Chute Performance and Design for Rapid Flow Conditions

Many industrial chute applications are characterised by rapid flow conditions in which the bulk solid stream thickness or depth is less than the chute width. Under these conditions, it is possible to describe the stream flow by means of a lumped parameter model which takes into account the frictional drag around the chute boundaries as well as making allowance for inter‐particle friction. Equations of motion to describe the chute flow are presented and their application to the determination of chute profiles to achieve optimum flow is illustrated. By means of design examples, the problems associated with the feeding of bulk solids onto belt conveyors and conveyor transfers are discussed. Criteria for the selection of the most appropriate chute geometry to minimise chute wear and belt wear at the feed point are presented. The determination of optimum chute profiles to achieve specified performance criteria is outlined.     

Modeling of Caked Contacts in DEMs

When modeling the caking properties of bulk solids, it is not only necessary to incorporate the yield properties of individual particle contacts, but also to extend them to a many‐particle system. To accomplish this by means of Distinct Element Method (DEM) simulations a contact model for (spherical) particles, including a yield criterion for combined load is proposed. An application to the simulation of a caking test is presented and compared to experiments.     

Numerical Simulation of Open‐Circuit Continuous Mills Using a Non‐Linear Population Balance Framework: Incorporation of Non‐First‐Order Effects

Population balance modeling has been used as a tool for simulating, optimizing, and designing various particulate processes, including milling. A fundamental tenet of the traditional models for milling processes is the first‐order breakage kinetics. Ample data obtained from batch milling studies show that this assumption is not necessarily valid for certain milling systems. In the present theoretical investigation, an attempt has been made to incorporate these experimentally observed non‐first‐order effects into continuous mill models within the context of a novel non‐linear population balance framework. In view of two idealized flow regimes, i.e., perfect mixing and plug‐flow, continuous mills operating in the open‐circuit mode are numerically simulated. The simulations indicate that not only does the product size distribution depend on the degree of mixedness in a continuous mill, but also on the non‐first‐order effects arising from multi‐particle interactions.     

Modeling of Particle Layer Detachment under Consideration of Transient Kinetic Effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the device running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely nonstationary concerning place and time, primarily due to changing conditions for the forces on the one hand and changes in the particle layer morphology on the other. This paper describes a model and a simulation considering such transient kinetic effects on filter cake detachment. Diverse computing results are presented and discussed.     

Modeling Gas‐Solid Reactions in the Bed of a Rotary Kiln

When dealing with gas‐solid reactions in rotary kilns, it is necessary to realize that the total particle surface within the granular bed can be much larger than the outer surface of the bed. Depending on the reaction conditions this inner surface can contribute considerably to the chemical conversion in the kiln. In this paper, a model is presented, which describes the reaction within the bed for the case of bed movement according to the cascade mode. In this case, gas is drawn into the rotating bed together with the particles. As a key quantity, an effectiveness factor η of the bed is defined. It is the ratio of the actual conversion to the conversion that would occur if the concentration of the reacting component remained unchanged throughout the bed, i.e. at its entrance concentration. An evaluation for reactions of order mshows this factor to be more than 25 % when the Damköhler number is smaller than 2. It approaches 100 % as the Damköhler number approaches 0. The Damköhler number used in this paper contains the void fraction of the particle bed in its denominator.     

Model for Gas‐Liquid Flow through Wet Porous Medium

A method involving bubbling of air through a fibrous filter immersed in water has recently been investigated (Agranovski et al. [1]). Experimental results showed that the removal efficiency for ultra‐fine aerosols by such filters was greatly increased compared to dry filters. Nuclear Magnetic Resonance (NMR) imaging was used to examine the wet filter and to determine the nature of the gas flow inside the filter (Agranovski et al. [2]). It was found that tortuous preferential pathways (or flow tubes) develop within the filter through which the air flows and the distribution of air and water inside the porous medium has been investigated. The aim of this paper is to investigate the geometry of the pathways and to make estimates of the flow velocities and particle removal efficiency in such pathways. A mathematical model of the flow of air along the preferred pathways has been developed and verified experimentally. Even for the highest realistic gas velocity the flow field was essentially laminar (Re ≈ 250). We solved Laplace's equation for stream function to map trajectories of particles and gas molecules to investigate the possibility of their removal from the carrier.     

Particle size distributions and viscosity of suspensions undergoing shear-induced coagulation and fragmentation

The dynamic behavior of concentrated suspensions (up to a solids volume fraction of 20%) of non-spherical particles is investigated theoretically by coupling a rheological law to a population balance model accounting for coagulation and fragmentation of the detailed particle size distribution. In these suspensions, the immobilization of matrix liquid renders the viscosity dependent on the particle aggregation state. The effect of initial solids volume concentration and shear rate on the transient behavior of particle size distribution and suspension viscosity is examined. Power law correlations for the equilibrium flow curves of aggregating suspensions are deduced and compared to experimental data. Steady-state or equilibrium particle size distributions are found to be self-preserving with respect to solids volume fraction and shear rate.     

Modeling and verification of fluid-responsive polymer pumps for microfluidic systems

The fundamental principles necessary to create and model a pump for microfluidic systems using fluid-responsive polymer particles are described. The pump is “activated” by the addition of water to the particles, which induces a significant particle volume expansion and pushes a stored fluid from an adjacent reservoir at a predicted flow rate. Two particle systems were investigated to examine how polymer properties affect the rate and amount of fluid delivered. Poly (acrylic acid) (PAA) particles obtained from Pampers^® diapers yield the best micropump swelling characteristics for delivering fluid at pressures above 1100 Pa, whereas the softer potassium-neutralized PAA particles from Aldrich are best only at lower pressures. The maximum flow rates produced by the Pampers^®and Aldrich particles with minimal backpressure are 0.5 and of PAA, respectively. The experimental results demonstrate good agreement with an analytical model describing equilibrium and dynamic polymer swelling coupled with pressure-driven flow through cylindrical channels under conditions in which gel-blocking was not important. Fluid-responsive polymer micropumps could provide an inexpensive and lightweight method for driving fluid flow in microfluidic and other applications.     

A mechanistic model to determine the critical flow velocity required to initiate the movement of spherical bed particles in inclined channels

This study presents a mechanistic model that predicts the critical velocity, which is required to initiate the movement of solid bed particles. The model is developed by considering fluid flow over a stationary bed of solid particles of uniform thickness, which is resting on an inclined pipe wall. Sets of sand bed critical velocity tests were performed to verify the predictions of the model. An flow loop with recirculation facilities was constructed to measure the critical velocities of the sand beds. The tests were carried out by observing the movement of the bed particles in a transparent pipe while regulating the flowrate of the fluid. Water and aqueous solutions of PolyAnoinic Cellulose were used as a test fluid. The critical velocities of four sand beds with different particle size ranges were measured. The model was used to predict the critical velocities of the beds. The model predictions and experimentally measured data show satisfactory agreement. The results also indicated that the critical velocity is influenced by the properties of the fluid, flow parameters, and particle size.