A.H. Alexopoulos

CFD analysis of turbulence non-homogeneity in mixing vessels A two-compartment model

Abstract A two-compartment model has been developed for calculating the droplet/particle size distribution in suspension polymerization reactors by taking into account the large spatial variations of the turbulent kinetic energy and its dissipation rate in the vessel. The two-compartment model comprised two mixing zones, namely an impeller zone of high local energy dissipation rates and a circulation zone of low kinetic energy. Computational fluid dynamics (CFD) was employed for generating the spatial distribution of energy dissipation rates within an unbaffled mixing vessel agitated by a flat two-blade impeller. A general methodology was developed for extracting, from the results of the CFD simulations, the volume ratio of the impeller over the circulation zone, the ratio of the average turbulent dissipation rates in the two zones, and the exchange flow rate between the two compartments. The effect of agitation rate, continuous phase viscosity, impeller diameter, and mixing vessel scale on the two-compartment model parameters was elucidated. The two-compartment model was then applied to a non-homogeneous liquid–liquid dispersion process to calculate the time evolution of the droplet size distribution in the mixing vessel. An excellent agreement was obtained between theoretical and experimental results on droplet size distributions obtained from a laboratory-scale reactor operated over a wide range of experimental conditions.

Use of CFD in prediction of particle size distribution in suspension polymer reactors

Abstract A two-compartment population balance model has been developed for taking into account the large spatial variations of the local turbulent kinetic energy, in order to predict the evolution of droplet sizes in a high holdup (i.e., 47–50 vol%) suspension polymerization system as a function of the most important process conditions. Phenomenological expressions were applied for describing the breakage and coalescence rates as a function of the local energy dissipation rate and physical properties of the system. Computational fluid dynamics (CFD) simulations were used for estimating the volume ratio of the impeller and circulation regions, the ratio of turbulent dissipation rates and the exchange flow rate of the two compartments at different agitation rates and continuous phase viscosities. A satisfactory agreement was obtained between theoretically and experimentally determined drop size distributions.

Steric stabilization in emulsion polymerization using oligomeric nonionic surfactants

Although nonionic surfactants show improved stabilization characteristics in emulsion polymerization as well as superior shear and freeze thaw stability of the final latex, their behaviour is generally not well understood. In the present paper a steric stabilization model is developed for describing particle stabilization in emulsion polymerization systems in the presence of nonionic oligomeric surfactants. The model takes into account the effect of unequal particle sizes on the steric interaction potential and the resulting enhanced heterocoagulation. An additional feature of the model is the incorporation of a possible surfactant lateral migration mechanism, which may be significant in the case of oligomeric nonionic surfactants. The proposed model can simulate reasonably well the experimentally observed conversion profiles and average particle sizes as a function of the surfactant molecular structure (i.e., lengths of stabilizing and adsorbing moieties) and surfactant concentration. As a result of the competing effects of the adsorbed volume fraction and surface coverage on particle stability, an optimum hydrophobicity/hydrophilicity ratio for the oligomeric nonionic surfactants can be derived.

Flow and particle deposition in the Turbuhaler: A CFD simulation

In this work the steady-state flow in a commercial dry powder inhaler device, DPI (i.e., Turbuhaler) is described using computational fluid dynamics. The Navier-Stokes equations are solved using commercial CFD software considering different flow models, i.e., laminar, k-ε, k-ε RNG, and k-ω SST as well as large Eddy simulation. Particle motion and deposition are described using a Eulerian-fluid/Lagrangian-particle approach. Particle collisions with the DPI walls are taken to result in deposition when the normal collision velocity is less than a critical capture velocity. Flow and particle deposition, for a range of mouthpiece pressure drops (i.e., 800-8800 Pa), as well as particle sizes corresponding to single particles and aggregates (i.e., 0.5-20 μm), are examined. The total volumetric outflow rate, the overall particle deposition as well as the spatial distribution of deposition sites in the DPI are determined. The transitional k-ω SST model for turbulent flow was found to produce results most similar to a reference solution obtained with LES, as well as experimental results for the pressure drop in the DPI. Overall, the simulation results are found to be in agreement with the available experimental data for local and total particle deposition.

Deposition and fine particle production during dynamic flow in a dry powder inhaler: a CFD approach.

In this work the dynamic flow as well as the particle motion and deposition in a commercial dry powder inhaler, DPI (i.e., Turbuhaler) is described using computational fluid dynamics, CFD. The dynamic flow model presented here is an extension of a steady flow model previously described in Milenkovic et al. (2013). The model integrates CFD simulations for dynamic flow, an Eulerian-fluid/Lagrangian-particle description of particle motion as well as a particle/wall interaction model providing the sticking efficiency of particles colliding with the DPI walls. The dynamic flow is imposed by a time varying outlet pressure and the particle injections into the DPI are assumed to occur instantaneously and follow a prescribed particle size distribution, PSD. The total particle deposition and the production of fine particles in the DPI are determined for different peak inspiratory flow rates, PIFR, flow increase rates, FIR, and particle injection times. The simulation results for particle deposition are found to agree well with available experimental data for different values of PIFR and FIR. The predicted values of fine particle fraction are in agreement with available experimental results when the mean size of the injected PSD is taken to depend on the PIFR.

Modelling of vinylidene fluoride emulsion polymerization

Abstract In the present study, a comprehensive mathematical model for the emulsion polymerization of vinylidene fluoride (VDF) in a semi-batch reactor is developed. The predictive capabilities of the model are demonstrated by a direct comparison of model predictions with experimental data on the monomer feed rate, monomer conversion, molecular weight averages and molecular weight distribution, mean particle size and particle size distribution, for a batch VDF emulsion polymerization reactor. It is shown that there is a good agreement between model predictions and experimental data.

An Integrated Computational Model of Powder Release, Dispersion, Breakage, and Deposition in a Dry Powder Inhaler

Abstract The present work describes an integrated computational model of airflow as well as particle dispersion, breakage and deposition in a Dry Powder Inhaler, DPI. The integrated model combines computational fluid dynamics, CFD, an Eulerian/Lagrangian model for particle motion and deposition, and a particle-wall collision model, which are employed to determine the parameters of a multi-compartment model of the DPI. Dynamic population balance models are solved in the compartment model to determine the breakup and deposition of particle agglomerates in the DPI during inhalation. This approach provides detailed information on the dispersion and deposition of powder particles in the DPI connecting formulation properties to key outflow features, e.g. emitted mass and fine particle fraction.

Solution of the Bi-variate dynamic population balance equation in batch particulate systems

Abstract This paper presents a comparative study on the application of different numerical methods for the solution of the dynamic bi-variate population balance equation (PBE) in batch particulate systems. Specifically, particulate processes operating under the combined action of particle aggregation and/or particle growth are examined. In order to solve the bi-variate PBE the Galerkin finite element method, the sectional grid technique, and the stochastic particle model are employed. The performance of these numerical methods (i.e., their accuracy and stability) is assessed by a direct comparison of the calculated bi-variate particle size distributions to available analytical solutions.

Computational Investigation of Vascular Surgical Interventions on Popliteal Artery Aneurysms

Abstract The present work describes an integrated CFD model of blood flow through a treated popliteal artery aneurism. The model is comprised of the treated region. Steady-state laminar and transitional-turbulent flow is employed to describe the blood flow through the stented region. The effect of stent development in the aneurism on blood flow and wall shear-stresses under relaxed and exerted conditions is determined. The proposed integrated model can identify arterial wall regions in danger of further disease progression and potentially can lead to guidelines for surgical interventions.

Airflow and Particle Deposition in a Dry Powder Inhaler: An Integrated CFD Approach

An integrated computational model of a commercial Dry Powder Inhaler, DPI, device (i.e., Turbuhaler) is developed. The steady-state flow in a DPI is determined by solving the Navier-Stokes equations using FLUENT (v6.3) considering different flow models, e.g., laminar, k-e, k-ω SST. Particle motion and deposition are described using an Eulerian-fluid/Lagrangian-particle approach. Particle/wall collisions are taken to result in deposition when the normal collision velocity is less than a size-dependent critical value. The flow rate and particle deposition are determined for a range of pressure drops (i.e., 800-8800Pa), as well as particle sizes corresponding to single particles and aggregates (i.e., 0.5-20μm). Overall, the simulation results are found to agree well with available experimental data for the volumetric outflow rate as well as the local and total particle deposition.