On the viscosity of magnetic fluid with low and moderate solid fraction

The design of a pressurized capillary rheometer operating at prescribed temperature is described to measure the viscosity of magnetic fluids （MFs） containing Fe3O4 magnetic nanoparticles （MNPs）. The equipment constant of the rheometer was obtained using liquids with predetermined viscosities. Experimentally measured viscosities were used to evaluate different equations for suspension viscosities. Deviation of measured suspension viscosities from the Einstein equation was found to be basically due to the influence of spatial distribution and aggregation of Fe3O4 MNPs. By taking account of the coating layer on MNPs and the aggregation of MNPs in MFs, a modified Einstein equation was proposed to fit the experimental data. Moreover, the influence of external magnetic field on viscosity was also taken into account. Viscosities thus predicted are in good agreement with experimental data. Temperature effect on suspension viscosity was shown experimentally to be due to the shear-thinning behavior of the MFs.     

Viscosity of suspensions in polymeric solutions

Viscosities of suspended particles in polymeric solutions depend upon dissolved polymer concentration, volume fraction of particles and shear rate. In this analysis of viscosity data, relative viscosity was defined as the ratio of suspension viscosity to solution viscosity at the same shear stress rather than shear rate. These relative viscosities reached asymptotic values at high shear stress for all concentrations of dissolved polymer and for all particle loadings. At a given particle loading, the asymptotic values of relative viscosity were nearly independent of the concentration of dissolved polymer. Realtive viscosities were correlated with volume fraction by the one-constant equation of Maron and Pierce.     

An experimental study of multimodal glass suspension rheology to test and validate a polydisperse suspension viscosity model

Experimental measurements of non-colloidal multimodal suspension viscosities are performed over a wide range of mixing ratios and used to test the robustness and predictive capability of a recent viscosity model (Mwasame et al. in Phys Fluids 28:061701, 2016b), subsequently referred to as the MWB model. Three unimodally distributed particle suspensions with narrow size distributions are blended to make the bimodal and trimodal suspensions used in the rheological experiments. We demonstrate how predictions for mixture viscosities can be made using the MWB model only requiring the volume-weighted average particle sizes and viscosity correlations of the individual unimodal suspensions comprising the blend. The resultant model predictions are found to be in good agreement with measured bimodal and trimodal viscosity data to within expected experimental uncertainty. The datasets provided here can be used to validate future modeling efforts, and the MWB model can be used to optimize the viscosity of multimodal suspension mixtures for specific performance criteria.     

Viscosity measurement by spheres falling in a magnetic field

A new rheometer suitable for the region of very high viscosities is presented. To measure at reasonable time and avoid degradation of the polymer, gravitational forces on iron spheres are replaced by magnetic ones. The extent of the region depends on the strength of the magnetic field available. The velocity of the falling sphere is measured by interrupting the beam of a He-Ne-Laser which is registrated by a photoresistor. Results are analysed with the help of Stokes' law for falling spheres. By measuring the magnetic forces on the sphere with a special device based on glass springs absolute values of the viscosity are obtained and liquids for calibration are not needed.Dedicated to Prof. Dr. K. Winsauer on the occasion of his 60th birthday     

Elongational viscosity by fiber spinning

Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers.     

Pressure-dependent viscosity and free volume of atactic and syndiotactic polystyrene

The effect of pressure on viscosity is an important but often overlooked aspect of the flow properties of polymeric materials. In this work, two polymers (an atactic and a syndiotactic Polystyrene) were characterized to determine the effect of pressure on viscosity. In particular, a device was adopted to increase the exit pressure of a standard capillary rheometer, thus obtaining data of viscosity under high pressure and high shear rates. The Simha-Somcynsky equation of state was applied to the pressure–volume–temperature experimental data of both materials to obtain the dependence of free volume on temperature and pressure. The Doolittle equation was eventually employed to verify the dependence of viscosity on free volume. It was found that, for both materials, a linear relationship holds between the logarithm of zero-shear-rate viscosity (at several temperatures and pressures) and the inverse of free volume.     

Viscosity of a Newtonian fluid calculated from the deformation of droplets covered with a surfactant under a linear shear flow

The viscosity of small fluid droplets covered with a surfactant is determined using drop deformation techniques. This method, proposed by Hu and Lips, is here extended to the case of the presence of a surface-active adsorpted at the liquid–liquid interface, to consider more general scenarios. In these experiments, a droplet is sheared by another immiscible fluid of known viscosity, both Newtonian liquids. From the steady-state deformation and retraction mechanisms, the droplet viscosity is calculated using an equation derived from the theories of Taylor and Rallison. Although these theories were expressed for surfactant-free interfaces, they can be applied when a surfactant is present in the system if the sheared droplet reaches reliable steady-state deformations and the surfactant attains its equilibrium adsorption concentration. These determinations are compared to bulk viscosities measured in a rheometer for systems with different viscosity ratios and surfactant concentrations. Very good agreement between both determinations is found for drops more viscous than the continuous phase.     

Comparison of schemes for preparing magnetic Fe3O4 nanoparticles

Magnetic Fe3O4 nanoparticles were prepared by means of coprecipitation using NH3·H2O in water and in alcohol, and using NaOH in water. A series of instruments such as SEM, TEM, HRTEM, FT-IR, XRD and VSM were used to characterize the properties of the magnetic nanoparticles.was the longest. The process using NaOH in water was the simplest and the reaction time was the shortest, but the particle characteristics were inferior to those of the other two methods. The mean size of magnetic Fe3O4 nanoparticles prepared by coprecipitation in alcohol was the smallest among the three, but the nanoparticles aggregated severely. The magnetic Fe3O4 nanoparticles were coated with oleic acid using saturated sodium coated successfully and thoroughly.     

Investigation of the stability of a plane-channel suspension flow with account for finite particle volume fraction

Within the framework of the two-fluid approach, a variant of a heterogeneous-medium model which takes into account a finite volume fraction of the inclusions and a small but finite phase velocity slip is proposed. The interphase momentum exchange is described by the Stokes force with the Brinkman correction for the finite particle volume fraction. The suspension viscosity depends on the particle volume fraction in accordance with the Einstein formula. Within the framework of the model constructed, a formulation of the problem of linear stability of plane-parallel two-phase flows is proposed. As an example, the stability of a channel suspension flow is considered. The system of equations for small disturbances with the boundary conditions is reduced to an eigenvalue problem for a fourth-order ordinary differential equation. Using the orthogonalization method, the dependence of the critical Reynolds number on the governing nondimensional parameters of the problem is studied numerically. It is shown that taking a finite volume fraction of the inclusions into account significantly affects the laminar-turbulent transition limit.     

Single-Fluid Model of a Mixture for Laminar Flows of Highly Concentrated Suspensions

A model of laminar flow of a highly concentrated suspension is proposed. The model includes the equation of motion for the mixture as a whole and the transport equation for the particle concentration, taking into account a phase slip velocity. The suspension is treated as a Newtonian fluid with an effective viscosity depending on the local particle concentration. The pressure of the solid phase induced by particle-particle interactions and the hydrodynamic drag force with account of the hindering effect are described using empirical formulas. The partial-slip boundary condition for the mixture velocity on the wall models the formation of a slip layer near the wall. The model is validated against experimental data for rotational Couette flow, a plane-channel flow with neutrally buoyant particles, and a fully developed flow with heavy particles in a horizontal pipe. Based on the comparison with the experimental data, it is shown that the model predicts well the dependence of the pressure difference on the mixture velocity and satisfactorily describes the dependence of the delivered particle concentration on the flow velocity.     

Equibiaxial extensional flow of polymer melts via lubricated squeezing flow. I. Experimental analysis

The technique of lubricated squeezing flow is evaluated using experiments in both constant strain rate and constant stress flows of two low-density polyethylene melts. Experimental parameters that include the lubricant viscosity and sample aspect ratio are systematically varied to examine their effect on the viability of the technique in the linear viscoelastic regime by comparing measured quantities to those predicted by finite linear viscoelastic theory. An evaluation is also made by comparing viscosities measured using the lubricated squeezing flow technique and Meissner's rotating clamp (MAD) rheometer in the non-linear regime. In both cases, deviations between the expected and measured viscosities were observed, indicating that the technique is not applicable to large strains for constant strain rate and constant stress flows. It is suggested that this limit is the result of lubricant thinning. Received: 22 March 2000 Accepted: 31 May 2000     

Composite viscoelasticity in glassy,transitional and molten states

As part of a study of viscous and elastic behaviors, over a range of temperatures from below the glass transition up to the hot melt, we here report steady-shear viscosities at 0.007 to 13 s^?1 and at 160 to 220 °C of polystyrene containing 0 to 60% by mass of 0.18-micron diameter titanium dioxide particles. The materials were shearthinning without a yield stress, with a constant activation energy at constant stress, but having a shear-dependent activation energy at constant shear rate — proportional to the volume fraction of the polymer matrix. Superposition of the flow curves at different temperatures for the unfilled and filled systems was possible. All the data were represented by one equation with four parameters: 1) a shear stress coefficient (units Pa · s²); 2) a characteristic stress level for non-Newtonian behavior, independent of temperature and composition; 3) an activation energy at constant stress; and 4) an Einstein coefficient (or intrinsic viscosity of the filler). Other equations also fitted the data, but the others diverged widely when extrapolated.     

The effect of a magnetic field on the rheodynamic behavior of ferromagnetic suspensions

In this work a simplified analytical model and the results of an experimental investigation of the influence of an external magnetic field on the rheological characteristics of a suspension of iron particles in silicon oil is presented. The particles of iron were approximately of a circular shape, from 3 to 5 μm, with a maximum concentration of 10¹⁰ particles/cm³. The viscosity of the carrying fluid varied from 80 to 240 cP.The experimental channel was located in a closed circuit of forced circulation of the ferromagnetic suspension. The entire length of 750 mm was placed in an area of a homogeneous magnetic field, with the velocity vector of the suspension being perpendicular to the direction of the magnetic field. The strength of the magnetic field could be changed continually from 0 to 9000 G.The results obtained are shown in the form of parametrical dependencies of the rheological characteristics of the ferromagnetic suspension. With that, the concentration of the solid phase of the suspension is parametrically changed, along with the strength of the external magnetic field and the viscosity of the carrying fluid.In the range of parameters studied, the external magnetic field leads to a Bingham character of behavior of the ferromagnetic suspension.     

Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow

The behavior of short glass fiber–polypropylene suspensions in extensional flow was investigated using three different commercial instruments: the SER wind-up drums geometry (Extensional Rheology System) with a strain-controlled rotational rheometer, a Meissner-type rheometer (RME), and the Rheotens. Results from uniaxial tensile testing have been compared with data previously obtained using a planar slit die with a hyperbolic entrance. The effect of three initial fiber orientations was investigated: planar random, fully aligned in the stretching flow direction and perpendicular to it. The elongational viscosity increased with fiber content and was larger for fibers initially oriented in the stretching direction. The behavior at low elongational rates showed differences among the various experimental setups, which are partly explained by preshearing history and nonhomogenous strain rates. However, at moderate and high rates, the results are comparable, and the behavior is strain thinning. Finally, a new constitutive equation for fibers suspended into a fluid obeying the Carreau model is used to predict the elongational viscosity, and the predictions are in good agreement with the experimental data.     

The rheology of suspensions of porous zeolite particles in polymer solutions

We present data and predictive models for the shear rheology of suspended zeolite particles in polymer solutions. It was found experimentally that suspensions of zeolite particles in polymer solutions have relative viscosities that dramatically exceed the Krieger–Dougherty predictions for hard sphere suspensions. Our investigations show that the major origin of this discrepancy is due to the selective absorption of solvent molecules from the suspending polymer solution into zeolite pores. The effect raises both the polymer concentration in the suspending medium and the particle volume fraction in the suspension. Consequently, both the viscosity of the polymer solution and the particle contribution to the suspension viscosity are increased. We propose a predictive model for the viscosity of porous zeolite suspensions by incorporating a solvent absorption parameter, α, into the Krieger–Dougherty model. We experimentally determined the solvent absorption parameter by comparing viscosity data for suspensions of porous and nonporous MFI zeolite particles. Our results are in good agreement with the theoretical pore volume of MFI particles.     

磁悬浮隔振器动态电磁力实验与建模

磁悬浮隔振器的核心部件是电磁作动器,得到其输出电磁力与线圈电流及气隙之间的模型对实现磁悬浮隔振器的主动隔振有着重要的意义.实际系统中,磁悬浮隔振器运动频率对电磁力模型参数有较大影响,为了得到比较精确的符合实际的电磁力模型,对原有模型进行了修正,给出了新的考虑频率因素的修正模型;并且设计了基于MTS809的动态电磁力实验建模方案,直接根据电磁力实时测量数据辨识得到动态电磁力修正模型,而不需要对磁路进行任何假设.实验结果表明,该方法建立的电磁力修正模型更符合实际情况.     

Experimental and conceptual problems in the rheological characterization of wheat flour doughs

Wheat flour dough is an industrially important material and a better understanding of its rheological behavior could have long ranging impact on the agricultural and the food processing industries. However, rheological characterization of dough is proving to be difficult due to a range of testing issues and anomalies in flow behavior. In a cone-and-plate rheometer wheat flour doughs “roll-out” of the gap before steady state viscosities can be established, as discussed by Bloksma and Nieman (1975). However, the mirror image of the transient viscosity-time plot obtained using a cone-and-plate viscometer has been used to obtain an estimate of steady shear viscosity behavior (Gleissle, 1975). To check this transient methodology for doughs, a second method, in addition to cone-and-plate transient flow, for determination of the shear viscosity, was needed. For this, capillary extrusion was chosen. Both a piston-driven and pressure driven capillary rheometer were employed. End corrections were determined to provide information on both the shear viscosity and, following Binding (1988), the extensional viscosity of the doughs. There are few data available on end corrections for doughs, though published data by Kieffer indicate that the corrections are unexpectedly very high. In this present work it was found that the end correction experiments were very difficult and imprecise in part due to the time-dependent nature of the doughs and difficulties in preparing replicate batches required to compare dies of differing L/R values. Further it was unexpectedly found that the samples, though prepared by normal mixing procedures to the “optimum” level, were so heterogeneous that large fluctuations in the pressure at constant output rate (in the piston-driven rheometer) and in output rate at constant pressure (in the pressure-driven instrument) were observed. These fluctuations could be eliminated by overmixing of the doughs, but overmixed doughs are of little practical interest. Although the problems encountered in this work were significant, it was encouraging that even these preliminary studies indicate that rheological measurements are effective in differentiating between spring and winter wheats. Defining a constitutive model for dough rheology still remains a major challenge, as results from one type of testing do not corroborate the findings from a different type of testing. Received: 19 May 1998 Accepted: 27 July 1998