Cleaning of viscous drops on a flat inclined surface using gravity-driven film flows

We investigate the fluid mechanics of cleaning viscous drops attached to a flat inclined surface using thin gravity-driven film flows. We focus on the case where the drop cannot be detached either partially or completely from the surface by the mechanical forces exerted by the cleaning fluid on the drop surface. Instead a convective mass transfer establishes across the drop–film interface and the fluid in the drop dissolves into the cleaning film flow, which then transports it away. The characteristic time scale of dissolution is much longer than the advection time scale in the film flow. Thus, the shape and size of the drop can be considered as quasi-steady. To assess the impact of the shape and size of the drop on the velocity of the cleaning fluid, we have developed a novel experimental technique based on particle image velocimetry. We show the velocity distribution at the film surface in the situations both where the film is flowing over a smooth surface, and where it is perturbed by a solid obstacle representing a very viscous drop. We find that at intermediate Reynolds numbers the acceleration of the starting film is overestimated by a plane model using the lubrication approximation. In the perturbed case, the streamwise velocity is strongly affected by the presence of the obstacle. The upstream propagation of the disturbance is limited, but the disturbance extends downstream for distances larger than 10 obstacle diameters. Laterally, we observe small disturbances in both the streamwise and lateral velocities, owing to stationary capillary waves. The flow also exhibits a complex three-dimensional converging pattern immediately below the obstacle.     

Transitional behavior of polymeric hollow microsphere formation in turbulent shear flow by emulsion diffusion method

Polymeric hollow microspheres have attracted growing attention because of their unique properties and extensive applications. We report a facile emulsion diffusion process to fabricate polylactic acid (PLA) hollow microspheres driven by viscous turbulent fluid flow. The process involves the emulsification of PLA–ethyl acetate solution in the water–glycerol medium under high viscous turbulent shear flow where emulsion droplets coalesce into multiple emulsions, and the solidification of PLA by the diffusion of ethyl acetate. The addition of glycerol changed the viscosity of the continuous aqueous phase, resulting in the transition of fluid flow from inertial turbulent to viscous turbulent dominant regime and thus PLA particle size and shape from solid nanospheres to hollow microspheres. The emulsification temperature also needs to exceed the glass transition temperature of PLA to form hollow microstructure. This method allows the easy control of PLA particle shape and size for different applications.     

A comprehensive phenomenological model for erosion of materials in jet flow

A phenomenological erosion model, which captures the effects of impingement velocity, angle, particle size, properties of target, has been developed. The model incorporates removal of material due to both deformation damage and cutting. For the cutting removal, the volume loss has a power-law relation with particle's impingement velocity, angle, mass and size and the exponents depend on the particle's shape (cutting ways). Two critical cases, line cutting and area cutting, indicate that the range of the exponent of impingement velocity is 2∼2.75 which is consistent with the experimental findings. For deformation damage removal, the model indicates that the exponent of the particle's mass is independent on the target material, while the exponents of particle's impingement angle, velocity and density depend on the properties of target material. To validate the model, the simplified version of the model was applied to predict erosion rates, impingement angle where the maximum weight loss occurs and particle size effect. The predictions are in good agreement with the experiments conducted by Finnie. Such models could be used locally together with CFD models to predict erosion and wear patterns under varying flow scenarios.     

Hydrodynamics of Taylor flow in noncircular capillaries

In this work, volume of fluid (VOF) technique, one computational fluid dynamics (CFD) method, was used to investigate the upward Taylor flow in vertical square and equi-triangular capillaries. For saving computation time, the simulations were carried out in a moving frame of reference attached to Taylor bubbles. The main flow parameters, involving bubble size and shape, liquid film thickness, velocity field and two-phase relative velocity, were studied as functions of capillary number. The numerical simulations were in good agreement with previous reports and showed that the flow in the sides and corners of polygonal capillaries were different. A comparative study was also conducted on Taylor flow in square and equi-triangular capillaries and their circular counterparts, where the influence of capillary geometry on the characteristics of Taylor flow was illustrated clearly.     

搅拌槽内假塑性流体洞穴研究进展

介绍了在假塑性流体层流搅拌中广泛存在的洞穴现象,表明其对物料的传质和传热极为不利;说明了假塑性流体剪切变稀的流变特性,阐述了预测洞穴大小的3种数学模型：球形模型、圆柱形模型和环形模型,同时综述了不同搅拌器洞穴形状及大小变化的最新研究成果,认为圆柱形模型（EN模型）能更好地描述假塑性流体洞穴的形状及其随雷诺数的变化,洞穴边界速度定义为 0.01U_tip;最后指出了利用 CFD 技术研究洞穴变化以及流场特征是必然趋势。     

Attrition and secondary nucleation in crystallizers

The mean crystal size of coarse crystalline products is determined by secondary nucleation and crystal growth. Secondary unclei are mainly produced by contacts of crystals with parts of the crystallizer or with other crystals. As a consequence, attrition effects are very important. In this paper, a model is proposed in order to calculate the attrition rate of crystals, depending on the physical properties of the crystalline product, the geometry of the crystallizer and on the operating conditions such as the stirrer speed or the suspension density. The effective rate of secondary nucleation can be expressed in terms of the attrition rate by introducing effective values for number and size of attrition particles. Finally, a scale-up criterion based on this model is derived. This criterion allows to predict effective rates of secondary nucleation and mean crystal sizes if data obtained in a laboratory crystallizer are available.     

Effect of motive gases on fine grinding in a fluid energy mill

A research program spanning over 30 years in DuPont has concentrated on fundamental understanding of the fluid mechanics in confined vortex fluid energy mills. Extensive internal reports and patents have documented numerous accomplishments. Direct visualization and measurement of velocity profiles, computational fluid dynamic modeling, in-line particle size measurement, and experimental study of gas molecular weight effect have resulted in optimized operation and improved energy efficiency. This paper will only discuss the effect of motive gases on the grinding performance. Helium, steam, air, and CO₂ are studied as motive gases to provide a broad range of molecular weight that determines the gas specific sonic velocity and resultant kinetic energy. The experimental results indicated that a fully developed flow in the grinding chamber is needed for the built-in air classification to control the product top size. The shape of particle size distributions is not significantly affected by the properties of motive gases. The gas/solid ratio or the energy intensity does not determine the grinding limit, rather how fast the limit is reached. It is very clear, however, that the motive gas with the lighter molecular weight has the capability to reach a finer grinding limit. Simply, helium gas will be able to grind finer than steam, steam grinds finer than compressed air or nitrogen, and they are all better than CO₂.     

Cold Flow Model Study of an Oxyfuel Combustion Pilot Plant

The fluid‐dynamic behavior of a circulating fluidized bed pilot plant for oxyfuel combustion was studied in a cold flow model, down‐scaled using Glicksman's criteria. Pressures along the unit and the global circulation rate were used for characterization. The analysis of five operating parameters and their influence on the system was carried out; namely, total solids inventory and the air velocity of primary, secondary, loop seal and support fluidizations. The cold flow model study shows that the reactor design allows stable operation at a wide range of fluidization rates, with results that agree well with previous observations described in the literature.     

Fractal analysis of invasion depth of extraneous fluids in porous media

Applications of the fractal theory to analyze transport properties of porous media in science and engineering have received steady attention in the past two decades. However, the theory was rarely used to analyze invasion by extraneous fluids into a permeable bed where there is initially no such fluid present. Spills and leaks of non-aqueous phase liquids (NAPLs) and formation damage in drilling and completion wells are two typical examples. In this work, a fractal capillary model is proposed to analyze the depth of extraneous fluid invasion, where the tortuosity of capillaries and capillary pressure effect are taken into account. The quantitative relationship between average flow velocity and average beeline velocity are discussed based on the fractal geometry theory. Based on the proposed model, the depth of extraneous fluid invasion can be determined when the operation conditions, extraneous fluid properties and formation structure parameters are available, and the model predictions are in good agreement with the available data.     

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.     

Flow Compartments in Viscoelastic Fluids Using Radial Impellers in Stirred Tanks

The influence of viscoelastic flow properties on fluid dynamics using radial impellers is investigated. The use of transparent model fluids allows for the optical measurement of general flow behavior with a fluorescence dying technique. By varying viscoelastic flow properties, size of agitators and rotational frequency, the impact of these parameters on fluid dynamics is analyzed. Toroidally shaped, cavern‐like flow compartments form around the agitators in all fluids in specific rotational frequency ranges, preventing an efficient mixing. By balancing elastic with centrifugal forces, a simple model is developed with which compartment sizes can be predicted with good accuracy. The results indicate a good suitability of the elasticity number as a scale‐up criterion.     

Effect of particle and fluid properties on the pickup velocity of fine particles

Systems involving fluid-particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids.In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems.     

Solutions approximatives pour l'absorption dans un solide poreux

The adsorption of a solute by porous solid particles can be represented with good accuracy by a simple approximate formula of the “penetration” type. The corresponding “kinetic” model makes use of average lumped concentrations of the two phases. It can be applied, by introduction of the fluid—solid slip velocity, either to the agitated vessel, or to the co- or counter-current moving bed. With the external specific area of the particle sample, the formula also represents correctly the, absorption by particles of any shape and any size distribution.     

Effects of reactant crossover and electrode dimensions on the performance of a microfluidic based laminar flow fuel cell

A mathematical model is developed to simulate the performance of a laminar flow fuel cell with reactant crossover using the Poisson-Nernst-Plank (PNP) equations. The model includes a more general treatment of reactant (fuel or oxidant) crossover than the common method where it is assumed that the crossover flux is fully utilized as crossover current. This new model allows for the analysis of very narrow channels and estimation of parasitic crossover current at both the anode and the cathode. It also allows for the consideration of a laminar flow fuel cell with a significant amount of reactant crossover where the crossover species are not fully consumed by the crossover current. Moreover, the combination of the PNP equations and the general reactant crossover treatment reveal the two-dimensional developing region for electrode mixed potentials which is a novel result. The parameters considered in this study are electrode length and separation (channel height). Numerical results show that the reactant crossover, transport limitations, and Ohmic losses are the primary performance limitation factors. The current distributions along the anode and cathode are presented as well as the reactant concentrations at the anode as evidence of these performance limitations. It is also shown that the fluid velocity field, as it changes with channel height, plays a small role in the development of the depletion boundary layer.     

Two-dimensional population balance modeling for shape dependent crystal attrition

Many suspension crystallization processes can be described by growth and secondary nucleation. The prevailing mechanism for secondary nucleation in industrial processes is attrition caused by crystal-impeller collisions. The understanding and prediction of attrition rates is of fundamental importance for product and process design.Attrition of a crystal is affected by the size of the crystals and, as experimental evidence reveals, by their shape. For crystals with the same mass, the attrition rate is significantly larger if crystals have distinct and sharp corners, than if they were spherical. Because of the associated modeling and computational effort, shape dependent behavior has mostly been disregarded in crystallization process modeling. In this work, a two-dimensional population balance model is formulated. The inner variables are the size and the shape of the crystals. Consequently, the model accounts for size and shape dependent process behavior. In order to close the model equation shape modification function are introduced. The reinforcement function specifies the increase in attrition resistance by rounding the sharp corners and increasing material strength. The face attrition ratio represents the differences of material removal from sharp corners and flat faces.The sensitivity of the results with respect to these shape modification functions is investigated. The results show that the model is capable of reflecting shape dependent attrition behavior in a physically meaningful way. To fit experimental data, mainly the parameters of the shape modification function need to be tuned.     

Nonrecirculating flow of a yield stress fluid around a circular cylinder in a poiseuille flow

Although yield stress fluids are very present today in everyday life and in industry, their flow behavior is still poorly understood and the databases are incomplete at this time. The present experimental and numerical study focuses on laminar nonrecirculating flows of an elastoviscoplastic model fluid in a rectangular duct. An original experimental set‐up has been developed. The Particle Image Velocimetry method is used for analyzing the kinematical fields. Results provided concern the morphology of the flow and the evolution of the velocity field around a cylindrical obstacle. Information is provided on the size of the rigid zones where the fluid behaves as a solid. The experimental data are compared with numerical results involving a regularized Herschel–Bulkley viscoplastic model. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4554–4563, 2016     

USE OF X-RAY MICROTOMOGRAPHY TO FOLLOW THE CONVECTIVE HEAT DRYING OF WASTEWATER SLUDGES

X-ray microtomography is proposed as a new tool to investigate the evolution of size, shape and texture of soft materials during a drying operation. This study is focused on the drying of mechanically dewatered sludges from a secondary wastewater treatment. The shrinkage phenomenon is shown to play a crucial role in the control of the drying process. The shrinkage curves are determined by analysing the shape and size of cross sectional microtomographic images of sludge extrudates at different levels of drying. The observation of drying and shrinkage curves allows us to determine 3 critical water content values, which define different drying zones where extragranular, intragranular or mixed limitations prevail. When drying is externally controlled, the decrease of the drying rate observed during experiments can be related to the reduction of the external area of the sample, i.e., to shrinkage. When drying is internally controlled, resistances inside the solid govern the process. Between these two extreme situations, the drying rate reduction is the result of both the external area decrease and the development of internal resistances limiting drying. A multizone model is proposed to describe quantitatively these observations. The analysis of the internal texture of the sludge extrudates reveals crack formation at the end of the drying process. The onset of crack formation is clearly related to the appearance of internal transfer limitations, i.e., humidity and temperature gradients inside the material.     

CFD–DEM modeling of gas fluidization of fine ellipsoidal particles

Particle characteristics are important factors affecting gas fluidization. In this work, the effects of both particle size and shape on fluidization in different flow regimes are studied using the combined computational fluid dynamic–discrete element method approach. The results are first analyzed in terms of flow patterns and fluidization parameters such as pressure drop, minimum fluidization, and bubbling velocities. The results show that with particle size decreasing, agglomerates can be formed for fine ellipsoidal particles. In particular, “chain phenomenon,” a special agglomerate phenomenon exists in expanded and fluidized beds for fine prolate particles, which is caused by the van der Waals force. The minimum fluidization velocity increases exponentially with the increase of particle size, and for a given size, it shows a “W” shape with aspect ratio. A correlation is established to describe the dependence of minimum fluidization velocity on particle size and shape. Ellipsoids have much higher minimum bubbling velocities and fluidization index than spheres. © 2015 American Institute of Chemical Engineers AIChE J, 62: 62–77, 2016     

Experimental studies and numerical model validation of overflowing 2D foam to test flotation cell crowder designs

A computational fluid dynamics model of froth motion has been developed to assess different flotation cell designs. This work presents an implementation of the model in a 2D case, to compare the simulated bubble velocity distribution and streamlines to an experimental foaming system. The model uses finite elements to solve Laplace's equation for a potential function from which the foam velocity can be obtained. It requires the air recovery, or the amount of air that overflows a flotation cell as unburst bubbles, as an input parameter to calculate the foam velocity distribution and bubble streamlines. The air recovery was obtained by image analysis from a vertical, overflowing monolayer of foam (2D) created in a Hele-Shaw column, which mimicked important flowing properties of flotation froths such as coalescence. Inserts were included in the foam column to represent potential crowder designs for industrial flotation cells. Three different designs were chosen to compare the effect of insert depth and shape, including rectangles and a triangle. The effect of the insert design on the overflowing foam is obvious from visual assessment of the bubble streamlines and velocity distribution, which were closely agreed by both the experiment and model.