Combined slit and plate–plate magnetorheometry of a magnetorheological fluid (MRF) and parameterization using the Casson model

We describe a magneto-slit die of 0.34 mm height and 4.25 mm width attached to a commercial piston capillary rheometer, enabling the measurement of apparent flow curves of a magnetorheological fluid (MRF) in the high shear rate regime (apparent shear rates 276 up to 20,700 s^???1, magnetic flux density up to 300 mT). The pressure gradient in the magnetized slit is measured via two pressure holes. While the flux density versus coil current without MRF could directly be measured by means of a Hall probe, the flux density with MRF was investigated by finite element simulations using Maxwell® 2D. The true shear stress versus shear rate is obtained by means of the Weissenberg–Rabinowitsch correction. The slit die results are compared to plate–plate measurements performed in a shear rate regime of 0.46 up to 210 s^???1. It is shown that the Casson model yields a pertinent fit of the true shear stress versus shear rate data from plate–plate geometry. Finally, a joint fit of the slit and plate–plate data covering a shear rate range of 1 up to 50,000 s^???1 is presented, again using the Casson model. The parameterization of the MRF behavior over the full shear rate regime investigated is of relevance for the design of MR devices, like, e.g., automotive dampers. In the Appendix, we demonstrate the drawbacks of the Bingham model in describing the same data. We also show the parameterization of the flow curves by applying the Herschel–Bulkley model.     

Reliable plate–plate MRF magnetorheometry based on validated radial magnetic flux density profile simulations

The apparent shear stress from plate–plate magnetorheometry, using the commercial magnetocell MRD180/1T (Physica/Anton Paar) in standard configuration, is distinctly overestimated. The effect is due to a flux density maximum near the sample rim and radial migration of iron particles towards the rim. Radial magnetic flux density profiles were investigated by finite element simulations using the Maxwell^®2D code and by direct Hall probe measurements. The reliability of the finite element method results, both for the empty magnetocell and with magnetorheological fluid (MRF) in the measuring gap, allows conclusions on the true flux density within the MRF, which cannot be accessed by Hall probe measurements. If the MRF sits on top of the bottom yoke (standard configuration), the flux density maximum reaches twice the plateau value (0.74 T for 3 A coil current and 0.3 mm gap height of the investigated MRF). This yields a higher effective flux density and causes radial iron particle migration, resulting in an additional magnetic flux increase near the rim due to augmented MRF magnetisation. As a result, the rotor torque at constant rotary speed increases with time. Reliable results are achieved by a modification of the magnetocell, such that the MRF sits on a non-magnetic Hall disc of 1.5 mm thickness, allowing an online flux density measurement by a FW Bell Hall probe. In this configuration, the radial flux density profile near the rim remains sufficiently flat and no iron particle migration is detected.     

Effects of bottom shear stresses on the wave-induced dynamic response in a porous seabed：PORO-WSSI （shear） model

When ocean waves propagate over the sea floor,dynamic wave pressures and bottom shear stresses exert on the surface of seabed.The bottom shear stresses provide a horizontal loading in the wave-seabed interaction system,while dynamic wave pressures provide a vertical loading in the system.However,the bottom shear stresses have been ignored in most previous studies in the past.In this study,the effects of the bottom shear stresses on the dynamic response in a seabed of finite thickness under wave loading will be examined,based on Biot’s dynamic poro-elastic theory.In the model,an "u-p" approximation will be adopted instead of quasi-static model that have been used in most previous studies.Numerical results indicate that the bottom shear stresses has certain influences on the wave-induced seabed dynamic response.Furthermore,wave and soil characteristics have considerable influences on the relative difference of seabed response between the previous model(without shear stresses) and the present model(with shear stresses).As shown in the parametric study,the relative differences between two models could up to 10% of p0,depending on the amplitude of bottom shear stresses.     

Viscous effects on the non-classical Rayleigh–Taylor instability of spherical material interfaces

The viscous and conductivity effects on the instability of a rapidly expanding material interface produced by a spherical shock tube are investigated through the employment of a high-order WENO scheme. The instability is influenced by various mechanisms, which include (a) classical Rayleigh–Taylor (RT) effects, (b) Bell–Plesset or geometry/curvature effects, (c) the effects of impulsively accelerating the interface, (d) compressibility effects, (e) finite thickness effects, and (f) viscous effects. Henceforth, the present instability studied is more appropriately referred to as non-classical RT instability to distinguish it from classical RT instability. The linear regime is examined and the development of the viscous three-dimensional perturbations is obtained by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the viscous effects on the growth of the disturbances for various conditions. The inviscid analysis does not show the existence of a maximum amplification rate. The present viscous analysis, however, shows that the growth rate increases with increasing the wave number, but there exists a peak wavenumber beyond which the growth rate decreases with increasing the wave number due to viscous effects.     

Investigating the effects of shear rate on the collapse time in a gas–liquid system by lattice Boltzmann

In order to evaluate the effects of shear rate on the time of collapse process in a two-phase; one component system, a free energy lattice Boltzmann model is developed. Considering a system consists of two droplets in the surrounding vapor it is observed that, for various physical and geometrical conditions, imposing shear flow has similar effects on the collapse time. Actually, for each case there is an optimum shear rate of collapse that is corresponded to highest collapse rate and smallest time. In all test cases, for shear rates smaller than the optimum value, increasing the shear rate raise collapse rate and reduce its time. But for higher shear rates, increasing the shear rate has reverse effect and decreases the collapse rate. The results also show that, higher droplet radius ratio, viscosity ratio, surface tension and interface thickness lead to a higher optimum shear rate of collapse while higher density ratio of liquid and vapor decreases that.     

DEM speedup： Stiffness effects on behavior of bulk material

A number of techniques exist for minimizing the computational cost of discrete element simulations （DEMs）. One such method is a reduction of particle stiffness, which allows for bigger time steps and therefore fewer iterations in a simulation. However, the limits and drawbacks of this approach are still unclear, and may lead to invalid results. This paper investigates the effect of a stiffness reduction on bulk behavior by examining three case studies. Two cases demonstrate that particle stiffness can be reduced without affecting the bulk material behavior, whereas the third test shows that a stiffness reduction influences the bulk behavior.     

Elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient

The elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient has been analyzed by using Seth’s transition theory and generalized strain measure. It has been observed that disc made of beryl and magnesium materials requires higher angular speed to yield at the inner surface in comparison to the disc made of brass material. The radial stress has a maximum at the internal surface of the disc made of beryl, magnesium and brass materials, but circumferential stress neither maximum nor minimum at this surface. With the introduction of thermal effect, the value of circumferential stress has a maximum at the external surface of the disc made of the beryl and magnesium, but the reverse results are obtained for the disc made of brass material. The combined impacts of temperature and angular speed have been displayed numerically and depicted graphically.

     

Studies on the axisymmetric sphere–sphere interaction problem in Newtonian and non-Newtonian fluids

In this research, experimental studies have been performed on the hydrodynamic interaction between two spheres by using particle image velocimetry and measuring the force between the spheres. To approach the system as a resistance problem, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion. Glycerin and a dilute solution of polyacrylamide in glycerin were used as Newtonian and non-Newtonian fluids, respectively. The polymer solution behaves like a Boger fluid when the concentration is 1000 ppm or less. The experimental results were compared with the asymptotic solution of Stokes equation. The result shows that fluid inertia and unsteadiness play important roles in the particle–particle interaction in the Newtonian fluid. This implies that the motion of two particles in suspension is not reversible even in the Newtonian fluid. In the non-Newtonian fluid, in addition to inertial effect, normal stress differences and viscoelasticity play important roles as expected. In dilute solutions weak shear thinning and the migration of polymer molecules in the inhomogeneous flow field also appear to affect the physics of the problem.     

Generation of a magnetic field in the shear deformation region of a conducting material upon high–velocity penetration

It is shown that when a high–velocity impactor penetrates into a conducting target with a transverse magnetic field, conditions for considerable field amplification are produced in the shear deformation region on the lateral surface of the impactor. Field generation in a conducting medium deformed in shear is considered within the framework of a plane one–dimensional problem of magnetohydrodynamics. The results obtained indicate that along the boundary of the cavity produced by the impactor in the target with a magnetic field, a thin layer with a very high field intensity (about 100 T) is formed. The possibility of explosion of this layer due to the magnetic pressure acting in it is analyzed.     

Average and extremal properties of heat transfer and shear stress on a wall surface in Rayleigh–Bénard convection

In this study surface-averaged and extremal properties of heat transfer and shear stress on the upper wall surface of Rayleigh–Bénard convection are numerically examined. The Prandtl number was raised up to 10³, and the Rayleigh number was changed between 10⁴ and 10⁷. As a result, average Nusselt number Nu and shear rate τ/Pr depends on Pr, Ra, and the entire numerical results are distributed between two correlation equations corresponding to small and large Pr. The small and large Pr equations are closely related to steady and unsteady flow regimes, respectively. Nevertheless, a single relation τ/Pr ~ Nu ^3.0 exists to explain the entire results. Similarly the change of local maximal properties Nu _max and τ _max/Pr depends on Pr, Ra, and these values are also distributed between two correlation equations corresponding to small and large Pr cases. Despite such complicated dependence we can obtain a correlation equation as a form of τ _max/Pr ~ Nu _max^2.6, which has not been obtained theoretically.     

Rayleigh–Taylor instability of immiscible fluids in porous media

The time development of an interface separating two immiscible fluids of different densities in heterogeneous two-dimensional porous media is studied. The governing equations are simplified with the help of approximate Green’s functions which allow computation of the shape of the interface directly without resolving the fluid flow in the entire domain. The new formulation is amenable to numerical approximation, and the reduction in dimension leads to a significant gain in efficiency in the numerical simulation of the interfacial dynamics. Several test cases are investigated, and the numerical solutions are compared to known exact solutions and experimental data.     

Effect of Conduction in Bottom Wall on Darcy–Bénard Convection in a Porous Enclosure

Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K _r ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure.     

Grain–boundary interactions and orientation effects on crack behavior in polycrystalline aggregates

A dislocation-density grain–boundary interaction scheme has been developed to account for the interrelated dislocation-density interactions of emission, absorption and transmission in GB regions. The GB scheme is based on slip-system compatibility, local resolved shear stresses, and immobile and mobile dislocation-density accumulation at critical GB locations. To accurately represent dislocation-density evolution, a conservation law for dislocation-densities is used to balance dislocation-density absorption, transmission and emission from the GB. The behavior of f.c.c. polycrystalline copper, with different random low and high angle GBs, are investigated for different crack lengths. For aggregates with random low angle GBs, dislocation-density transmission dominates at the GBs, which can indicate that the low angle GB will not significantly change crack growth directions. For aggregates with random high angle GBs, extensive dislocation-density absorption and pile-ups occur. The high stresses associated with this behavior, along the GBs, can result in intergranular crack growth due to potential crack nucleation sites in the GB.     

“Everything flows?”: elastic effects on startup flows of yield-stress fluids

It is now 30 years since Barnes and Walters published a provocative paper in which they asserted that the yield stress is an experimental artifact. We now know that the situation is far more complicated than understood at the time, and that the mechanics of the solid material prior to yielding must be considered carefully. In this paper, we examine the response of a well-studied “simple” yield-stress material, namely a Carbopol gel that exhibits no thixotropy, and demonstrate the significance of the pre-yielding behavior through a number of elementary measurements.     

Rankine–Hugoniot conditions for fluids whose energy depends on space and time derivatives of density

By using the Hamilton principle of stationary action, we derive the governing equations and Rankine–Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system of equations is a time reversible dispersive system of conservation laws for the mass, momentum and energy. We obtain additional relations to the Rankine–Hugoniot conditions coming from the conservation laws and discuss the well-founded of shock wave discontinuities for dispersive systems.     

Direct numerical simulations of gas–solid–liquid interactions in dilute fluids

The dynamic interactions between gas bubbles, rigid particles and liquid can lead to profound nonlinearities in the aggregate behavior of a multiphase fluid. Predicting the nonlinear dynamics of the multiphase mixture hence requires understanding how the phases interact at the scale of individual interfaces, but these interactions are notoriously difficult to resolve in models. The goal of this paper is to develop and validate a computational method capable of capturing the complex flow interactions between gas bubbles and rigid particles immersed in a Newtonian liquid. We focus on multiphase systems that are dilute enough for the solid and gas components to move through and be moved by the ambient liquid. We use level sets with a topology-preserving advection scheme to track the gas interfaces. To include the motion of the rigid particles, we couple distributed Lagrange multipliers to an immersed-boundary method. The high viscosity contrast between the liquid and the gas requires both time splitting and approximate factorization to efficiently solve the governing equations consisting of the conservation of mass, momentum and energy. To resolve interactions between interfaces that vary drastically in size, we refine our mesh adaptively in the vicinity of the boundary.     

Computing flow-induced stresses of injection molding based on the Phan–Thien–Tanner model

A numerical approach is introduced to solve the viscoelastic flow problem of filling and post-filling in injection molding. The governing equations are in terms of compressible, non-isothermal fluid, and the constitutive equation is based on the Phan–Thien–Tanner model. By introducing some hypotheses according to the characteristics of injection molding, a quasi-Poisson type equation about pressure is derived with part integration. Besides, an analytical form of flow-induced stress is also generalized by using the undermined coefficient method. The conventional Galerkin approach is employed to solve the derived pressure equation, and the ‘upwind’ difference scheme is used to discrete the energy equation. Coupling is achieved between velocity and stress by super relax iteration method. The flow in the test mold is investigated by comparing the numerical results and photoelastic photos for polystyrene, showing flow-induced stresses are closely related to melt temperatures. The filling of a two-cavity box is also studied to investigate the viscoelastic effects on real injection molding.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

Long-term aging effects on the rheology of neat laponite and laponite–PEO dispersions

We observe aging behavior of neat laponite systems over the course of 1,000 or more days. Under basic conditions, low laponite concentrations (1 wt%) slowly evolve from a viscoelastic liquid to a glass made of clusters acting as constituent elements interacting via long-range repulsion. Higher concentrations of laponite (3 wt%) quickly form a glass of individual particles. Intermediate concentrations of laponite form a glass that is a combination of clusters and individual particles. The aging rheological response and upturn of the loss modulus at low frequencies are well predicted by models of soft glassy systems (Fielding et al., J Rheol, 44(2):323–369, 2000; Sollich, Phys Rev E, 58(1):738–759, 1998). If low amounts of high-molecular-weight (M _n ≥ 163 kg/mol) poly(ethylene oxide) (PEO) are added, the aging behavior follows the dynamical response of the clay. Above a critical ratio, φ, of the free polymer chains in solution to the total laponite surface area, the PEO dynamics dominate at high frequencies. It appears that the dynamics of these complex laponite-PEO systems are governed by the parameter φ.