A model for gas-solid flow in a horizontal duct with a smooth merge of rapid-intermediate-dense flows

Granular flow in the rapid flow regime is dominated by particle-particle collisions and the constitutive relations for the solid stress are obtained from the classic kinetic theory of granular flow. In the dense flow regime, on the other hand, particles interact via enduring contacts and the solid stress can be deduced from soil mechanics theories. In this paper, constitutive equations, recently proposed by Tardos et al. [2003. Slow and intermediate flow of frictional bulk powder in the Couette geometry. Powder Technology 131, 23-39.] has been incorporated in the simulation of gas-solid flow in a horizontal duct. These equations smoothly merge the rapid granular flow solution with the so-called “intermediate” regime (where both kinetic/collisional and frictional contributions might play a role) and reduce to Coulomb yield condition for slow frictional flow (shear rate → 0). The results of this new modelling approach have shown good qualitative agreement with the reported experimental observation on wide range of gas-solid flow conditions. In this study, we also present the definition of boundaries between rapid-intermediate-dense flow regimes based on the dimensionless shear rate (λ), and a modified Reynolds number (Re). We have shown that the intermediate flow regime can be classified at approximately 0.1<λ<1.0 and 100<Re<3000.     

Development of a virtual Couette rheometer for aerated granular material

A novel rheometer to study the behavior of granular materials in an aerated bed of particles has been developed. The device, called the aerated bed virtual Couette rheometer, is shown to be able to measure the shear stresses in the quasi-static and in the intermediate flow regimes. To validate the instrument, a Newtonian fluid of known viscosity was first sheared. The device was then used for measuring the shear stress of nonaerated glass beads with three -3D printed cells of different sizes to validate the optimal radial position, r*, where both shear rate and shear stress are independent of the cell radius. The results for the nonaerated glass beads displayed Coulomb behavior. The same behavior was observed when the bed was aerated. These experiments also showed that for a fixed shear rate the shear stress decreases as the aeration velocity, U. increases.     

An investigation of frictional and collisional powder flows using a unified constitutive equation

This is an experimental and numerical study of dry, frictional powder flows in the quasi-static and intermediate regimes using the geometry of the Couette device. We measure normal and shear stresses on the shearing surface and extract from the data, constitutive equations valid in the slow frictional, quasi-static and the intermediate (dense), collisional regimes of flow. This constitutive equation is then used in a new, specially developed FEM solver (FeatFlow—Ouazzi et al., 2005 [18]) to obtain solutions of the continuum equations of motion as well as stress and velocity distributions in the powder. While the measurements to obtain the constitutive equation are performed in a concentric Couette device, the numerical scheme is used to predict the torque and stresses in two additional geometries. These geometries are an eccentric Couette where the inner, rotating cylinder is placed off-center with different eccentricities and a more complicated geometry where a cylindrical body is introduced in the middle between the rotating and stationary cylinders and obstructs part of the shearing gap. The purpose of these calculations is to show the versatility of the numerical solution.     

Shear flow of assemblies of cohesive granular materials under constant applied normal stress

We have studied plane shear flow of nearly homogeneous assemblies of uniformly sized, spherical, cohesive particles in periodic domains under constant applied normal stress. Our focus has been on (a) exploration of the effect of inter-particle attractive forces on the flow behavior manifested by dense assemblies under constant applied normal stress, and (b) comparison of the rheological characteristics observed under constant-applied normal stress and constant-volume conditions. As a model problem, the cohesion resulting from van der Waals force acting between particles is considered. Simulations were performed for different strengths of cohesion, shear rates, and applied stresses. From each simulation, the volume fraction, shear stress and the average coordination number have been extracted. We find that cohesive assemblies sheared under constant applied normal stress shear differently from those sheared at constant volume only in the dynamic sense, while the time-averaged rheological characteristics are essentially indistinguishable. At constant volume, the fluctuations in shear stress are larger than, but have the same dependence on cohesion as under constant applied normal stress. This study has also exposed a pronounced dependence of the apparent coefficient of friction on particle volume fraction in the quasi-static flow regime.     

Avalanching flow of cohesive powders

The flow dynamics of cohesive powders is investigated in rotating cylinders with an L : R ratio of 3 : 1 using experiments and DEM simulations. Flow onset and steady-state behavior are compared for free-flowing (cohesionless) dry glass beads, wet glass beads, and “dry” cohesive powders (lactose, microcrystalline cellulose). The avalanching dynamics of powders is substantially different from those observed for free-flowing or wet-cohesive glass beads. Dry cohesive powders exhibit history-dependent flow dynamics, significant dilation, aperiodic avalanche frequencies, and variable avalanche size. These behaviors also provide a route for effective characterization of cohesive forces under dilated conditions characteristic of unconfined flows.     

Rheological behavior of cement pastes from MRI velocimetry

From MRI measurements, it is shown that in a flowing cement paste the thixotropic effects dominate over short time scales, while aging effects become significant over larger timescales. The steady state behavior, defined as flow properties in the intermediate period, exhibits a yielding behavior which differs from the prediction of usual yield stress models. The transition from the “solid” to the “liquid” regime is abrupt: the shear rate changes suddenly from zero to a finite value (critical shear rate) when the shear stress overcomes a critical value. These critical shear rates and shear stresses are independent of the flow conditions so that they may be considered as intrinsic material parameters. It was also shown that these results are consistent with usual macroscopic observations from conventional rheometry.     

Dry water: From physico-chemical aspects to process-related parameters

Water-rich powders known as “dry water” consist of aqueous liquid droplets encapsulated by a protective shell formed by self-assembled superhydrophobic nanoparticles. The water-rich product contains considerable amounts of aqueous liquids (up to 98% w/w). However, despite this large amount of liquid, the product possesses the same flow properties as a dry powder. Water can easily be released by mechanical stress, e.g. by rubbing it onto the skin. The process does not make use of any organic solvent and can easily be developed on an industrial scale. Although “dry water” has been known since the 1960s, it is only recently that fundamental aspects of water encapsulation in dry water have been studied. This paper aimed to describe the elementary mechanisms responsible for dry-water formation. It was found that the success of encapsulation depends on the relative importance of process-related parameters with respect to the physico-chemical properties of the material used. A “regime map” for dry water production is also proposed based on comparison between the mechanical energy due to stirring and the energy of immersion of particles.     

A revised mono-dimensional particle bed model for fluidized beds

The formulation of the equations of change proposed by Foscolo and Gibilaro in their original mono-dimensional particle bed model (PBM) for the prediction of the fluid-bed stability of Geldart's group A powders has been revisited along with the relevant closure relationships. The buoyancy has been expressed in accordance with its “classical” definition, which regards it as being equal to the weight of the fluidizing fluid displaced by the particle phase. A new constitutive equation has been developed for the drag force; this proves more accurate than the expression used in the original PMB particularly in the intermediate flow regimes comprised between the viscous and inertial ones. The “elastic” force has been estimated by employing a rigorous approach which needs not resort to equilibrium-based relations. The result, enhanced in accuracy and breadth of validity, considers “elastic” force and drag force proportional. The equations of change themselves have been partly revised. The pressure gradient is no longer shared by the two phases in proportion to their volume fractions, but has been accounted for only in the continuous one. Conversely, the “elastic” force has been included, with opposite signs, in the linear momentum equations pertaining to both phases, so that the principle of action and reaction, to which the force is subjected, is fulfilled. The revised model has been validated by performing a fluid-bed stability analysis on a wide range of Geldart's group A powders at different operating temperatures. Predicted values for the minimum bubbling voidage estimated by means of the revised model have been compared with experimental values and with predictions from both the original Foscolo and Gibilaro model and that previously revised by Jean and Fan. The latter has been found to be always in good agreement with the model proposed here, whereas the former has seemed to somewhat underestimate the bed minimum bubbling voidage thus anticipating the transition between homogeneous and bubbling fluidization. All of the models have proved to yield predictions whose validity is strongly dependent on the particular powder in hand and on the operating conditions considered.     

Coagulation of bentonite suspension by polyelectrolytes or ferric chloride: Floc breakage and reformation

Coagulation process usually involves different hydrodynamic conditions, in particular when it is followed by a filtration step. In this study, coagulation performance was investigated under a wide range of shear stress. Floc behaviour was followed in-line by laser granulometry to determine size distribution and structure. Synthetic suspension of bentonite in tap water was used as a reference for mineral solids in surface water. Three cationic polymers (polyamine based and polyDADMAC) and ferric chloride were tested using different coagulation reactor geometries. Jar-test indicated coagulation performance under mild hydrodynamic conditions and Taylor–Couette reactors were used to create shear stresses up to 8 Pa. Flocs formed with ferric chloride are not able to grow under middle shear stress like 1.5 Pa. On the contrary, polyelectrolytes lead to large flocs, dense (D_f = 2.6) and resistant to shear stress. A qualitative comparison of floc resistance to shear depending on hydrodynamic conditions and coagulant type is given through the calculation of the strength factor. Fractal dimension measurements indicate a mechanism of particle erosion when flocs are subjected to a higher shear stress in Taylor–Couette reactor. Floc re-growth is also investigated, and breakage appears to be non-reversible regardless of coagulant and conditions experimented.     

Applying dry powder coatings to pharmaceutical powders using a comil for improving powder flow and bulk density

A method for applying nano-sized silicon dioxide guest particles onto host pharmaceutical particles (a.k.a. “dry-coating” or “nanocoating”) has been developed using conventional pharmaceutical processing equipment. It has been demonstrated that under selected conditions, a comil can be used to induce sufficient shear to disperse silicon dioxide particles onto the surfaces of host particles such as active pharmaceutical ingredients (API) without significant host particle attrition. In accordance with previous studies on dry coating, the dispersed silicon dioxide adheres to the host particle surface through van der Waals attractions, and reduces bulk powder cohesion. In this work, laboratory and pilot scale comils were used to dry coat pharmaceutical API and excipient powders with 1% w/w silicon dioxide by passing them through the mill with an appropriate combination of screen and impeller. In general, the uncoated powders exhibited poor flow and/or low bulk density. After dry coating with a comil, the powders exhibited a considerable and in some cases outstanding improvement in flow performance and bulk density. This coating process was successful at both the laboratory and pilot scale with similar improvements in flow. The superior performance of the coated powders translated to subsequent formulated blends, demonstrating the benefit of using nanocoated powders over uncoated powders. This particle engineering work describes the first successful demonstration of using a traditional pharmaceutical unit operation that can be run continuously to produce uniform nanocoating and highlights the substantial improvements to powder flow properties when this approach is used.     

Modelling thixotropic behavior of fresh cement pastes from MRI measurements

From MRI measurements we show that in a flowing cement paste thixotropic effects dominate over short time scales while irreversible effects become significant over larger timescales. The steady and transient flows exhibit a yielding behavior which differs from usual yield stress model: the transition from the solid to the liquid regime is abrupt. We propose a simple thixotropic model based on these observations. The validation is done on the steady and transient state on local experimental tests. We build the “local” rheogram which is representative of the intrinsic rheological properties. Comparisons with “apparent” rheograms demonstrate that it is possible to use correction techniques from the literature to have access to the real behavior law of the material from standard measurements but that, in the case of the material studied in this paper, this would nevertheless lead to an underestimation of the yield stress.     

Measuring the hydrophobicity of lubricated blends of pharmaceutical excipients

This paper discusses how the hydrophobicity of lubricated pharmaceutical formulations is affected by process variables such as shear rate and strain. Hydrophobicity is a critical property that affects the dissolution of powder formulations, tablets and capsules as well as the performance of tablet coating and granulation operations. In this paper, hydrophobicity is measured using a modified Washburn method. Results show that, in the absence of lubricant, the hydrophobicity of powders does not change substantially as a function of shear rate or strain. However, when magnesium stearate is present (concentrations studied here range between 0.5% and 2%), hydrophobicity increases as a function of strain, shear rate and lubricant concentration. Observed changes range over several orders of magnitude, readily explaining common “overlubrication” observations of delayed drug dissolution.     

The effect of liquid viscosity on sheared granular flows

This work investigates the effect of transport properties in sheared granular flows with adding different silicone oils. We performed a series of experiments in a shear cell device using 2-mm soda lime beads as the granular materials by adding little amount of different silicone oils. The viscosity of silicone oils added was changed in different tests. By particle tracking method, the velocities, the velocity fluctuations and the self-diffusion coefficients were measured and analyzed. It was found that for the granular system with adding the more viscous silicone oil, the system became less active due to the greater shear force and cohesive force, which resulted in the decrease of velocity fluctuations and diffusions. Three bi-directional stress gages were installed to the upper wall to measure the normal and shear stresses of the granular materials along the upper wall. Thus, the effective viscosities of the wet granular material systems could be evaluated. The dimensionless normal and shear stresses, and the effective viscosity in the wet sheared granular flow were found to decrease with the increase of the viscosity of the added silicone oil. The influence of the viscosity of added fluid on these transport properties of wet granular systems will be discussed.     

A calculation device for air permeametry

A “calculation aid” which copes with powders of different densities, powder “beds” of different porosities and cross-sectional areas, and various types of permeametric apparatus, has been found to be of particular value when working with friable materials and explosives (e.g. RDX and HMX) where it may be inappropriate to compress a bed of the powder to a fixed voidage. The device consists of a single scale marked on a sliding strip, which replaces the orthodox strip in the stock of a normal slide-rule, and which enables the specific surface areas of powders to be calculated in a second or two.     

Ultrafine cohesive powders: From interparticle contacts to continuum behaviour

Continuum mechanical models and appropriate measuring methods to determine the material parameters are available to describe the flow behaviour of cohesive powders. These methods are successfully applied to design process equipment as silos. In addition, “microscopic” studies on the particle mechanics can give a better physical understanding of essential “macroscopic” constitutive functions describing a powder “continuum”. At present, by means of the discrete element method (DEM), a tool is available that allows one to consider repulsive and frictional as well as attractive adhesion forces in detail. Within the framework of Newton's equations of motion, each particle in the system is tracked, and reacts to the forces acting.The knowledge of the interaction forces between particles is thus a prerequisite for understanding (via DEM) the stability and flow of particulate systems and other phenomena. In this study, macroscopic cohesion and friction are related to their microscopic counterparts, adhesion and contact-friction. The macroscopic cohesion is found to be proportional to the maximal microscopic adhesion force, and the macroscopic friction coefficient is a non-linear function of the contact friction, dependent (or independent) on the preparation procedure for yielding (or steady-state flow).One of the few methods available for the direct measurement of surface and contact-forces is the atomic force microscope (AFM) and, related to it, the so-called particle interaction apparatus (PIA). A contact model for ultrafine cohesive particles (average radius ) is introduced, based on such experiments. Plugged into DEM, consolidation, incipient yielding, and steady-state flow of the model powders are studied. Also the dynamic formation of the shear zone is examined and compared with experimental observations. Eventually, the shear experiments with volumetric strain measurements in a translational shear cell are used for validation.     

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.     

Note on the interpretation of powder shear test data

Powder shear testing has been used to assess flowability of powders for at least 48 years [A.W. Jenike, Storage and Flow of Solids, Bull., Eng. Exp. Station, Univ. Utah, vol. 123, 1964]. A fundamental part of the data interpretation involves construction of Mohr’s circles such that they are tangent to the experimental locus; a set of powder shear strengths, τ_m, measured at variable applied compressive normal stresses, σ_N. Despite the customary application of this tangency criterion, we have found justifications for it to be scant.In this work, we revisit the Mohr’s circle construction and find that proper construction would require measurement of reactionary lateral powder stresses, σ_r. We further provide reasoning to support placement of the experimental locus passing through the apex (top) of Mohr’s circles for isotropic or orthotropic powders and not tangentially to them. This placement is not unexpectedly in agreement with the results of a recent numerical simulation [C. Thornton, L. Zhang, Numerical simulations of the direct shear test, Chem. Eng. Technol. 26 (2) (2003) 153-156], and reveals errors in subsequently calculated constants on the order of 20%.     

Relationship between the hearth life of open-hearth furnaces and the metal charge and grading of the magnesite powder

Summary The relationship established for the metal charge and the life of the lining permits a better assessment of the influence of porosity of the hearth on its destruction.With the use of fine-grained powders, the effect of metal charge on 1 m² of hearth is greatly reduced: down-time of the furnaces for repairs is reduced. Therefore, it is desirable to use such powders in furnaces of any tonnage.It is necessary to organize the grinding of powder at the Magnesit Factory in order to convert all open-hearth furnaces in the country to the use of ground magnesite powder.With existing means and known methods of creating denser working layers in the hearth, ramming from ground powder should be preferred to fettling.Research work of metallurgists and refractory workers should be aimed at finding methods and means of getting the densest working layer.The Magnesit Factory, together with the refractories institutes and Gipromez, should decide the matter of the supply and storage of fine powders at the consumer sites.     

Influence of shear deformation on carbon nanotube networks in polycarbonate melts: Interplay between build-up and destruction of agglomerates

Shear-induced destruction and formation of conductive and mechanical filler networks formed by multi-wall carbon nanotubes in polycarbonate melts were investigated by simultaneous time-resolved measurements of electrical conductivity and rheological properties under steady shear and in the quiescent melt. The steady shear experiments were performed at shear rates between 0.02 and 1 rad/s and for nanotube concentrations ranging from 0.5 to 1.5 wt%. The influence of thermo-mechanical history on the state of nanotube dispersion and agglomeration was studied in detail.For melts with well-dispersed nanotubes a shear-induced insulator-conductor transition was observed, which is explained by the agglomeration of nanotubes under steady shear and the formation of an electrical conductive network of interconnected agglomerates. Simultaneously, a drastic decrease of the shear modulus (G^∗ = G′ + iG″) during steady shear was observed, which can be related to a reduction of mechanical reinforcement due to agglomeration of dispersed nanotubes. These findings indicate a substantial difference in the nature of “electrical” and “mechanical” network and contradict earlier assumptions that steady (or transient) shear is always destructive for the conductive filler network in highly viscous polymer composites.It was also shown that after a certain time of steady shear the filler network asymptotically reaches its steady state characterized by the constant electrical conductivity and shear modulus of the composite melt. Such asymptotic behaviour of composite properties was experimentally shown to be related to the interplay of the destructive and build-up effects of steady shear. For modelling of the electrical conductivity in presence of steady shear a kinetic equation was proposed for filler agglomeration with shear-dependent destruction and build-up terms. This equation was coupled to the generalized effective medium (GEM) approximation for insulator-conductor transition.