Linear Shear Research Articles

Dynamical Properties of Concentrated Suspensions of Block Copolymer Stars in Shear Flow.

Block copolymer stars (BCSs) have been demonstrated to constitute versatile, self-assembling building blocks with tunable softness, functionalization, and shape. We investigate the dynamical properties of suspensions of short-arm BCSs under linear shear flow by means of extensive particle-based multiscale simulations. We determine the properties of the system for representative values of monomer packing fraction ranging from semidilute to concentrate regimes. We systematically analyze the formed network structures as a function of both shear rate and packing fraction, the reorganization of solvophobic patches, and the corresponding radial correlation functions. Connecting our findings with rheology, we calculate the viscosity as a function of shear rate and discuss the implications of the found shear thinning behavior.

Response spectrum-based seismic response of bridge embankments

A single degree of freedom model is presented for calculating the free-field seismic response of bridge embankments due to horizontal ground shaking using equivalent linear analysis and a design response spectrum. The shear wave velocity profile, base flexibility, 2D shape, and damping ratio of the embankment are accounted for in the model. A step-by-step procedure is presented for calculating the effective cyclic shear strain of the embankment, equivalent homogeneous shear modulus and damping ratio, fundamental period of vibration, peak crest acceleration, peak shear stress profile, peak shear strain profile, equivalent linear shear modulus profile, and peak relative displacement profile. Model calibration and verification of the proposed procedure is carried out with linear, equivalent linear, and nonlinear finite element analysis for embankments with fundamental periods of vibration between 0.1 and 1.0 s. The proposed model is simple, rational, and suitable for practical implementation using spreadsheets for a preliminary design phase of bridge embankments.

Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions

Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.

Progressive flexural–gravity waves with constant vorticity

Abstract

Lift and drag forces acting on a particle moving with zero slip in a linear shear flow near a wall

Abstract

Characterizing long-chain branching in commercial HDPE samples via linear viscoelasticity and extensional rheology

It is well established that polymer chain architecture and the distribution of molecular weight play a key role in the flow behavior (processing) and performance of a given polymer material. Long-chain branching (LCB) in particular is known to strongly affect the processability and the material performance of polymers. Often branching is a result of the polymerization process and therefore must be quantified in every sample. We study four commercial high-density polyethylene (HDPE) samples with unknown degrees of polydispersity and LCB. We first use size-exclusion chromatography and linear shear rheology to identify differences in molecular weight, polydispersity, and LCB. Each material is then tested in constant rate and constant stress uniaxial extension using a filament stretching rheometer to quantify extensional viscosity and strain hardening. Correlations between nonlinear extensional rheology, LCB and polydispersity are discussed. We show that the combination of the van Gurp-Palmen plot and extensional rheology allows for a full characterization of the LCB fraction and their effect on extensional rheology.

The impact of stretching-enhanced mixing and coalescence on reactivity in mixing-limited reactive flows

We analyze the dynamics of solute mixing and reaction in a mixing-limited reactive flow by considering the transport of a tracer in a linear shear flow and in a Rankine vortex. The action of a shear flow, in general, achieves stretching of fluid elements due to the heterogeneous nature of the flow. A vortex flow exhibits not only stretching but also folding of fluid elements in a way that brings adjacent fluid elements closer at every turn. A strong stretching along the tangential direction is accompanied by a concomitant thinning in the radial direction leading to a strong diffusive flux, which may cause the material from neighboring regions of the mixing interface to aggregate. Through a Lagrangian concentration evolution technique, the diffusive strip method, we obtain the concentration field and pinpoint the signature of coalescence of two neighboring concentration regions by analyzing the concentration distribution profiles. The role of substrate deformation on the reaction kinetics of a classical heterogeneous chemical reaction is also studied where we derive analytical expressions for the coupling between the rate of product formation and the Péclet number in different time limits. Finally, the impact of coalescence on reaction rates is studied for a Rankine vortex, a result that holds important implications for simple bimolecular reactions. This analysis is useful to understand scalar dispersion in vortical flow structures and the consequences of stretching-enhanced diffusion in mixing-limited reactive flows.

Drag, lift, and torque on a prolate spheroid resting on a smooth surface in a linear shear flow

Understanding the aerodynamic forces on particles resting on a surface is important for studies of surface contamination, non-contact sampling, and environmental and health assessments. Though the aerodynamic forces acting on a spherical particle are well studied, in many real-world applications, the particles are non-spherical, and there are currently no established relations for forces on non-spherical particles resting on a surface. We developed new relations for the aerodynamic forces on prolate-spheroidal particles attached to a surface in a linear shear flow using direct numerical simulations. The reduced-order model predicts drag, lift, and torque coefficients as a function of the particle aspect ratio, flow incidence angle, and Reynolds number. The predictive model agrees with the direct numerical simulations (DNS) results for the drag and lift coefficients within 0.3% and 3%, respectively.

Gravity-capillary waves modulated by linear shear flow in arbitrary water depth* *Project supported by the National Natural Science Foundation of China (Grant No. 41830533) and the National Key Research and Development Program of China (Grant Nos. 2016YFC1401404 and 2017YFA0604102).

Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrödinger equation (NLSE) describing the evolution dynamics of gravity-capillary wavetrains in arbitrary constant depth. The gravity-capillary waves (GCWs) are influenced by a linear shear flow (LSF) which consists of a uniform flow and a shear flow with constant vorticity. The modulational instability (MI) of GCWs with the LSF is analyzed using the NLSE. The MI is effectively modified by the LSF. In infinite depth, there are four asymptotes which are the boundaries between MI and modulational stability (MS) in the instability diagram. In addition, the dimensionless free surface elevation as a function of time for different dimensionless water depth, surface tension, uniform flow and vorticity is exhibited. It is found that the decay of free surface elevation and the steepness of free surface amplitude change over time, which are greatly affected by the water depth, surface tension, uniform flow and vorticity.

Testing and Evaluation of Linear Shear Mode Magnetorheological (MR) Damper Based on Rheological Properties of MR Fluid

Abstract Magnetorheological (MR) fluid exhibits variable yield stress and viscosity with the magnetic field, which is why it is classified under smart materials. Because of its controllable properties, MR fluid has many applications. The most common application of MR fluid is MR fluid damper. According to the flow of MR fluid, three types of dampers are possible; flow mode, squeeze mode, and shear mode. In this article, rheological properties of MR fluid, which has a high Bingham number (ratio of MR force on-state to off-state), are synthesized and the MR properties are studied. Based on these properties, a linear shear mode MR damper is designed and evaluated for its performance. A unique model is adopted to evaluate the performance of MR damper. In this model, the dimensionless Mason number is applied to establish the relation between test data of damper and rheological properties of MR fluid. This is verified for two different volume fractions of magnetic particles in MR fluid.

On two-dimensional acoustic-entropy waves in a mean flow with uniform velocity and laterally varying sound speed

Acoustic-entropy waves are considered as linear, compressive perturbations of a non-dissipative non-homentropic uniform flow. The acoustic-entropy wave equation for the pressure satisfies a modified convected wave equation with non-uniform sound speed. In the case of plane flow with a linear entropy shear profile the exact solution is obtained in terms of Bessel functions of an exponential variable. The acoustic-entropy waves in a uniform flow with a linear entropy shear are considered in: (i) a parallel sided duct; (ii) an unbounded boundary over a flat wall; (iii) a boundary layer of finite thickness matched to a uniform free stream.

The Non-Stationary Dynamic Analytical Solution of a Spherical/Cylindrical Cavity Expansion

Abstract A review of the pertinent literature related to the dynamic expansion of a spherical/cylindrical cavity shows that all the solutions with kinematic boundary conditions deal with a constant velocity at the cavity boundary. This paper develops a new general solution of the nonstationary dynamic problem of cavity expansion, which allows the application of time-dependent motion conditions at the cavity boundary. This solution can be used, for example, in the development of approximate approaches for projectiles penetrating with a non-constant velocity into different targets. Due to the complexity of the nonlinear nonstationary problem, an analytical solution of the problem may be developed if simplified constitutive relationships are used. In the present model, a simplified material model with a locked equation of state and a linear shear failure relationship is implemented. This solution may be applied to different materials such as concrete, soil, and rock. Special cases of the newly developed nonstationary solution are compared with different spherical and cylindrical cavity expansions solutions reported in the literature, and a good agreement is obtained. The capability of the present model is demonstrated in a following investigation of representative cases of cavity expansion with zero, constant, and variable acceleration of the cavity boundary. A significant difference in the stress variation for the different cases is shown. Along with the general solution which deals with an elastic–plastic region, a simplified solution which disregards the contribution of the elastic region is presented and the evaluation of the elastic region effect may be assessed.

From Mesoarchean drips to modern–style tectonics in the Carajás Province, Amazonian Craton

The beginning of modern–style plate tectonics on Earth is not a consensus, but many authors suggest that it happened transitionally, from 3.2 to 2.5 Ga. In the Amazonian Craton, Brazil, the contrasting crustal architecture of the Rio Maria and the Carajás domains is marked by dome–and–keel and linear belt, respectively, which may represent a shift in the tectonic styles along the Mesoarchean to Neoarchean transition. Here, we discuss this hypothesis combining existing literature and an interpretation of airborne geophysical data for the Caracol Dome. This Archean TTG (Trondhjemite–Tonalite–Granodiorite) Dome shows a concentric lithological variation, with older 2.97–2.96 Ga trondhjemites at the edges and younger 2.95–2.92 Ga tonalites within the inner parts. The Caracol Dome exhibits a similar magmatic evolution to other Archean domes worldwide (e.g., Yalgoo and Mt. Edgar Domes), commonly interpreted as the record of vertical tectonics (e.g., drip–tectonics). However, the subsequent geological record in the Carajás Province is more likely related to the onset or transition to modern–style tectonics, such as large continental shelf sedimentation (Carajás Basin), steeply dipping linear shear zones with 2.76–2.73 Ga syn–tectonic intrusions and Neoarchean iron oxide–copper–gold (IOCG) mineralization. Finally, late Neoarchean to Paleoproterozoic tectonic events with new (and/or remobilized) IOCG deposits are also recorded in the Carajás Province.

Numerical simulation of vortex-induced vibration of a marine riser with a multiphase internal flow considering hydrate phase transition

To investigate the effect of a multiphase internal flow with hydrate phase transition on the vortex-induced vibration (VIV) of a marine riser, a numerical model is established that first solves the flow parameters, and the natural frequencies of risers with different gas intake ratios are obtained. Then, a VIV equation that considers the effect of the multiphase internal flow is established. The Newmark - β method is used to solve the VIV equation in the time domain. Finally, the effect of the gas intake ratio on the natural frequencies and the vortex induced vibration response is studied. The results show that the natural frequencies increase with an increase of the gas intake ratio, and the changing trends of higher modes are quite obvious. When the riser is subjected to a linear shear flow, the VIV show a multi-mode response, and the structural response changes from high-order mode dominant to low-order mode dominant with an increase of the gas intake ratio. This can be explained in terms of the natural frequency of riser, which increases with the increase of the gas intake ratio. Moreover, the spanwise reduced velocity decreases, which makes frequency locking occur more easily in the low-order modes.

Punching of RC slabs without transverse reinforcement supported on elongated columns

The paper investigates the influence of support elongation on punching resistance at internal slab column connections without shear reinforcement. Nonlinear finite element analysis (NLFEA) with 3-D solid elements is used to study the influence of column elongation on stress and strain in the slab around the column. Punching failure is shown to be triggered by localised peaks in shear stress around the corners of the support. Significantly, one-way shear is shown to increase the shear resistance of slabs supported on columns with cross sectional dimensions greater than around six times the slab effective depth (d). The common laboratory practice of supporting slabs in punching tests on elongated plates rather than columns is investigated numerically and is found to be reasonable despite uplift occurring in the central region of elongated plates. NLFEA with solid elements gives useful insights into punching failure but nonlinear shell elements are better suited to the practical assessment of slabs in building structures. The disadvantage of conventional nonlinear shell elements is that shear failure can only be detected through post processing of results. To circumvent this, the authors have previously developed a novel modelling approach in which 3-D joint elements are used to connect shell elements located to either side of a punching control perimeter positioned at 0.5d from the column face. The joint shear resistance is calculated using the Critical Shear Crack Theory (CSCT) in which punching resistance is related to slab rotation. Based on insights gained using the solid element modelling, this paper extends the use of the joint model to the modelling of punching failure at elongated supports by including one-way joints to model linear shear.

Hydrocarbon-bearing characteristics of the SB1 strike-slip fault zone in the north of the Shuntuo Low Uplift, Tarim Basin

The SB1 strike-slip fault zone, which developed in the north of the Shuntuo Low Uplift of the Tarim Basin, plays an essential role in reservoir formation and hydrocarbon accumulation in deep Ordovician carbonate rocks. In this research, through the analysis of high-quality 3D seismic volumes, outcrop, drilling and production data, the hydrocarbon-bearing characteristics of the SB1 fault are systematically studied. The SB1 fault developed sequentially in the Paleozoic and formed as a result of a three-fold evolution: Middle Caledonian (phase III), Late Caledonian–Early Hercynian and Middle–Late Hercynian. Multiple fault activities are beneficial to reservoir development and hydrocarbon filling. In the Middle–Lower Ordovician carbonate strata, linear shear structures without deformation segments, pull-apart structure segments and push-up structure segments alternately developed along the SB1 fault. Pull-apart structure segments are the most favourable areas for oil and gas accumulation. The tight fault core in the centre of the strike-slip fault zone is typically a low-permeability barrier, whilst the damage zones on both sides of the fault core are migration pathways and accumulation traps for hydrocarbons, leading to heterogeneity in the reservoirs controlled by the SB1 fault. This study provides a reference for hydrocarbon exploration and development of similar deep-marine carbonate reservoirs controlled by strike-slip faults in the Tarim Basin and similar ancient hydrocarbon-rich basins.

Detection of alteration zones using ASTER imagery and geological field observations: Al Wajh area, Northwestern Arabian Shield, Saudi Arabia

Neoproterozoic rocks are exposed in the southwestern Midyan terrane, which is located in the northwestern Arabian Shield. This terrane contains ophiolitic and metavolcanic rocks and arc-related intrusions. A NW-trending sinistral fault system (Najd Fault System, NFS) affected these Neoproterozoic rocks. The integration of remote sensing techniques, such as band combinations and band ratios of ASTER images, with field observations, helped to discriminate sulfide-rich rocks and to delineate alteration zones, gossans, and quartz veins, which commonly host ore mineralization. The band ratios used were the Al-OH minerals/advanced argillic alteration and the silica and Fe2+ band ratios. ASTER images were used to discriminate different rock units and construct an alteration map of the study area. Additionally, principal component analysis and frequency filtering techniques for ASTER images were used to extract linear faults and shear zone structures. Remote sensing ASTER images helped in the discovery of ancient mines that had not been previously recorded in the study area.

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.

Robust optimum design of a tuned mass damper inerter

The current work describes the optimum design of a tuned mass damper inerter (TMDI) to control a benchmark 10-story base-excited linear shear building under seismic excitations. Mass and inertance ratios are preselected, and optimum free vibration parameters of the TMDI (i.e., natural frequency and damping ratios) are calculated for single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) models with different configurations of single and double inerter TMDIs at different locations using the colliding bodies optimization technique. Four different inherent damping values are considered for each analysis. Minimizing the $$H_{\mathrm{\infty }}$$ norm of the roof displacement transfer function is considered as the objective function for robust control of the building. Additionally, the optimum designed damper performance and its robustness is assessed in both the frequency and time domains. Results show that while being robust, the SDOF-based optimized TMDI approach should be used with caution and it is recommended to optimize and employ the TMDI using the MDOF model. Results indicate the superior performance of the proposed well-tuned damper with proper configuration in comparison to a same weight/mass classical TMD.

Hydrodynamic forces on a clean spherical bubble translating in a wall-bounded linear shear flow

The three-dimensional flow around a spherical clean bubble translating steadily in a wall-bounded linear shear flow is studied numerically. The present work is concerned with the drag and lift forces experienced by the bubble over a wide range of Reynolds number (0.1 ≤ Re ≤ 103, Re being based on the bubble diameter and relative velocity with respect to the ambient fluid), wall distance (1.5 ≤ LR ≤ 8, LR being the distance from the bubble center to the wall normalized by the bubble radius), and relative shear rate (−0.5 ≤ Sr ≤ 0.5, Sr being the ratio between the velocity difference across the bubble and the relative velocity). Based on the above range of parameters, situations where the bubble is repelled from or attracted to the wall are both covered. The flow structure and vorticity field are analyzed to obtain qualitative insight into the interaction mechanisms at work. The drag and lift forces are computed as well. Their variations agree well with theoretical predictions available in the limit of low-but-finite Reynolds number and, when the fluid is at rest, in the potential flow limit. Numerical results and analytical expressions are combined to provide accurate semi-empirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance.