an oscillatory shear flow may be explained by (i) chain disentanglement or (ii) motion along the polymer chain axes (called reptation) or (iii) macromolecular orientation. Of these radically different and yet otherwise equally effective approaches, only (iii) allows the macromolecular structure to be varied arbitrary so that the effect of molecular architecture on the rheology can be explored. Though much has been written about a large-amplitude oscillatory shear flow, we understand little about the role of molecular structure on the measured behaviors, and this has limited its usefulness. In this work, we explain the higher harmonics of both the shear stress (first and third), the first normal stress differences (zeroth, second, and fourth), and the second normal stress differences (zeroth and second) arriving at analytical expressions for all three. These expressions, written in dimensionless form, express the dimensionless rheological responses in large-amplitude oscillatory shear flow in terms of the ratio of the two principal macromolecular moments of inertia. To get these expressions, we derive the first five terms of the orientation distribution function, by solving the general diffusion equation in Euler coordinates. We then integrate in phase space with this orientation result to arrive at our expression for the first seven terms of the polymer contribution to the extra stress tensor. From this tensor, we next write down the Fourier coefficients for the shear stress responses, and the normal stress difference responses, in large-amplitude oscillatory shear flow for a suspension of macromolecules sculpted from a rigid bead-rod structure of any arbitrary axisymmetric shape.

EFFECTS OF SURFACTANT ON LIFT COEFFICIENT OF ELLIPSOIDAL BUBBLES IN THE VISCOUS-FORCE DOMINANT REGIME

Effects of surfactants on lift coefficients, <i>C<sub>L</sub></i>, of single ellipsoidal bubbles rising through linear shear flows were investigated. Two types of surface-active agents, Triton X-100 and 1-octanol, were used. The liquid properties except for the surface tension were identical to those in a clean system of logM = -5.5, where M is the Morton number. The range of the bubble Reynolds number was 0.1 < Re < 70. Bubble shapes were either spherical or ellipsoidal. Comparing with clean bubbles, less deformation of contaminated bubbles was confirmed. A shape correlation without taking the dimensionless shear rate into account gave good evaluations of the bubble aspect ratio, which means that the shear rate is not a dominant factor causing the change of shape deformation. However, drag coefficients were affected by the shear rate. A new correlation of drag coefficients was deduced, which agreed well with the experimental data. Both clean and contaminated <i>C<sub>L</sub></i> data showed a similar tendency: after a drastic decrease in <i>C<sub>L</sub></i>, <i>C<sub>L</sub></i> slightly increases and then decreases to a negative value while increasing the bubble Reynolds number, Re. A difference in concentration of Trion X-100 resulted in only a slight change in <i>C<sub>L</sub></i> at high Re regime. Different types of surfactant resulted in noticeably different values of <i>C<sub>L</sub></i> especially at low Re. The <i>C<sub>L</sub></i> of small bubbles in contaminated systems could be reproduced by a correlation for solid particles, supporting that fully contaminated spherical bubbles behave like solid spheres. For deformed bubbles, <i>C<sub>L</sub></i> can be expressed by relating the negative lift force due to shape deformation with the drag force.

Macromolecular microfluidic concentrators

Microfluidic design, fabrication, and experiments have developed rapidly, leading to lab-on-chip separation or fractionation. In this work, we design a continuous concentrator for macromolecular solutions. Our design relies on the analytical solutions for orientational diffusion under laminar pressure-driven slot flow through a microchannel [W. Stasiak and C. Cohen, “Dilute solutions of macromolecules in a rectilinear Poiseuille flow,” J. Chem. Phys. 78, 553 (1983)]. Using rigid dumbbell theory, we provide analytical solutions for the design of our microfluidic macromolecular hydrodynamic chromatography. We arrive at our design through the use of well-known confinement-driven composition profiles. Using a pair of razor-sharp blades, our design separates the slot flow into a symmetric core inner slot (concentrated) between two outer slots (diluted). We discover a minimum dimensionless blade leading edge separation for complete fractionation, and that this decreases with confinement and also decreases with dimensionless shear rate.

Shear Flows in Far-from-Equilibrium Strongly Coupled Fluids.

Although the viscosity of a fluid ranges over several orders of magnitude and is extremely sensitive to microscopic structure and molecular interactions, it has been conjectured that its (opportunely normalized) minimum displays a universal value which is experimentally approached in strongly coupled fluids such as the quark-gluon plasma. At the same time, recent findings suggest that hydrodynamics could serve as a universal attractor even when the deformation gradients are large and that dissipative transport coefficients, such as viscosity, could still display a universal behavior far from equilibrium. Motivated by these observations, we consider the real-time dissipative dynamics of several holographic models under large shear deformations. In all the cases considered, we observe that at late time both the viscosity-entropy density ratio and the dimensionless ratio between energy density and entropy density approach a constant value. Whenever the shear rate in units of the energy density is small at late time, these values coincide with the expectations from near equilibrium hydrodynamics. Surprisingly, even when this is not the case, and the system at late time is far from equilibrium, the viscosity-to-entropy ratio approaches a constant which decreases monotonically with the dimensionless shear rate and can be parametrically smaller than the hydrodynamic result.

Stability and Deformation of Vesicles in a Cylindrical Flow.

In this work, we used dissipative particle dynamics to study the stability, deformation, and rupture of polymer vesicles confined in cylindrical channels under the flow field. The morphological evolution, elongation, and rupture of vesicles and the corresponding mechanisms were intensively investigated. Bullet-like vesicles, leaking vesicles, spherical micelles, hamburger-like micelles, and bilayers were observed by changing the degree of confinement and dimensionless shear rate. We found that increasing the dimensionless shear rate and the degree of confinement can cause the deformation or rupture of polymeric vesicles. The asphericity parameter was utilized to describe the degree of elongation of vesicles deviating from the sphere in the direction of the flow. The results show that the aggregates are more likely to be spherical when the confinement is weak, while they become elongated bullet-like shapes when the confinement is strong. The investigation of dynamics reveals that the degree of confinement and the dimensionless shear rate can affect the chain stretching and reorganization during the process of vesicle elongation. Furthermore, the rupture time of the vesicle shows a nonlinear decrease with an increase in the dimensionless shear rate, and the confinement also contributes to the rupture. The results are very useful for guiding the application of vesicles in a flow environment.

Assessment of the flow behavior of power-law fluids in spinnerets

We employed the computational fluid dynamics (CFD) simulation to capture the flow behavior in spinnerets based on various flow angles (90°, 75°, 60°, and 30°), different power-law fluids (0.5 ≤ n ≤ 1), and two different flow rates (0.2 mL/min and 1.4 mL/min). The simulation results moderately agreed with the semi-analytical solution obtained from the literature. The sensitivity analysis was performed, showing that spinneret's flow angles and power-law indices are additional critical variables that facilitate the alignment of the polymeric chain in the dope solution due to the enhanced shear rate. The maximum viscosity reduction is observed in this study when a more shear-sensitive dope fluid extrudes through the spinneret at a given flow rate. The low shear rate gradient prevalence elevates the viscosity in the annular spinneret region, strongly dependent on the flow and shear-sensitive fluid (n < 1). The trends of dimensionless velocity, shear rate, and viscosity distribution are independent of the dope solution flow rates at the exit of a spinneret except for the more shear-sensitive fluids at 60° flow angle spinneret. We attempted to correlate the shear rate and viscosity distributions of the dope solution at the exit of the spinneret with the literature finding on the hollow fiber morphology under wet spinning conditions. It shows a possibility of producing finger-like macrovoids near the outer/inner membrane layer while extruding the hollow fiber through straight/conical spinneret due to relatively low shear rate and lower viscosity region.

STEADY MHD MIXED CONVECTION NEWTONIAN FLUID FLOW ALONG A VERTICAL STRETCHING CYLINDER EMBEDDED IN POROUS MEDIUM

A viscous electrically conducting fluid is considered and its steady mixed convective flow along a vertical stretching cylinder is investigated. It is assumed that the cylinder is embedded in a porous medium and, external magnetic field, heat source/sink are also taken into account. Suitable similarity transformations are used to reduce the governing equations and associated boundary conditions into a system of nonlinear ordinary differential equations. This system along with the boundary conditions is solved by fourth order Runge-Kutta method with shooting technique. Variations in fluid velocity and temperature due to various physical parameters such as heat source/sink parameter, mixed convection parameter, magnetic parameter are presented through graphs. Effect of these parameters on dimensionless shear stress and rate of heat transfer are discussed numerically through tables.

Signature of Transition between Granular Solid and Fluid: Rate-Dependent Stick Slips in Steady Shearing.

Despite extensive studies on either smooth granular-fluid flow or the solidlike deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of interparticle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers J decades below reported values, we answer how a granular system can transition to the regime sustained by solid-to-solid friction that goes beyond existing paradigms based on suspension rheology.

Heat Transfer in Fully Developed, Laminar Flows of Dissipative Pseudoplastic and Dilatant Fluids in Circular Conduits

Abstract This paper reports the results of a numerical study that determined the Nusselt number for hydrodynamically and thermally fully developed, laminar, dissipative flows of pseudoplastic and dilatant fluids through circular conduits. Two boundary conditions were considered, constant heat flux and constant temperature. Constitutive equations were used that describe the entire flow curve, from the zero-shear rate through the infinite shear rate Newtonian regions, so that computed Nusselt numbers are valid for whatever shear rates may exist in the flow field. Nusselt numbers are reported as a function of a dimensionless shear rate parameter that establishes the region of the flow curve where the system is operating and are shown to be bound by the Newtonian and power law values. The conditions required for the system to perform at these asymptotic limits are quantified.

Evidence of a non-local ø(I) response

Granular dilatancy has been previously characterised through a simple linear relationship between the packing fraction and dimensionless shear rate. However, this relationship was developed for granular flows in a simple shear cell geometry. Here we examine inertial volume changes in a shear cell with gravity, a vertical chute, and a pseudo-2D hopper. In so doing, we show that the packing fraction displays both a local and non-local response, analogous to what is typically observed for the stress ratio µ.

Viscosity Models for Drilling Fluids—Herschel-Bulkley Parameters and Their Use

An evaluation is presented of the practical usage of the Herschel-Bulkley viscosity model for drilling fluids. If data from automatic viscosity measurements exist, the parameters should be selected from relevant shear rate ranges to be applicable. To be able to be used properly, viscosity measurements must be measured with a sufficient accuracy. It is shown that a manual reading of standard viscometers may yield insufficient accuracy. It is also shown that the use of yield point/plastic viscosity (YP/PV) as measured using API or ISO standards normally provide inaccurate viscosity parameters. The use of the Herschel-Bulkley model using dimensionless shear rates is more suitable than the traditional way of writing this model when the scope is to compare different drilling fluids. This approach makes it also easier to make correlations with thermodynamic quantities like pressure and temperature or chemical or mineralogical compositions of the drilling fluid.

Fluid flow and heat transfer around single and tandem square cylinders subjected to shear flow

Linear shear flows, forces, and heat transfer across a single and two tandem square cylinders are numerically investigated at Reynolds numbers Re = 70–150 and a Prandtl number Pr = 0.71, with the dimensionless inlet shear rate K = 0–0.2. For the two tandem cylinders, the scaled cylinder-gap spacing (S*) is varied from 1.0 to 5.0. The flow is assumed laminar and two-dimensional. The numerical method is based on a finite-volume technique. The effects of K, Re, and S* are investigated on the heat transfer topology, flow structures, and aerodynamic parameters including vortex shedding frequency, pressure coefficient, lift and drag forces, and Nusselt number. For the single cylinder, when K ≠ 0, the time-mean lift force is negative for Re = 70 and 100 but positive for Re = 150. The lift magnitude linearly increases with K. For tandem cylinders, employing three initial conditions for some S* values yields two solutions linked to hysteresis (modes I and II) in the flow, forces, and heat transfer. Hysteresis is observed for S* = 2.0–5.0 when K = 0.2 and Re = 150. Mode I turns in a smaller time- and surface-averaged Nusselt number than mode II. In general, the inlet shear has more effect on the flow around the downstream cylinder than that around the upstream cylinder.

Viscous fluid flow in a wide annular gap of two rotating coaxial cylinders

The Couette-Taylor flow is considered in a wide gap between coaxial cylinders in the case when the outer cylinder is at rest and the inner one rotates at a constant speed. Unsteady motion of a viscous fluid is described by the system of Navier-Stokes equations. The problem is solved by the control volume method in the OpenFOAM software. Two stable states were obtained depending on the surface rotation speed: the cylindrical Couette flow and the Taylor vortex flow. The calculation results are compared with the known data of other authors. The dependence of the dimensionless shear rate on the Taylor number is obtained.

Comparison study between lateral flow immunochromatographic assay and hemoglobin H staining for the screening of alpha thalassaemia

This paper presents a numerical study of the heat transfer improvement around a bubble rising near a wall in a shear flow. The Navier Stokes equations and energy equation are solved in a frame of reference following the bubble to examine the dependence of the wall to liquid heat transfer on flow patterns around the bubble. The front tracking method is used to track the interface of non-condensable gas bubbles, and the finite volume method is used to solve for temperature and momentum. Our simulations show an enhancement and a diminishment of heat transfer in the downstream and upstream regions of the bubble, respectively. The enhancement and reduction of heat transfer are attributed to the reversal of flow that occurs near the wall due to the presence of a bubble. The heat transfer rate non-monotonically varies with the dimensionless shear rate γ̇‾=γ̇dg. In the range of 0.3⩽γ̇‾≤2.25, the heat transfer rate first increases, attains a maximum value and then decreases. The optimum γ̇‾ increases as the Archimedes number is increased. The heat transfer rate is found to decrease as the Laplace number is increased. The flow reversal near the wall is characterized by two parameters, namely the ‘reversal height’ and ‘reversal width’. A control volume analysis is performed for a simplified 2D version of the problem in order to relate heat transfer enhancement to the reversal height and width. The functional dependence of heat transfer enhancement on reversal height and width from our 3D simulations match the result of the control volume analysis. The analytical solution of an inviscid shear flow over a cylinder is used for qualitative insights into flow reversal mechanism. Our simulations of transient heat transfer showed that the fractional improvement in heat transfer compared to a single phase flow attains a constant value after a certain amount of time. Finally, we report the results of heat transfer enhancement due of an array of bubbles rising near a wall.

Dynamic characteristics of a deformable capsule in a simple shear flow

The dynamic characteristics of a two-dimensional deformable capsule in a simple shear flow are studied with an immersed boundary-lattice Boltzmann method. Simulations are conducted by varying the Reynolds number (Re) from 0.0125 to 2000 and the dimensionless shear rate (G) from 0.001 to 0.5. The G-Re plane can be divided into four regions according to the deformation dependence on the parameters considered: viscous dominant, inertia dominant, transitional, and anomalous regions. There are four typical dynamic behaviors over the G-Re plane: steady deformation, prerupture state, quasisteady deformation, and continuous elongation. Analysis indicates that the pressure distribution and its variations due to the interplay of the fluid inertia force, the viscous shear stress, and the membrane elastic force determines the complex behaviors of the capsule. The effects of the bending rigidity and the internal-to-external viscosity ratio on the dynamics of the capsule are further studied. It is found that the capsule experiences smaller deformation when the higher bending rigidity is included, and the low bending rigidity does not have a remarkable influence on the capsule deformation. The capsule normally experiences smaller deformation due to the increase of the internal-to-external viscosity ratio.

Drag and Lift Forces Acting on a Sphere in Shear Flow of Power-Law Fluid

Laminar flow of a power-law fluid over a sphere is considered for unbounded shear flow. The Navier–Stokes equations with power-law viscosity are solved numerically using an in-house developed CFD package. Vorticities structures downstream of particle are suppressed for powerlaw fluid. The shear rate influence on drag force is negligible for power index close to unit, and the drag force appreciably decreases with falling power index. For small Reynolds numbers, the lift force coefficient monotonically decreases against the power index and exhibits an opposite behavior for moderate values of Reynolds numbers. The results of the parametric studies are used to derive correlations for the drag force and to detect the hydrodynamic differences from uniform flow. The investigation parameters varied within the following ranges: power-law index 0.3 ≤ n ≤ 1, Reynolds number 0 < Re ≤ 150, and dimensionless shear rate 0.05 ≤ s ≤ 0.4.

Thermodynamic instability of polymeric liquids in large-amplitude oscillatory shear flow from corotational Maxwell fluid

When polymeric liquids are subjected to oscillatory shear flow, if the amplitude of the shear rate is high enough, the shear stress response will become aperiodic. This has been variously attributed to fracture, common line ingress, slip, shear-banding and phase change, however, the underlying causes for these is unclear. In this paper we explore the creation of new thermodynamic phases as the trigger for these phenomena. Specifically, we examine two thermodynamic instability criteria that have been suggested for large-amplitude oscillatory shear flow (LAOS). One of these criteria is based on non-equilibrium thermodynamics (the Ziegler criterion), and the other, on equilibrium thermodynamics (the free energy criterion). The advent of exact solutions for stress responses to LAOS provokes this investigation. We use one such exact solution to evaluate these criteria for the simplest relevant constitutive model, the corotational Maxwell fluid. By relevant, we mean at least predicting higher harmonics in LAOS. We find that, in steady shear flow, the Ziegler instability arises when the dimensionless shear rate exceeds the square root of the golden ratio, Applying our results to instability measurements on dissolved polybutadiene, we find the Ziegler criterion to be useful at low frequency, and the free energy criterion to be useful elsewhere.