Granular flow and segregation in a four-bladed mixer

In this study, we experimentally examine flow and segregation of granular material in a cylindrical mixer geometry agitated by four 45 pitched blades, which is representative of equipment such as high-shear granulators and filter-dryers. We observe that the free surface of the granular bed deforms, rising where the blades are present and falling between blades passes. Using particle image velocimetry (PIV), we measure the instantaneous, average, and fluctuating velocity fields at exposed surfaces (top surface and near the wall), for both near-monodisperse and polydisperse granular materials. The radial and axial point-velocity profiles indicate three-dimensional recirculation patterns indicative of avalanching and bed penetration. For polydisperse mixtures, we find that depending on the shear rate, different segregation mechanisms can take place. Under low shear, complex lobe and striation segregation patterns occur through stretching and folding due to surface avalanching. This leads to enhanced initial mixing rates in a manner consistent with spontaneous chaotic granular mixing. At high-shear rates, segregation is controlled by the rotation of the blades. As a result, coarse particles have a tendency to migrate both to the free surface and the outer wall independently of initial bed loading conditions.     

The examination of segregation of granular materials in a tumbling mixer

This paper describes the use of a sampling scheme designed to detect segregation of the components of a mixture of granular solids in a horizontal rotating cylinder mixer.     

A study on the mixing of flour in a motionless Sulzer (Koch) mixer using a radioactive tracer

This work was concerned with the evaluation of the motionless Sulzer (Koch) mixer for radial mixing of flour. A radioactive tracer technique was employed. The tracer employed, mainly radiosotope ⁵⁶Mn, was created by neutron activation with a neutron flux of 1.44 × 10¹² n/cm² sec. The method has a high degree of accuracy and the advantage that no physical differences exist between the bulk and tracer materials. The concentration distribution in the radial direction was measured, and the resulting degrees of mixedness of the mixture after passing through the mixer for 1, 2, 3, 5 and 10 passes were determined. The degress of mixedness in the radial direction increased with the number of passes. The experimental results were compared to the same mixture passing through an empty column without mixing elements inserted. The comparison indicated that the mixing elements enhanced the mixing process in a predictable way. Finally, a mechanistic model was developed and verified by the experimental results.     

A modified coalescence—dispersion model for the axial mixing of segregating particles in a motionless mixer

A modified coalescence—dispersion model has been developed for the axial mixing of segregating particle systems in a motionless mixer (Kenics mixer). This model is capable of generating the concentration distribution as a function of time and its applicability is not constrained by the initial concentration distribution in the mixture. Two important parameters in this model are the coalescence rate and the distribution ratio. It has been found that the former can be correlated as a linear function of the number of helices in the mixer, and the latter depends heavily upon the physical properties of the individual particles. The validity of the present model has been tested against the available experimental data [16].     

Stochastic diffusion model of non-ideal mixing in a horizontal drum mixer

Since a non-ideal solid particle system contains particles of different sizes and/or densities, mixing of non-ideal particle systems in a horizontal drum mixer is complex and stochastic in nature. In the present work such non-ideal mixing process has been modeled by the Kolmogorov diffusion equation.Two parameters appearing in the Kolmogorov diffusion equation, the diffusion coefficient and drift velocity, have been determined in this work from one-step tracer experiments, and their physical significances have been discussed. The convective or drift velocity, which varies with respect to the axial position of the mixer, appears to be important in illucidating the non-ideal mixing characteristics. A good agreement between the model and the experimental data has been observed.     

A continuum model for the segregation of bidisperse particles in a blade mixer

The process of blending powders using stirring blades involves complicated granular flows, particle-scale mechanisms, and blade–particle interactions, which is challenging to predict and control. This article proposes a continuum-based model for such a process by incorporating the flow rheology, isotropic particle diffusion and the percolation of granular materials. A method combining finite element method (FEM), finite difference method (FDM), and immersed boundary method (IBM) is developed to numerically implement the continuum model and applied to a cylindrical blade mixer. The model well describes the tempo-spatial distribution of small/large particles in the stirring process, such as the accumulation of small particles in the vicinity of blades. Remarkably, this model can capture the various intricate effects of blade parameters, including the blade rake angle, rotating speeds, filling level, and the friction coefficient of the mixer wall. It is therefore promising for optimizing the blade mixers in industries.     

Stochastic modeling of polymerization in a continuous flow reactor

A stochastic approach, namely, a continuous time Markov chain (Markov process), is employed to analyze and model, in a unified fashion, both polymerization and dispersive mixing in a continuous flow reactor. Results include the distribution of numbers of active and dead polymers with chain length j both inside the reactor and at the exit. This approach can be extended to the determination of the degree of polymerization of a copolymer. Expressions are derived for the mean and variance of the number of monomers of a given type in a copolymer chain. The model can be applied to both the time homogeneous and heterogeneous processes.     

Numerical modeling of the outflow of a viscous liquid from a bulk mixer

The slow flow of a viscous liquid with a free surface in the drain from bulk mixers at a given flow rate is modeled. A mathematical problem is formulated in a creeping-flow approximation. On the basis of the boundary element method, a numerical algorithm for solving the problem in a planar formulation is developed. Parametric studies of the main characteristics of the process as functions of control parameters are performed. Two flow patterns are studied. The dependence of the liquid holdup on control parameters at the moment the free surface reaches the plane of the drain hole is described. The stress distribution in the flow region is found. The calculation results are compared with the data of numerical and physical modeling of the drain in an axysimmetric formulation and also with the solution of the problem in the creeping-flow approximation.     

Stochastic modeling of particle motion along a sliding conveyor

The sliding conveyor consists of a plane surface, known as the track, along which particles are induced to move by vibrating the bed sinusoidal with respect to time. The forces on the particle include gravity, bed reaction force and friction. Because friction coefficients are inherently variable, particle motion along the bed is erratic and unpredictable. A deterministic model of particle motion (where friction is considered to be known and invariant) is selected and its output validated by experiment. Two probabilistic solution techniques are developed and applied to the deterministic model, in order to account for the randomness that is present. The two methods consider particle displacement to be represented by discrete time and continuous time random processes, respectively, and permits analytical solutions for mean and variance in displacement versus time to be found. These are compared with experimental measurements of particle motion. Ultimately this analysis can be employed to calculate residence‐time distributions for such items of process equipment. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Nonisothermal modeling of heat transfer inside an internal batch mixer

A nonisothermal transient process of temperature increase due to viscous heating was simulated for a 69 cm³ internal batch mixer (BM) using a computational fluid dynamics (CFD) software, Polyflow 3.9 form ANSYS, Inc., to obtain the temporal temperature distribution and characterize the heat transfer between polymer melt and mixer wall. The melt temperature obtained from simulation was verified with experiments. Starting from a uniform temperature of 463 K, when a rotation speed of 5.24 rad/s is imposed, viscous heating caused a maximum temperature rise of 3 K for a polyethylene (PE) resin, and 6 K for a polystyrene (PS) resin. The transient flow fields inside the batch mixer were characterized with velocity profiles and a mixing index parameter, which show that laminar flow dominates inside the mixer while a small percentage of elongational flow, converging flow, and recirculation flow is also present. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Heat transfer during polymerization in motionless mixers

Investigation of the performance of a large-diameter conventional motionless mixer used as a continuous reactor for styrene polymerization showed that it behaved adiabatically. Computer simulation (in which the mixer is treated as an ideal plug-flow reactor having perfect radial mixing) predicts this tendency in terms of axial temperature profile. To avoid adiabatic polymerization, with its attendant problems of plant operability and polymer quality, the use of motionless mixers having internal heat transfer surface is indicated.     

Stochastic modeling and simulation of photopolymerization process

In this study, the effect of photoinitiator concentration on the gelation time of different resins were studied in the absence of oxygen in the reaction volume by using passive microrheology technique. Four different monomers which are ethoxylated pentaerythritol tetraacrylate (SR494), trimethylolpropane triacrylate (SR351), triethylene glycol diacrylate (SR272), and 2(2‐ethoxyetoxy) ethyl acrylate (SR256) were used in these experiments. Resins were prepared from these four different monomers by mixing them with various amount of 2,2‐dimethoxy 1,2‐diphenylethanone photoinitiator molecule with high absorption coefficient at the frequency of UV light used in these experiment. The simulations of the results obtained from microrheology experiments were carried out with the new model based on the stochastic Monte Carlo approach in order to account for the inherently random and discrete nature of the photopolymerization reactions. The model captures the nonlinear decrease of gelation time with increasing photoinitator concentration and number of acrylate fragments on each monomer. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

Stochastic modeling of bubble formation on the grid in a gas-solid fluidized bed

Bubble formation on the grid in a three-dimensional fluidized bed was studied by means of a mini-capacitance probe coupled with the on-line correlation technique. Experiments were carried out in fluidized beds with relatively shallow bed heights of 50, 80 and 100 mm. The present study has confirmed the well-known observation that bubbles detach from the end of a jet with a formation frequency of about 19 Hz. The stochastic process proposed, more specifically, a renewal counting process corresponding to the gamma distributed inter-arrival times, has been found to describe the process of bubble formation well.     

Hydrodynamic modeling of particle rotation for segregation in bubbling gas-fluidized beds

A multi-fluid Eulerian model has been improved by incorporating particle rotation using kinetic theory for rapid granular flow of slightly frictional spheres. A simplified model was implemented without changing the current kinetic theory framework by introducing an effective coefficient of restitution to account for additional energy dissipation due to frictional collisions. Simulations without and with particle rotation were performed to study the bubble dynamics and bed expansion in a monodispersed bubbling gas-fluidized bed and the segregation phenomena in a bidispersed bubbling gas-fluidized bed. Results were compared between simulations without and with particle rotation and with corresponding experimental results. It was found that the multi-fluid model with particle rotation better captures the bubble dynamics and time-averaged bed behavior. The model predictions of segregation percentages agreed with experimental data in the fluidization regime where kinetic theory is valid to describe segregation and mixing.     

Stochastic modeling of a fluid batch mixed system with variable dispersion coefficient

This contribution presents the numerical solution of the one-dimensional stochastic differential equation with a diffusion coefficient which is a function of the spatial coordinate, as a model of a fluid batch system stirred by a rotating mechanical impeller. It is demonstrated that neither the Ito nor the Stratonovich methods of solution, which are widely used to solve equations of this kind, lead to a uniform distribution of concentration of the blended species component at steady-state. A method of solution is suggested, with the aid of the so-called transport integral, which converges to the uniform steady-state distribution, consistent with the physical conception of the course of the mixing process.     

Experiments and modeling of flow of elastomers in an internal mixer with intermeshing rotors

The direct observation of flow in the internal mixer with various rotor geometries is described. With decreasing distance between two rotors, additional transfer flow was observed in the inter-rotor area. The FAN (Flow Analysis Network) method with assumption of fully filled, Newtonian fluid and isothermal condition was employed to simulate the flow patterns in the mixer with non-intermeshing and intermeshing rotors. The distributive mixing capability was considered in terms of the fractional flow in the mixer calculated for various rotor geometries.     

撞击流气化炉内颗粒停留时间分布的随机模拟

根据多喷嘴对置式气化炉流场测试,将气化炉划分为若干区域,运用时间离散、状态离散的马尔可夫链随机模型,模拟了气化炉内颗粒相的停留时间分布(RTD)。当颗粒在撞击区和射流区间的回流比为0.5,向下撞击流股区和管流区为平推流模型,其他区域按全混流模型处理时,模拟值与实验值吻合较好。随着进料流量的增大,平均停留时间减小,量纲1方差减小;随着回流比的增加,平均停留时间增大;气固两相平均停留时间接近,但RTD存在一定差异。     

Mass transfer in bubble columns packed with motionless mixers

The cocurrent upward mode was employed to absorb pure oxygen into water in bubble columns packed with Koch (Sulzer) motionless mixers. The liquid-side volumetric mass transfer coefficient, K_La, in the packed bubble column was found to be always larger than that in the unpacked bubble column. In the range of liquid velocities from 6.7 cm/sec to 39.9 cm/sec, the value of K_La in the packed bubble column increased with the increasing liquid velocity while that in the unpacked bubble column was almost independent of the liquid velocity. The equation of the formK_La= mν_l^β? was successfully adopted to correlate the K_La data.