Numerical and experimental study of dispersive mixing of agglomerates

Best paper 2006 award in the Extrusion divisionInternational audienceThe degree of filler dispersion has a major influence on the physical properties of rubber compounds. Typical fillers, e.g. carbon black and silica, are difficult to disperse, particularly if they are fine and low structured. As a result, the quantity of undispersed fillers generally amounts for 1% to 10% of the compound. The elimination, or at least the reduction, of agglomerates will result in rubber parts (e.g. tires, seals, belts) with improved properties and higher reliability. Clearly, a better understanding of the physics of batch mixers would help improve their mixing performance. Due to the complexity of the real process, experiments on a representative device were held from which a model has been deduced. It appears to be a generalization of the law of Kao and Mason, but for high viscous matrices. The next step was to get a model available for statistically large number of pellets as can be found in any sample taken out of the mixer. A statistical approach is used where we define a model describing the evolution of mass density function of agglomerate sizes. Eventually, we implement this model within available numerical simulation tools to estimate dispersion in real mixers

Parental Burnout Around the Globe: a 42-Country Study

High levels of stress in the parenting domain can lead to parental burnout, a condition that has severe consequences for both parents and children. It is not yet clear, however, whether parental burnout varies by culture, and if so, why it might do so. In this study, we examined the prevalence of parental burnout in 42 countries (17,409 parents; 71% mothers; M_{age} = 39.20) and showed that the prevalence of parental burnout varies dramatically across countries. Analyses of cultural values revealed that individualistic cultures, in particular, displayed a noticeably higher prevalence and mean level of parental burnout. Indeed, individualism plays a larger role in parental burnout than either economic inequalities across countries, or any other individual and family characteristic examined so far, including the number and age of children and the number of hours spent with them. These results suggest that cultural values in Western countries may put parents under heightened levels of stress

Finite-element simulation of mixing .1. Two-dimensional flow in periodic geometry

Complex mixing flows and mixing parameters are calculated to evaluate mixing quality on the basis of kinematic parameters together with a statistical analysis. The results allow for a comparative evaluation in terms of geometry and flow parameters. The evaluation is limited to two-dimensional flows with moving boundaries in periodic motion such as the flow in the cross section of a twin-cam mixer. The finite-element calculation requires a remeshing procedure for every time step with special techniques to upgrade mixing variables from one time step to the next. The relative mixing quality of single cam and co- or counterrotating cam devices are compared by evaluating segregation scale, length stretch, and efficiency. The numerical results exhibit a good correspondence with their experimental counterpart

Finite-element simulation of mixing .2. Three-dimensional flow through a kenics mixer

Numerical tools for the analysis of complex 3-D mixing devices were developed Calculations are based on the finite-element method. The flow calculation is combined with that of pathlines for a fairly large number of material points; along these pathlines, relevant kinematic variables, which are then subjected to a statistical treatment, are evaluated. These numerical techniques are applied to the analysis of a Kenics mixer. It is assumed that the geometry is periodic in the axial direction, that is, that the miter contains an infinite number of blades; the finite-element analysis may then be completed on a single wavelength of the geometry. To test the accuracy of the three-dimensional calculation, a Kenics device was mounted in order to mit clays of different colors, and photographs of experimental cross-sections were compared with numerical results showing concentration maps. A statistical treatment was performed on some 8, 000 material points crossing the entry section to evaluate miring quality

Analysis of mixing in corotating twin screw extruders through numerical simulation

Mixing is a major ingredient in many industrial processes to obtain desired and uniform material properties. Nowadays, many materials, pigments, additives, gas or reactants, are mixed to create new products combining the characteristics of different raw materials to obtain specific product properties. The quality of the mixing, i.e. the uniformity of the mixture, is a key issue that will determine the morphology and the properties of the resulting compound [1, 2]. An insight in the physics of mixing is therefore necessary in order to achieve a good quality of mixing or maintain it when scaling equipment, for example. Such information can now be obtained through the numerical simulation of the transient flow in extruder components. To improve greatly the ease of obtaining such information, a new technique introduced in a finite elements software is presented. This technique simplifies the meshing, reduces the meshes needed and eliminates complex remeshing algorithms to simulate flow in screws, pumps and mixing devices. This technique is validated versus traditional simulation methods (i.e. conforming meshes). 3-D transient numerical simulations of two twin screw extruder configurations are then presented. A further quantitative comparison of their mixing behavior is developed as statistical information (of the RTD, deformations, dispersion, etc.) can be obtained to compare both configurations in a synthetic and quantitative way

Non-isothermal modeling of co-rotating and contra-rotating twin screw extruders

The quality of the mixing of different raw materials, i.e. the uniformity of the mixture, is a key issue that will determine the morphology and the specific product properties of the resulting compound [1,2]. Numerical simulation of flow in extruder components provides a new insight, both qualitative and quantitative, into those features. 3-D transient numerical simulations of twin screw extruder (TSE) configurations are presented. A special method, the mesh superposition technique (MST), has been introduced to provide a convenient way to model intermeshing TSEs without involving any remeshing complexity [3]. It has been validated in previous work for isothermal cases [4]. To account for the important non-isothermal effects, the method is compared against numerical and experimental results for additional, non-isothermal validation [5]. We present an analysis of different non-isothermal features that characterize the flow induced by a co-rotating as well as a contra-rotating configuration. Both cases are compared in terms of pressure profiles, temperature fields, resulting torque imposed on the screws and from a mixing point of view to illustrate a typical analysis of different TSEs and provide objective information to select the most appropriate configuration for specific process requirements

Parametric study of the mixing efficiency in a kneading block section of a twin-screw extruder

Twin-screw extruders are often used to distribute and disperse additives into polymers. The mixing efficiency of the extruders highly depends on the geometry of the kneading blocks of the mixing section. In this paper the impact of some geometrical parameters, such as the stagger angle and the width of the discs, are investigated by three dimensional time dependent finite element calculations. Results are obtained with the finite element software Poly-flow. The robustness and the accuracy of the mesh superposition technique is evaluated. It appears that conclusions obtained by the numerical experiments can be used to improve the geometry of the kneading blocks. The mixing efficiency is evaluated by comparing the residence time and the total shear distributions of a large set of virtual particles launched in the flow domain

Numerical simulation of distributive mixing in 3-D flows

A numerical simulation is performed for analysing the mixing of the stirring tank. The influence of the stirring tank geometry and of the Reynolds number is investigated. Statistical tools are used for predicting the evolution of quantities such as area stretch and global mixing efficiency

On the development of secondary motions in straight channels induced by the second normal stress difference: Experiments and simulations

The effect of second normal stress difference is analysed by observing the co-flow of two batches of the same viscoelastic fluid, each with a different pigmentation, in straight ducts. The development of secondary motions is observed by tracking the motion of the interface between both fluids. Numerical simulations are also performed on the basis of a multi-mode differential viscoelastic fluid model and are compared with the experiments. A good agreement is found between the experimental observations and their numerical counterparts. (C) 1997 Elsevier Science B.V