Multiphase Hydrodynamics In Steady And Pulse Jet Mixing Systems

The goal of the present study is to evaluate the mixing performance of jet mixers in both liquid and solid-liquid mixing processes. Jet mixers have been studied for decades for its uses in liquid blending and solid-liquid mixing applications. In solid suspension processes, jet mixers can be just as useful if not more useful than conventional impeller mixers. However, there is a lack of phenomenological models that exist. The erosion and subsequent suspension of solids beds, as well as the suspension of a low concentration of solid particles must be better understood. The specific objectives were to develop analytical, experimental and numerical models that simulate a liquid, submerged, steady or pulsing jet mixer. Furthermore, specific objectives were to determine the performance of jet mixers in solid suspension processes by measuring the cloud height, develop a model that describes the erosion of a solids bed, and determine the effect of cohesive particles on the dispersion of particles once eroded. The results showed that the mixing performance, in terms of mixing time, was not enhanced with the use of pulsing jet flows. The results showed that the cloud height below about 24000 is not dependent on the jet Reynolds number. The erosion profiles of solids were found for solids beds composed of particles with different Archimedes numbers and results showed that there appears to be two different regimes present. The regimes occur based on the erosion mechanisms that are taking place, mainly entrainment and surface erosion. Results of the axial concentration studies showed that the time dependence of the concentration ceases to exist after a certain period, which is a function of the weight percent of cohesive particles

Controlled Nanoparticle Formation by Diffusion Limited Coalescence

Polymeric nanoparticles (NPs) have a great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scales, a mixing and a coalescence time, are identified and their ratio is shown to determine the final NP diameter. The size is found to scale in a universal manner and is predominantly sensitive to the mixing time and the polymer concentration if the surfactant concentration is sufficiently high. The model predictions are in good agreement with experimental data. Hence the theory provides a solid framework for tailoring nanoparticles with a priori determined size.Comment: 4 pages, 3 figure

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. In this formulation the effective or eddy diffusivity depends on the entropy gradient, $\partial S/\partial r$, as well as entropy. First we present a simplified model with semi-analytical solutions, highlighting the large dynamic range of $\partial S/\partial r$, around 12 orders of magnitude, for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple, stable numerical scheme able to capture the large dynamic range of $\partial S/\partial r$ and provide a flexible and robust method for time-integrating the energy equation. We then consider a full model including energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using $\partial S/\partial r$ as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. Our computational framework is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations arising in other disciplines, particularly for non-linear functional forms of the diffusion coefficient

HIx system thermodynamic model for hydrogen production by the sulfur-iodine cycle

The HIx ternary system (H2O – HI – I2) is the latent source of hydrogen for the Sulfur – Iodine thermo-chemical cycle. After analysis of the literature data and models, a homogeneous approach with the Peng-Robinson equation of state used for both the vapor and liquid phase fugacity calculations is proposed for the first time to describe the phase equilibrium of this system. The MHV2 mixing rule is used, with UNIQUAC activity coefficient model combined with of hydrogen iodide solvation by water. This approach is theoretically consistent for HIx separation processes operating above HI critical temperature. Model estimation is done on selected literature vapor – liquid, liquid – liquid, vapor – liquid – liquid and solid – liquid equilibrium data for the ternary system and the three binaries subsystems. Validation is done on the remaining literature data. Results agree well with the published data, but more experimental effort is needed to improve modeling of the HIx system

On the viscoelasticity-induced particle migration in stirred vessels

The objective of this thesis is the investigation of the behaviour of solid particles suspended in a viscoelastic liquid and subjected to mixing in a stirred vessel. In particular, the well-known phenomenon of viscoelasticity-induced particle migration, was observed for the first time in the flow field generated in stirred vessel. This thesis is divided in three parts. First, we performed an experimental campaign aimed at the study of the mixing of a non-Newtonian liquid-solid suspension in a cylindrical vessel equipped with a dual-blade impeller. The experiments were performed with liquids with different rheological behaviours. Particle image velocimetry (PIV) was used to measure the velocity filed of the liquid while particle tracking velocimetry (PTV) was employed to measure velocity and concentration fields of the solids. We show that in the presence of viscoelasticity, the particles accumulate at the centre of the vortices created by the impeller. We then focused on the viscoelasticity-induced migration in the flow field created by a Rushton turbine in an unbaffled vessel. We propose a scaling law for predicting the migration time as a function of the Weissenberg number ($Wi$). The experimental campaign shows that the particles migrate in the radial direction driven by the presence of gradients of shear-rate. Finally, the scaling law is validated against experimental data obtained at different $Wi$. The third part, describes the development of CFD tool, based on the volume of fluid (VOF) framework, for the simulation of particles in viscoelastic fluids. The objectives were, (i) to use the VOF model to simulate a solid sphere in flow, and (ii) to simulate the rotational velocity of a sphere in a viscoelastic fluid. Although, the model was capable of simulating a solid sphere with good accuracy in the Newtonian case, the viscoelastic case failed to reproduce the results available in the literatur

Heterogeneous flow structure and gas-solid transport of riser

This study aims to understand physical mechanisms of gas-solid transport and riser flow, investigate heterogeneous flow structures of gas-solid transport and their formation mechanism of the in riser flows, both in axial and radial directions. It provides sound interpretation for the experimental observation and valuable suggestion to riser reactor design. Chemical reaction is also coupled with flow hydrodynamics to board the industrial applications. This study mainly focuses on mathematical modeling approach based upon physical mechanism, and endeavor to validate model prediction against available experimental data. First of all, most important physical mechanisms including inter-particle collision force, gas/solid interfacial force and wall boundary effects, which are believed to be most important aspects of the flow hydrodynamics, have been investigated in this part. An energy-based mechanistic model was developed to analyze the partitions of the axial gradient of pressure by solids acceleration, collision-induced energy dissipation and solids holdup in gas-solid riser flows. Thought this part of study, important understanding of the inter-particle collision force (Fc), gas/solid interfacial force (FD) inside the momentum equations and energy dissipation (F), especially in dense and acceleration region, has been reached, Based on these understandings, a mechanistic riser hydrodynamic model was developed on the basis of gas-solid continuity and momentum equations, along with the better formulated drag force correlation and new formulation for moment dissipation of solids due to solids collisions. The proposed model is capable of yielding the coupled hydrodynamic parameters of solid volume fraction, gas and solid velocity, and pressure distribution along the whole riser. At the same time, special considerations are given to solids back-mixing and resultant cross- section area variation for the upward flow, which is especially prominent for low solids mass flow condition. With the further understanding of solid collision, gas/solid interfacial and wall boundary effects, in order to soundly interpret the well-known core-annulus 2-zone flow structure, newly discovered core-annulus-wall 3-zone structure and provide reasonable explanation for the choking phenomena, a comprehensive modeling of continuous gas-solids flow structure both in radial and axial directions has been presented. This model, assuming one-dimensional two-phase flow in each zone along the riser, consists of a set of coupled ordinary-differential equations developed from the conservation laws of mass, momentum, and energy of both gas and solids phases. This part of study not only provides reasonable explanation for the 2-zone and 3-zone structure , but also finds out the potential reasons for the choking phenomenon. In order to investigate the different riser inlet configuration\u27s effects on gas-solid mixing in dense region and improve the uniform inlet condition assumption in above models, a systemically study regarding with different inlet conditions have been done based on commercial package, Those simulation results are directly combined with model approach which reached the conclusion that riser flow structure an flow stability are weakly dependent on the type of solids feeding configuration. This part of study is specifically focused on chemical reaction coupled gas-solid transport flow hydrodynamics. The aim of this work is to develop a generic modeling approach which can fully incorporate multiphase flow hydrodynamics with chemical reaction process. This modeling approach opens up a new dimension for making generic models suitable for the analysis and control studies of chemical reaction units. The chemical reaction model was represented by a relatively simple four-lump based FCC reaction kinetic model, which will not bring us too complicated mathematical derivation without losing its popular acceptance. As a first endeavor to consider the significant mutual coupling between the flow hydrodynamics and cracking reaction, a localized catalyst to oil ratio is introduced. The new developed chemical reaction coupled hydrodynamic model was capable of quickly evaluating the flow parameters including gas and solid phase velocity and concentration, temperature and reaction yield profiles as the function of riser height

Three-dimensional numerical study of flow characteristic and membrane fouling evolution in an enzymatic membrane reactor

In order to enhance the understanding of membrane fouling mechanism, the hydrodynamics of granular flow in a stirred enzymatic membrane reactor was numerically investigated in the present study. A three-dimensional Euler-Euler model, coupled with k-e mixture turbulence model and drag function for interphase momentum exchange, was applied to simulate the two-phase (fluid-solid) turbulent flow. Numerical simulations of single- or two-phase turbulent flow under various stirring speed were implemented. The numerical results coincide very well with some published experimental data. Results for the distributions of velocity, shear stress and turbulent kinetic energy were provided. Our results show that the increase of stirring speed could not only enlarge the circulation loops in the reactor, but it can also increase the shear stress on the membrane surface and accelerate the mixing process of granular materials. The time evolution of volumetric function of granular materials on the membrane surface has qualitatively explained the evolution of membrane fouling.Comment: 10 panges, 8 figure

Crystallization diagram for antisolvent crystallization of lactose : using design of experiments to investigate continuous mixing- induced supersaturation

This study investigates the effects of key process parameters of continuous mixing-induced supersaturation on the antisolvent crystallization of lactose using D-optimal Design of Experiments (DoE). Aqueous solutions of lactose were mixed isothermally with antisolvents using a concentric capillary mixer. Process parameters investigated were the choice of antisolvent (acetone or isopropanol), concentration of lactose solution, total mass flow rate, and the ratio of mass flow rates of lactose solution and antisolvent. Using a D-optimal DoE a statistically significant sample set was chosen to explore and quantify the effects of these parameters. The responses measured were the solid state of the lactose crystallized, induction time, solid yield and particle size. Mixtures of α-lactose monohydrate and β-lactose were crystallized under most conditions with β-lactose content increasing with increasing amount of antisolvent. Pure α-lactose monohydrate was crystallized using acetone as the antisolvent, with mass flow ratios near 1:1, and near saturated solutions of lactose. A higher resolution DoE was adopted for acetone and was processed using multivariate methods to obtain a crystallization diagram of lactose. The model was used to create an optimized process to produce α-lactose monohydrate and predicted results agreed well with those obtained experimentally, validating the model. The solid state of lactose, induction time, and solid yield were accurately predicted