Computational Fluid Dynamics data for improving freeze-dryers design.

Computational Fluid Dynamics (CFD) can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular data concerning the freeze-dryer chamber and the duct connecting the chamber with the condenser, with the valves and vanes eventually present are given here, and can be used to understand the behavior of the apparatus allowing an improved design. Pilot and large scale freeze-drying chambers have been considered; data of a detailed simulation of a complete pilot scale apparatus, including duct and condenser, are included. Data on conductance of an empty duct with different L/D ratio, on disk valves with different geometry, and on mushroom valve are presented. Velocity, pressure, temperature and composition fields are reported on selected planes for chambers and valves. Results of dynamic simulations are also presented, to evaluate possible performance of monitoring devices in the chamber. Some further data, with detailed interpretation and discussion of the presented data can be found in the related research article by Barresi et al. [1] and Marchisio et al. [2].

Extended Charge-On-Particle Optimized Potentials for Liquid Simulation Acetone Model: The Case of Acetone-Water Mixtures.

It is well-known that classical molecular dynamics simulations of acetone-water mixtures lead to a strong phase separation when using most of the standard all-atom force fields, despite the well-known experimental fact that acetone is miscible with water in any proportion at room temperature. We describe here the use of a charge-on-particle model for accounting for the induced polarization effect in acetone-water mixtures which can solve the demixing problem at all acetone molar fractions. The polarizability effect is introduced by means of a virtual site (VS) on the carbonyl group of the acetone molecule, which increases its dipole moment and leads to a better affinity with water molecules. The VS parameter is set by fitting the density of the mixture at different acetone molar fractions. The main novelty of the VS approach lies on the transferability and universality of the model because the polarizability can be controlled without modifying the force field adopted, like previous efforts did. The results are satisfactory also in terms of the transport properties, that is, diffusivity and viscosity coefficients of the mixture.

Use of computational fluid dynamics for improving freeze-dryers design and process understanding. Part 1: Modelling the lyophilisation chamber.

This manuscript shows how computational models, mainly based on Computational Fluid Dynamics (CFD), can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular, the freeze-dryer chamber and the duct connecting the chamber with the condenser, with the valves and vanes eventually present are analysed in this work. In Part 1, it will be shown how CFD can be employed to improve specific designs, to perform geometry optimization, to evaluate different design choices and how it is useful to evaluate the effect on product drying and batch variance. Such an approach allows an in-depth process understanding and assessment of the critical aspects of lyophilisation. This can be done by running either steady-state or transient simulations with imposed sublimation rates or with multi-scale approaches. This methodology will be demonstrated on freeze-drying equipment of different sizes, investigating the influence of the equipment geometry and shelf inter-distance. The effect of valve type (butterfly and mushroom) and shape on duct conductance and critical flow conditions will be instead investigated in Part 2.

Use of computational fluid dynamics for improving freeze-dryers design and process understanding. Part 2: Condenser duct and valve modelling.

This manuscript shows how computational models, mainly based on Computational Fluid Dynamics (CFD), can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular in this part the duct connecting the chamber with the condenser, with its valves, is considered, while the chamber design and its effect on drying kinetics have been investigated in Part 1. Such an approach allows a much deeper process understanding and assessment of the critical aspects of lyophilisation. This methodology will be demonstrated on freeze-drying equipment of different sizes, investigating influence of valve type (butterfly and mushroom) and shape on duct conductance and critical flow conditions. The role of the inlet and boundary conditions considered has been assessed, also by modelling the whole apparatus including chamber and condenser, and the influence of the duct diameter has been discussed; the results show a little dependence of the relationship between critical mass flux and chamber pressure on the duct size. Results concerning the fluid dynamics of a simple disk valve, a profiled butterfly valve and a mushroom valve installed in a medium size horizontal condenser are presented. Also in these cases the maximum allowable flow when sonic flow conditions are reached can be described by a correlation similar to that found valid for empty ducts; for the mushroom valve the parameters are dependent on the valve opening length. The possibility to use the equivalent length concept, and to extend the validity of the results obtained for empty ducts will be also discussed. Finally the presence of the inert gas modifies the conductance of the duct, reducing the maximum flow rate of water that can be removed through it before the flow is choked; this also requires a proper over-sizing of the duct (or duct-butterfly valve system).

Recirculation zones induce non-Fickian transport in three-dimensional periodic porous media.

In this work, the influence of pore space geometry on solute transport in porous media is investigated performing computational fluid dynamics pore-scale simulations of fluid flow and solute transport. The three-dimensional periodic domains are obtained from three different pore structure configurations, namely, face-centered-cubic (fcc), body-centered-cubic (bcc), and sphere-in-cube (sic) arrangements of spherical grains. Although transport simulations are performed with media having the same grain size and the same porosity (in fcc and bcc configurations), the resulting breakthrough curves present noteworthy differences, such as enhanced tailing. The cause of such differences is ascribed to the presence of recirculation zones, even at low Reynolds numbers. Various methods to readily identify recirculation zones and quantify their magnitude using pore-scale data are proposed. The information gained from this analysis is then used to define macroscale models able to provide an appropriate description of the observed anomalous transport. A mass transfer model is applied to estimate relevant macroscale parameters (hydrodynamic dispersion above all) and their spatial variation in the medium; a functional relation describing the spatial variation of such macroscale parameters is then proposed.

Cotton fabric functionalisation with menthol/PCL micro- and nano-capsules for comfort improvement.

OBJECTIVE: Cotton functionalisation with poly-ɛ-caprolactone (PCL) micro- and nano-capsules containing menthol was carried out with the aim of introducing a long-lasting refreshing sensation. MATERIALS AND METHODS: The preparation of the polymer micro- and nano-capsules was carried out by solvent displacement technique. A confined impinging jets mixer was used in order to ensure fast mixing and generate a homogeneous environment where PCL and menthol can self-assemble. RESULTS: The micro- and nano-capsules and the functionalised fabrics were characterised by means of DSC, FT-IR spectroscopy and SEM imaging. Micro- and nano-capsules of different size, from about 200 to about 1200 nm, were obtained varying menthol to PCL ratio (from 0.76 to 8), overall concentration and flow rate (i.e. mixing conditions). The inclusion of menthol was confirmed by DSC analysis. DISCUSSION AND CONCLUSION: A patch test was carried out by 10 volunteers. Micro-capsules were found to be effective in conferring the fabric a refreshing sensation without altering skin physiology.

Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media.

In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed.

Dynamic light scattering and X-ray photoelectron spectroscopy characterization of PEGylated polymer nanocarriers: internal structure and surface properties.

In this work, nanospheres and nanocapsules are precipitated in confined impinging jet mixers through solvent displacement and characterized. Acetone and water are used as the solvent and antisolvent, respectively, together with polymethoxypolyethylene glycol cyanoacrylate-co-hexadecylcyanoacrylate and Miglyol as the copolymer and oil, respectively. Characterization is performed with dynamic light scattering, with electrophoretic measurements, and for the first time with X-ray photoelectron spectroscopy. Results show that the presence of polyethylene glycol chains seems to be more pronounced on the surface of nanospheres than on that of nanocapsules. The thickness of the copolymer layer in nanocapsules ranges from 1 to 10 nm, depending on the value of the oil:copolymer mass ratio. Fast dilution is confirmed to have a positive effect in suppressing aggregation but can induce further copolymer precipitation.

Size control in production and freeze-drying of poly-ε-caprolactone nanoparticles.

This work is focused on the control of poly-ε-caprolactone nanoparticle characteristics, notably size and size distribution, in both the production and preservation (by using freeze-drying) stages. Nanoparticles were obtained by employing the solvent displacement method in a confined impinging jets mixer. The effect of several operating conditions, namely, initial polymer concentration and solvent-to-antisolvent flow rate ratio, and the influence of postprocessing conditions, such as final dilution and solvent evaporation, on nanoparticle characteristics was investigated. Further addition of antisolvent (water) after preparation was demonstrated to be effective in obtaining stable nanoparticles, that is, avoiding aggregation that would result in larger particles. On the contrary, solvent (acetone) evaporation was shown to have a small effect on the final nanoparticle characteristics. Eventually, freeze-drying of the solutions containing nanoparticles, after solvent evaporation, was also investigated. To ensure maximum nanoparticles stability, lyoprotectants (e.g., sucrose and mannitol) and steric stabilizers (e.g., Cremophor EL and Poloxamer 388) had to be added to the suspensions. The efficacy of the selected lyoprotectants, in the presence (or absence) of steric stabilizers, and in various concentrations, to avoid particle aggregation during the freeze-drying process was investigated, thus pointing to the optimal formulation.

Microscale simulation of particle deposition in porous media.

In this work several geometries, each representing a different porous medium, are considered to perform detailed computational fluid dynamics simulation for fluid flow, particle transport and deposition. Only Brownian motions and steric interception are accounted for as deposition mechanisms. Firstly pressure drop in each porous medium is analyzed in order to determine an effective grain size, by fitting the results with the Ergun law. Then grid independence is assessed. Lastly, particle transport in the system is investigated via Eulerian steady-state simulations, where particle concentration is solved for, not following explicitly particles' trajectories, but solving the corresponding advection-diffusion equation. An assumption was made in considering favorable collector-particle interactions, resulting in a "perfect sink" boundary condition for the collectors. The gathered simulation data are used to calculate the deposition efficiency due to Brownian motions and steric interception. The original Levich law for one simple circular collector is verified; subsequently porous media constituted by a packing of collectors are scrutinized. Results show that the interactions between the different collectors result in behaviors which are not in line with the theory developed by Happel and co-workers, highlighting a different dependency of the deposition efficiency on the dimensionless groups involved in the relevant correlations.

Production of PEGylated nanocapsules through solvent displacement in confined impinging jet mixers.

The growth of importance of nanocapsules (and other particulate systems) in different fields requires fast and reproducible methods for their production. Confined impinging jet mixers were successfully used for the production of nanospheres and are now tested for the first time for the production of nanocapsules. This work focuses on the understanding of formation mechanisms and on the quantification of the effect of the most important operating parameters involved in their production. Solvent displacement is employed here for the assembly of the nanocapsules by using a PEGylated derivative of cyanoacrylate as copolymer. A comparison with nanospheres obtained under the same operating conditions is also reported. Results show that the oil-to-copolymer mass ratio (MR) is the main factor affecting the final size distribution and that small nanocapsules are obtained only at low oil-to-copolymer MR. The effect of mixing is significant, proving that mixing of solvent and antisolvent also affects the final size distribution; this depends mainly on the inlet jet velocity, but the size of the mixer is also important. The Reynolds number may be useful to take this into account for geometrically similar systems. Quenching by dilution allows to stabilize the nanocapsules, evidencing the role of aggregation and ripening.

Preparation of poly(MePEGCA-co-HDCA) nanoparticles with confined impinging jets reactor: experimental and modeling study.

In this work, the biodegradable copolymer poly(methoxypolyethyleneglycolcyanoacrylate-co-hexadecylcyanoacrylate) is used to prepare nanoparticles via solvent displacement in a confined impinging jets reactor (CIJR). For comparison, nanoparticles constituted by the homopolymer counterpart are also investigated. The CIJR is a small passive mixer in which very fast turbulent mixing of the solvent (i.e., acetone and tetrahydrofuran) and of the antisolvent (i.e., water) solutions occurs under controlled conditions. The effect of the initial copolymer concentration, solvent type, antisolvent-to-solvent ratio, and mixing rate inside the mixer on the final nanoparticle size distribution, surface properties, and morphology is investigated from the experimental point of view. The effect of some of these parameters is studied by means of a computational fluid dynamics (CFD) model, capable of quantifying the mixing conditions inside the CIJR. Results show that the CIJR can be profitably used for producing nanoparticles with controlled characteristics, that there is a clear correlation between the mixing rate calculated by CFD and the mean nanoparticle size, and therefore that CFD can be used to design, optimize, and scale-up these processes.

On the use of a dual-scale model to improve understanding of a pharmaceutical freeze-drying process.

The evolution of product temperature and of residual ice content in the various vials of a batch during a freeze-drying process can be significantly affected by local conditions around each vial. In fact, vapor fluid dynamics in the drying chamber determines the local pressure that, taking into account the heat flow from the shelf and, eventually, radiation from chamber surfaces, is responsible for the sublimation rate and product temperature. These issues have to be taken into account when using mathematical simulation to predict the evolution of the product as a consequence of the operating conditions (recipe design), as well as during the scale-up of a recipe obtained in a small-scale equipment to a large-scale unit. In this framework, a dual-scale model can significantly improve the understanding for pharmaceuticals freeze-drying processes: it couples a three-dimensional model, describing the fluid dynamics in the chamber, and a second mathematical model, either mono- or bi-dimensional, describing the drying of the product in each vial. Thus, it can be profitably used to gain knowledge about process dynamics, and to improve the design of the equipment, as well as the performance of the control system of the process.

Strategies to control the particle size distribution of poly-epsilon-caprolactone nanoparticles for pharmaceutical applications.

In this work turbulent precipitation through solvent displacement for the production of poly-epsilon-caprolactone (PCL) nanoparticles is investigated; two different PCL molecular weights have been employed, using acetone and water as solvent and anti-solvent, respectively. The main important thermodynamic and kinetic parameters, such as solubility and interfacial tension of PCL in water-acetone mixtures, are determined and the effect of the process operating conditions on the final particle size distribution is also investigated. Particles produced under different conditions into a Confined Impinging Jets Reactor (CIJR) were characterized by Dynamic Light Scattering, Zeta potential measurements and Scanning Electronic Microscopy. Results clearly show the strong effect of mixing on the particle size distribution and how mixing must be controlled in order to obtain a product with particular characteristics. Eventually the measured thermodynamic and kinetic parameters are used to interpret the obtained experimental data.

Quadrature method of moments for aggregation-breakage processes.

Investigation of particulate systems often requires the solution of a population balance, which is a continuity statement written in terms of the number density function. In turn, the number density function is defined in terms of an internal coordinate (e.g., particle length, particle volume) and it generates integral and derivative terms. Different methods exist for numerically solving the population balance equation. For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics (CFD) simulation. Such an approach requires the addition of a large number of scalars and the associated transport equations. This increases the CPU time required for the simulation, and thus it is clear that it is very important to use as few scalars as possible. In this work the quadrature method of moments (QMOM) is used. The QMOM has already been validated for crystal growth and aggregation; here the method is extended to include breakage. QMOM performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.