Rheology of carbon black suspensions. III. Sol-gel transition system

Linear viscoelastic properties of carbon black (CB) suspensions with various CB volume fractions () in a rosin-modified phenol resin type varnish (Varnish-1) were investigated at various temperatures (T). The CB/Varnish-1 suspensions exhibited a sol-gel transition on an increase in , and the _gel value at the gelation point decreased with increasing T. This T dependence of _gel, being opposite to the dependence seen for usual gelling systems, can be related to a phenol resin type polymeric component included in the Varnish-1. At low T, this polymeric component appeared to be rather well solvated in the Varnish-1 thereby allowing the gelation due to bare attraction between the CB particles at large . In contrast, at high T, the polymeric component appeared to have been less solvated, as evidence from a moderate failure of the time-temperature superposition of pure Varnish-1 and a decrease of its elasticity (in a shifted frequency scale) with increasing T. This less solvated polymeric component would have been adsorbed on the CB particles, thereby allowing the agglomeration of the particles at small _gel at high T.     

Upscaling of Stochastic Micro Model for Suspension Transport in Porous Media

Micro scale population balance equations of suspension transport in porous media with several particle capture mechanisms are derived, taking into account the particle capture by accessible pores, that were cut off the flux due to pore plugging. The main purpose of the article is to prove that the micro scale equations allow for exact upscaling (averaging) in case of filtration of mono dispersed suspensions. The averaged upper scale equations generalise the classical deep bed filtration model and its latter modifications.     

The influence of wall interaction on dynamic particle modelling of magneto-rheological suspensions between shearing plates

We report on the modelling of a magneto-rheological (MR) suspension bound between shearing parallel plates using a particle-level numerical simulation. The simulation is similar to an approach used previously but includes particle hydrodynamic interaction using elements of the Stokesian-dynamic method. Observations of initially chain-like aggregations are reported, and the evolving morphology of suspension particle clusters is explored. Our early-strain observations concur with the prevailing ideas of experimentalists on the important role that the microstructure has on bulk viscosity. We then study in particular the effects of simulation size and strain on viscosity. While initial viscous response is similar to previously reported observations in the literature, when left to run for longer strains, suspensions evolved into markedly different microstructures from those observed experimentally, or in electro-rheological suspensions, or MR simulations with artificial wall interaction. Substantial qualitative and quantitative divergence was observed over long strains. We argue that this divergence is due to the lack of a particle–wall interaction model for MR fluids. While current theories in MR modelling do not justify the requirement for a particle–wall interaction, these results suggest that one is required in order to match experimental observations.

Non-linear vibrations of suspension bridges with external excitation

Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of non-linear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined.     

悬索桥的非线性分析

为进行悬索桥的几何非线性分析，建立了梁单元的刚度矩阵及有关算法，通过算例验证了方法是可行的。     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process

The rheological characterizations of concentrated suspensions are generally carried out assuming “well-mixed” suspensions. However, the variation of the concentration distributions of the ingredients of the formulation, i.e., the “goodness of mixing”, the size and shape distributions of the particle clusters and the rheological behavior of the suspension all depend on the thermo-mechanical history that the suspension is exposed to during the mixing process. Here, various experimental tools are used for the characterization of the degree of mixedness (concentration distributions) of various ingredients along with the characterization of rheological material functions, wall slip behavior and the maximum packing fraction of a graphite/elastomer suspension. The degree of mixedness values of the ingredients of the suspensions processed using batch and continuous processes and under differing operating conditions were characterized quantitatively using wide-angle X-ray diffraction and thermo gravimetric analysis and were elucidated under the light of the electrical properties of the suspension as affected by the mixing process. Upon achieving better homogeneity of the graphite particles and the binder and decreases in the size and breadth of the size distributions of particle clusters (as inferred from electrical measurements and maximum packing fraction values), the elasticity (storage modulus) and the shear viscosity (magnitude of the complex viscosity from small-amplitude oscillatory shear and shear viscosity from steady torsional and capillary rheometry) of the suspension decreased significantly and the wall slip velocity values increased. These findings demonstrate the intimate relationships that exist between the rheological behavior of concentrated suspensions and the thermo-mechanical history that they are exposed to during the processing stage and suggest that the preparation conditions for suspensions should be carefully selected and well documented to achieve reproducible characterization of rheological material functions.     

Safety and comfort analysis of a 3-D vehicle model with optimal non-linear active seat suspension

A generalized nonlinear model is formulated for the dynamic analysis of suspension seats with passive, semi-active and active dampers. The model incorporates coulomb friction due to suspension linkages and bushings, forces arising from interactions with the elastic limit stops, a linear suspension spring and nonlinear damping force for passive, semi-active and active dampers, while the contribution due to biodynamics of the human operator is considered to be negligible. The semi-active and active dampers are characterized by force generators in accordance with the control laws based upon suspension mass velocity. Two different suspension seats are experimentally assessed in the laboratory under sinusoidal and random excitations arising from an urban bus, and the measured data is used to demonstrate the validity of the proposed generalized model. The results showed reasonably good agreement between the model results and the measured data. Optimal model parameters are selected using the sequential unconstrained minimization technique with an objective to minimize the acceleration due to vibration transmitted to the occupant mass. The comfort and safety performance characteristics of the optimal suspension seat with semi-active and active dampers are evaluated under both the sinusoidal and random excitations based on the guidelines provided by ISO-2631. From these results, it is concluded that the comfort performance of a suspension seat with semi-active and active dampers can be considerably enhanced by 20–30%.     

Rheological characterization of a solder paste for surface mount applications

Solder pastes used in surface mount soldering techniques (SMT) are very complex suspensions containing high volumes of metallic powder in a carrier fluid. The rheological complexity results largely from the carrier fluid itself, which is a suspension of colloidal particles. In this work, we have characterized the rheological properties of a typical carrier fluid and its solder paste containing 64 vol.% metallic powder. A six-blade vane geometry was used to avoid wall slip and sample fracture. All measurements were carried out following pre-shearing and rest time in order to obtain reproducible results. Steady shear experiments showed that the solder paste was highly shear-thinning and thixotropic. In oscillatory shear, the linear viscoelastic domain was found to be very narrow for both the suspending fluid and the paste. Frequency sweep tests in the linear domain revealed a gel-like structure with a nearly constant G′ for the suspending fluid and a slightly increasing G′ for the solder paste. From creep experiments, a yield stress of about 40 Pa was determined for the suspending fluid at temperatures between 25 and 40°C, and of 100 Pa at 4°C. A much larger yield stress, 480 Pa, was determined for the solder paste at 25°C.     

Three-dimensional numerical simulation of drops suspended in simple shear flow at finite Reynolds numbers

A three-dimensional study of suspension of drops in simple shear flow has been performed at finite Reynolds numbers. Results are obtained using a finite difference/front tracking method in a periodic domain. The effects of the Reynolds number and the Capillary number are addressed at two volume fractions: 0.195 and 0.34. It is observed that suspensions of deformable drops exhibit a shear-thinning behavior. Similar to the motion of a single drop, drops migrate away from the walls. The effective viscosity, the first and the second normal stress differences oscillate around a mean value in all cases. The first normal stress difference increases with the Capillary number, the Reynolds number and the volume fraction. Results show that drops deform more and orient more in the flow direction as the Capillary number or the volume fraction is increased. Also, the average size of clusters is smaller than for suspension of rigid particles. The radial dependence of the pair distribution function across the channel has been studied. This dependency shows that the tendency to form clusters is reduced as the Capillary number increases or the volume fraction decreases.