Experimental and numerical investigation on mixing and axial dispersion in Taylor–Couette flow patterns

Taylor–Couette flows between two concentric cylinders have great potential applications in chemical engineering. They are particularly convenient for two-phase small scale devices enabling solvent extraction operations. An experimental device was designed with this idea in mind. It consists of two concentric cylinders with the inner one rotating and the outer one fixed. Moreover, a pressure driven axial flow can be superimposed. Taylor–Couette flow is known to evolve towards turbulence through a sequence of successive hydrodynamic instabilities. Mixing characterized by an axial dispersion coefficient is extremely sensitive to these flow bifurcations, which may lead to flawed modelling of the coupling between flow and mass transfer. This particular point has been studied using experimental and numerical approaches. Direct numerical simulations (DNS) of the flow have been carried out. The effective diffusion coefficient was estimated using particles tracking in the different Taylor–Couette regimes. Simulation results have been compared with literature data and also with our own experimental results. The experimental study first consists in visualizing the vortices with a small amount of particles (Kalliroscope) added to the fluid. Tracer residence time distribution (RTD) is used to determine dispersion coefficients. Both numerical and experimental results show a significant effect of the flow structure on the axial dispersion.     

The flow of suspensions through tubes: V. Inertial effects

The behavior of particles undergoing Couette and Poiseuille flows at rates when inertial effects become significant was investigated. The rotation of rigid particles was similar to that in the Stokes flow regime, except for a drift of cylinders to limiting rotational orbits corresponding to the maximum energy dissipation. In Poiseuille flow, rigid particles migrated to an equilibrium radial position which depended on the density difference of two phases, the directions of sedimentation velocity and flow, and the ratio of particle to tube radius. Neutrally buoyant deformable particles always migrated to the tube axis. In concentrated suspensions a plasmatic layer developed near the tube wall as a consequence of radial migration. The formation of this layer modified the velocity profile and caused a reduction in the apparent viscosity coefficient.     

Smoothed particles as a non-Newtonian fluid: A case study in Couette flow

The rheological behavior in a two-dimensional Couette flow simulated using smoothed particle hydrodynamics (SPH) is studied. Newtonian behavior is found to be conditional and shear thinning is significant, leading to a non-linear relationship between apparent viscosity and shear rate, which can be well described by the Sisko model. The transient layered structure of particles with corresponding distortion in velocity profile is observed. The possibility of utilizing this inherent property of SPH for the simulation of non-Newtonian fluids is prospected finally.     

DROP PRODUCTION IN COUETTE AND MEDIA MILL DEVICES

The media mill is a device used in the paint and pigment industry for mixing and dispersing solid/liquid mixtures. The media consists of spheres which are agitated in a vessel and the hydrodynamic interactions between these media spheres cause the fine-scale dispersion. The details of the flow are very complex. A technique to characterize the dispersion efficiency of a media mill is presented which involves monitoring the maximum drop diameters of a dispersed organic phase in an aqueous continuous phase. The largest surviving drops reflect the maximum shear and elongation fields that exist in the flow. The maximum drop size scales as impeller speed to the -0·82 power. This dependence is much lower than the dependence for a Rushton turbine in a tank, which would be -1·38. The mechanism of breakup is clarified by experiments in a Couette geometry for large drop size to gap ratios, where the dependence of drop size on shear rate also scales to the -0·82 power. An analysis of the hydrodynamics involved in two approaching spheres explains the similarity between drop formation in a media mill and the narrow gap Couette cell; drop-solid surface interactions strongly influence breakup in both geometries.     

新颖环形喷动床颗粒喷动特性实验研究

一种新颖的环形喷动床由内外两个不同内径、同心的垂立圆筒组成,在环形空间底部设置多个喷口,在喷口两侧布置倾斜的导流板.研究颗粒在这种喷动床内的流动特性,探讨喷口结构、颗粒种类以及床内载料量对环形喷动床颗粒喷动特性的影响.实验结果表明:颗粒在环形喷动床内分为三个明显不同的区域,即颗粒填充移动区、密相喷动流化区以及稀相夹带区.当颗粒出现分区喷动后,随床内载料量的增多,填充移动区的高度维持不变,始终等于导流板的高度,而密相喷动区的高度不断增加.风量和颗粒种类对床层最大喷动量、密相喷动高度以及床层压力分布规律有着十分重要的影响.采用不同的喷口结构时,在相同的载料量下,直向喷口的密相喷动区高度更大,而且床内各测点的平均压力大于采用斜向喷口时的相应测点压力.     

Numerical Simulation of Taylor–Couette Flows with Rotating Outer Wall Using a Hybrid Spectral/Finite Element Method

Theoretical Foundations of Chemical Engineering - Taylor–Couette flow between independently rotating cylinders with a relatively small aspect ratio Γ = 2.4 has been investigated...     

CFD simulation of Taylor–Couette flow in scraped surface heat exchanger

The flow between two concentric cylinders which is termed as Taylor–Couette flow has been studied in scraped surface heat exchanger with and without blades. Shear rate in annular flow with and without blades was measured by Dumont et al. (2000a) using electrochemical method and determined the onset of Taylor vortices at specific Taylor number in both cases for Newtonian flow. CFD simulations have been carried out to determine the transition zone from laminar Couette flow to Taylor vortex flow using the same geometry for which Dumont et al. (2000a) had carried out the experiments. The Reynolds stress model (RSM) and k–? model are used for Taylor vortex flow (Ta > 300) to characterize the flow pattern in annular flow and SSHE respectively. The aim of the present work is to analyze the effect of rotating scraper on the existing flow patterns in simple annular flow using CFD simulations.     

Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow

In this study, the Lattice Boltzmann (LB) method is applied for computer simulation of suspension flow in Couette systems. Typical aspects of Couette flow such as wall effects and non-zero Reynolds numbers can be studied well with the LB method because of its time-dependent character. Couette flow of single, two and multi-particle systems was studied, where two-dimensional (2D) systems were compared with three-dimensional (3D) systems.Computations on multi-particle 3D suspensions, for instance to assess the viscosity or shear-induced diffusivity, were found to be very intensive. This was only partly a consequence of the 3D system size. The critical particle grid size, necessary for accurate results, was found to be relatively large, increasing the system to impractical sizes.It is however demonstrated that it is possible to carry out computer simulations on 2D suspensions and use relatively simple, linear scaling relations to translate these results to 3D suspensions, in this way avoiding intensive computations. By doing so, the LB method is shown to be well-suited for study of suspension flow in Couette systems, particularly for aspects as particle layering near solid walls, hydrodynamic particle interactions and viscous stresses at non-zero Reynolds numbers, which cannot be easily solved with alternative methods. It also opens the way to employ the LB method for other unexplored aspects, such as particle polydispersity and high Reynolds number flow, with large relevance to practical processing of suspensions.     

Domain nucleation dictates overall nanostructure in composites of block copolymers and model nanorods

The detailed nanostructure of composites formed from block copolymers and nanoparticles is known to depend sensitively on the preferred morphology of the block copolymer, on the shapes of the particles, and on interactions between the two components. But it can also depend on the kinetics of self-assembly in the polymer, and there are circumstances under which the kinetics of morphologically selective domain nucleation and growth determine the overall nanostructure of the composite. To study the mechanism of morphological seeding in block-copolymer nanocomposites, we have combined cylinder phases of polystyrene-block-polyisoprene diblock (as a solution in dibutylphthalate) and poly(styrene-block-isoprene-block-styrene) triblock (as a blend with homopolystyrene) copolymers with gold nanorods of different diameters and surface treatments. Polarized optical microscopy and transmission electron microscopy on these composites demonstrate that the nanorods selectively nucleate coaxial domains of copolymer cylinders (i.e., domains of cylinders aligned along the same axis as the nanorod). These single nucleation events occur regardless of nanorod diameter and surface character, and determine the order of most of the surrounding polymer. Mesoscale modeling of the nucleation process, performed with nanorods of different diameters and with different polymer-surface interactions, illustrates the mechanism by which copolymer-dispersed nanorods with different sizes and surface chemistry can template the organization of cylindrical copolymer domains.     

二维环形Couette设备中剪切引起的二维圆形固粒迁移的动态数值模拟

The shear-induced migration of neutrally-buoyant non-colloidal circular particles in a two-dimensional circular Couette flow is investigated numerically with a distributed Lagrange multiplier based fictitious domain method.The effects of inertia and volume fraction on the particle migration are examined.The results indicate that inertia has a negative effect on the particle migration.In consistence with the experimental observations,the rapid migration of particles near the inner cylinder at the early stage is observed in the simulation,which is believed to be related to the chain-like clustering of particles.The migration of circular particles in a plane Poiseuille flow is also examined in order to further confirm the effect of such clustering on the particle migration at early stage.There is tendency for the particles in the vicinity of outer cylinder in the Couette device to pack into concentric rings at late stage in case of high particle concentration.     

Dynamics of Capillary Electrochromatography: Experimental Study of Flow and Transport in Particulate Beds

The chromatographic performance with respect to the flow behavior and dispersion in fixed beds of nonporous and macroporous particles (having mean intraparticle pore diameters of 41, 105, and 232 nm) has been studied in capillary HPLC and electrochromatography. The existence of substantial electroosmotic intraparticle pore flow (perfusive electroosmosis) in columns packed with the macroporous particles was found to reduce stagnant mobile mass transfer resistance and decrease the global flow inhomogeneity over the column cross‐section, leading to a significant improvement in column efficiency compared to capillary HPLC. The effect of electroosmotic perfusion on axial dispersion was shown to be sensitive to the mobile phase ionic strength and mean intraparticle pore diameter, thus, on an electrical double layer interaction within the particles. Complementary and consistent results were observed for the average electroosmotic flow through packed capillaries. It was found to depend on particle porosity and distinct contributions to the electrical double layer behavior within and between particles. Based on these data an optimum chromatographic performance in view of speed and efficiency can be achieved by straightforward adjustment of the electrolyte concentration and characteristic intraparticle pore size.     

Circular couette flow of a polymerizing fluid

Flow of a polymerizing fluid between rotating concentric cylinders has been analyzed theoretically. A solution has been obtained employing a finite difference method. Using a RIMtype (reaction injection molding) urethane system as an example, the velocity, temperature, and NCO group concentration fields have been described as functions of time. A numerical example is given to demonstrate the applicability of the present analysis to reactive processing and viscometry. The mixing characteristics and the flow rate associated with circular drag flows involved, e.g., in reactive extrusion, have been shown to depend strongly on the operating conditions. It has also been demonstrated that the range of applicability of Couette viscometers to fast curing systems may be limited by the interfering time-dependent temperature gradients involved. It has been concluded that analysis of the. present nature provides a useful design and evaluation tool applicable to Couette flow problems in reactive processing and viscometry.     

Slow and intermediate flow of a frictional bulk powder in the Couette geometry

Most current research in the field of dry, non-aerated powder flows is directed toward rapid granular flows of large particles. Slow, frictional, dense flows of powders in the so-called quasi-static regime were also studied extensively using Soil Mechanics principles. The present paper describes the rheological behavior of powders in the “intermediate” regime lying between the slow and rapid flow regimes. Flows in this regime have direct industrial relevance. Such flows occur when powders move relative to solid walls in hoppers, bins and around inserts or are mixed in high and low shear mixers using moving paddles. A simple geometry that of a Couette device is used as a benchmark of more complicated flows.The constitutive equations derived by Schaeffer [J. Differ. Equ. 66 (1987) 19] for slow, incompressible powder flows were used in a new approach proposed by Savage [J. Fluid Mech. 377 (1998) 1] to describe flows in the intermediate regime. The theory is based on the assumption that both stress and strain-rate fluctuations are present in the powder. Using Savage's approach, we derive an expression for the average stress that reduces to the quasi-static flow limit when fluctuations go to zero while, in the limit of large fluctuations, a “liquid-like”, “viscous” character is manifested by the bulk powder.An analytical solution of the averaged equations for the specific geometry of the Couette device is presented. We calculate both the velocity profile in the powder and the shear stress in the sheared layer and compare these results to experimental data. We show that normal stresses in the sheared layer depend linearly on depth (somewhat like in a fluid) and that the shear stress in the powder is shear rate dependent. We also find that the velocity of the powder in the vicinity of a rough, moving boundary, decays exponentially so that the flow is restricted to a small area adjacent to the wall. The width of this area is of the order of 10-13 particle diameters. In the limit of very small particles, this is tantamount to a shear band-type behavior near the wall.     

EXTRUSION AND LUBRICATION FLOWS OF VISCOPLASTIC FLUIDS WITH WALL SLIP

The simplest model flow which approximates the extrusion (shallow screw channels) and lubrication flow is the steady, laminar flow occurring between two infinitely long parallel plates i.e., the generalized plane Couette flow. Here we develop an analytical model of the generalized plane Couette flow of viscoplastic fluids. The deformation and flow behavior of viscoplastic fluids can be realistically represented with the Herschel-Bulkley constitutive equation, which we have utilized as the basis for the development of our analytical model. Furthermore, as also demonstrated here, the deformation behavior of viscoplastic fluids is generally complicated by the presence of wall slip at solid walls, which occurs as a function of the wall shear stress. The wall slip versus the wall shear stress behavior of viscoplastic fluids can be experimentally characterized using viscomelric flows, including steady torsional and capillary flows. Thus determined Navier's wall slip coefficient can then be utilized in modeling of processing flows. In our analytical model of the generalized plane Couette flow of viscoplastic fluids the Navier's wall slip boundary condition was included. This model should be an important engineering tool, which provides design expressions for the extrusion and lubrication flows of viscoplastic fluids, with or without wall slip occurring at the walls. @KEYWORDS:Extrusion, lubrication, flow, viscoplastic, slip.     

Steady-state performance of an infinitely fast reaction in a three-dimensional open Stokes flow

We investigate the steady-state performance of a single irreversible mixing-controlled reaction between segregated reactant streams entering the annular gap between coaxial cylinders that can rotate independently. The three-dimensional Stokes flow results from the superposition of a pressure-driven Poiseuille flow along the mixer axis, and a cross-sectional Couette flow generated by the steady rotation of the inner and outer cylinders. Flow protocols associated with different geometries and different conditions of the rotating cylinders are considered. For each protocol, we analyze the axial behavior of reaction yield as a function of the Peclet number, quantifying the relative importance of convective vs. diffusive transport mechanisms. Following a well-established approach developed in the context of closed bounded flows, we connect the steady-state reactor performance with the spectral (eigenvalue-eigenfunction) structure of the advection-diffusion operator restricted to the system cross-section. For slim channels, this approach indicates that reaction performance is controlled by the real part, say -Λ (Λ>0), of the dominant eigenvalue of the advection-diffusion operator, and therefore the quantitative analysis of reaction performance consists of determining how Λ depends on the Peclet number for the assigned protocol. The presence of a nonuniform axial flow makes the spectral analysis different from previous studies focusing on transient mixing in closed two-dimensional autonomous flows in that it transforms the standard eigenvalue-eigenfunction formulation of the problem into a generalized form, where the axial velocity plays the role of weight function for the generic eigenvalue-eigenfunction. This difference is not just formal, as it can give rise to a variety of convection-enhanced regimes which cannot be observed in the standard eigenvalue formulation. Identifying the onset conditions and the range of existence of these regimes could greatly improve the rational design of geometry and operating conditions of micro and ordinary lengthscale continuous reactors operating under laminar flow conditions.     

An Instrument for the Classification of Aerosols by Particle Relaxation Time: Theoretical Models of the Aerodynamic Aerosol Classifier

A new aerosol particle classifier, the aerodynamic aerosol classifier (AAC), is presented and its classifying characteristics are determined theoretically. The AAC consists of two rotating coaxial cylinders rotating at the same angular velocity. The aerosol to be classified enters through a gap in the inner cylinder and is carried axially by particle-free sheath flow. The centrifugal force causes the particles between the rotating cylinders to move in the radial direction and particles of a narrow range of particle relaxation times exit the classifier through a gap in the outer cylinder with the sample flow. Particles with larger relaxation times impact and adhere to the outer cylinder and particles with smaller relaxation times exit the classifier with the exhaust flow. Thus, the aerosol is classified by particle relaxation time from which the aerodynamic equivalent diameter can easily be found. Four theoretical models of the instrument transfer function are developed. Analytical particle streamline models (with and without the effects of particle diffusion), like those often used for mobility classifiers, are developed for the case when the centrifugal acceleration field is assumed to be uniform in the radial direction. More accurate models are developed when this assumption is not made. These models are the analytical limiting trajectory model which neglects the effects of diffusion and a numerical convective diffusion model that does not. It is shown that these models agree quite well when the gap between the cylinders is small compared to the radii of the cylinders. The models show that, theoretically, the AAC has a relatively wide classification range and high resolution.

Copyright 2013 American Association for Aerosol Research     

The experimental transfer function of the Couette centrifugal particle mass analyzer

The Couette centrifugal particle mass analyzer (CPMA) classifies particles by their mass-to-charge ratio. Unlike the aerosol particle mass (APM) analyzer, the Couette CPMA uses a stable system of forces to improve the transfer function of the classifier. A prototype Couette CPMA has been built and tested. The experimental results from the prototype agree well with theory and it is found that indeed the transfer function of the Couette CPMA is better than the APM's. Experimental work is shown using a differential mobility analyzer (DMA) and Couette CPMA to classify polystyrene latex (PSL) and di-2-ethylhexyl sebacate (DEHS) particles. By measuring the mass of PSL particles the absolute uncertainty of the Couette CPMA was found to be 6.7–38% higher in terms of mass (or 2.2–11% higher in terms of equivalent diameter) than the expected value. However, when the DMA–CPMA system was calibrated with PSL particles the density of DEHS particles was measured to within approximately 3% of the expected value.     

The onset of instability in the flow induced by an impulsively started rotating cylinder

The onset of initial instability in a developing Couette flow following the impulsive starting of an inner rotating cylinder is analyzed using linear theory. It is well known that there is a critical Taylor number Ta_c at which Taylor vortices first appear between two concentric cylinders. For Ta>Ta_c Taylor-like vortices occur at a certain elapsed time. In the present study, the critical time t_c to represent the onset of this initiating instability, which then grows as toroidal vortices, is analyzed using propagation theory. For this purpose a self-similar transformation is forced through scaling analysis. The resulting stability criteria compare well with the available experimental data for vortices in water. The new measures represent the onset of the fastest growing instability and also suggest the detection time for the manifestation of secondary flow in the primary time-dependent Couette flow.     

Stimuli-response of chlorosilane-functionalized starch suspension under applied electric fields

Chlorosilane-functionalized starch particles were prepared and adopted as a dry-based potential stimuli-responsive electrorheological (ER) material under an applied electric field. This ER fluid, prepared by dispersing the chlorosilane-functionalized starch particles in silicone oil, is considered to be a smart and intelligent material because the state of fluid changes from liquid-like to solid-like very quickly and reversibly under applied external electric fields. The ER behavior of the chain formation was examined using optical microscopy, while flow curves and dynamic moduli were investigated using a rotational rheometer with a Couette geometry under applied electric field strengths. The fluid exhibited typical ER characteristics of shear-dependent yield stress as a function of electric filed strength with a slope of 2.0, following a polarization model. It was also found that its ER performance was well correlated with the fluid’s dielectric characteristics through Cole–Cole plot.     

Stochastic Modeling of a New Spectrometer

A new spectrometer for classifying aerosol particles according to specific masses is being considered (Ehara et al. 1995). The spectrometer consists of concentric cylinders which rotate. The instrument is designed so that an electric field is established between the cylinders. Thus, aerosol particles injected into the spectrometer are subjected to a centrifugal force and an electric force. Depending on the balance between these two forces, as well as Brownian motion, charged particles either pass through the space between the cylinders or stick to either cylinder wall. Particles which pass through are detected. Given the rotation rate, voltage drop and physical dimensions of the device, we calculate the probability of detection in terms of particle density, diameter and charge. This is the transfer function. In this work, the focus is on situations where Brownian motion is significant. To solve for the transfer function, the trajectory of a particle in the spectrometer is modeled with a stochastic differential equation. Laminar flow is assumed. Further, attention is restricted to spherical particles with uniform density. The equation is solved using both numerical and Monte Carlo methods. The agreement between methods is excellent.