Values Of Solid Fraction Research Articles

Implementation of mechanistic modeling and global sensitivity analysis (GSA) for design, optimization, and scale-up of a roller compaction process

The pharmaceutical industry has been shifting towards the application of mechanistic modeling to improve process robustness, enable scale-up, and reduce time to market. Modeling approaches have been well-developed for processes such as roller compaction, a continuous dry granulation process. Several mechanistic models/approaches have been documented with limited application to high drug-loaded formulations. In this study, the Johanson model was employed to optimize roller compaction processing and guide its scale-up for a high drug loaded formulation. The model was calibrated using a pilot-scale Minipactor and was validated for a commercial-scale Macropactor. Global sensitivity analysis (GSA) was implemented to determine the impact of process parameter variations (roll force, gap, speed) on a quality attribute [solid fraction (SF)]. The throughput method, which estimates SF values of ribbons using granule production rate, was also studied. The model predicted SF values for all 14 Macropactor batches within ± 0.04 SF. The throughput method estimated SF with ± 0.06 SF for 7 out of 11 batches. GSA confirmed that roll force had the largest impact on SF. This case study represents a process modeling approach to build quality into the products/processes and expands the use of mechanistic modeling during drug product development.

Modeling of Styl'One Evolution Correction Factors for Multicomponent Mixtures Scaling-up to Roller Compaction

Roll compaction (RC) is a cost-effective dry granulation method, widely implemented in the pharmaceutical industry. In early formulation development however, when the material availability is limited, being able to predict the most important parameters in RC, like gap width and specific compaction force (SCF), to obtain a target ribbon solid fraction (SF) would significantly improve the formulation development efficiency as it would avoid the need of performing experiments on the roller compactor itself. However, at the present state of things, experiments on RC mechanical simulators present an overestimation of the target SF, when compared to roller compactor SF values. Although numerous correction approaches have been developed to improve the predictive performance of different mathematical models applied to the simulation experimental results, no study has collected a database wide enough to demonstrate the validity of a correction factor that allows to accurately simulate the compaction behavior of multicomponent mixtures. Here, 25 different formulations at 40 % drug load are compacted at different SCFs, both on a RC mimicking device (Styl'One Evolution) and on an actual roller compactor (Gerteis Mini-Pactor): following a similar approach as Reimer et al. and implementing a simplified version of the Johanson's mathematical model, 4 different correction factors are calculated, depending on how their material properties and pressure dependencies are considered. In conclusion, one correction factor is identified as the optimal trade-off between the SF prediction accuracy on the Gerteis Mini-Pactor and its applicability to a wide range of formulations, as it is independent of the material properties. This finding is particularly relevant when applied to scale-up to this specific roller compactor or early development processes of new formulations that have not been mechanically characterized yet.

Modeling of solid-air multi-dendrite growth evolution driven by coupled thermal-solute using non-isothermal quantitative phase field method

The safety hazard posed by residual or infiltrated air condensing into external oxygen-rich solid-air (SA) particles in the liquid hydrogen container deserves attention. In this study, the patterns of morphological evolution, oxygen solute distribution, and growth rate of SA single- and multi-dendrite under various thermal environments are investigated using a non-isothermal quantitative phase field model for the first time. The lattice anisotropy problem of six-fold symmetric dendrites is effectively avoided. The results show that the Type II boundary condition is more suitable for the simulation of dendrite growth, which can avoid the influence of boundary conditions on dendrite growth. In addition, the suitability of the isotropic difference method for simulating the growth of SA multi-dendrites with six-fold symmetry is verified in this paper. The maximum values of solid fraction and oxygen solute concentration within the simulated domain are 0.62 and 0.435, respectively, for an initial subcooling degree of 4 K. The temperature distribution is significantly altered by the application of boundary heat flux and affects the growth pattern of SA dendrites. Compared to the scenario with no boundary heat flux, unilateral heat input and heat extraction decreased the solid fraction of SA dendrites by 31% and increased it by 43%, respectively, while the maximum concentration of oxygen solute was reduced to 144.8% and 97.3%, respectively. When boundary heat flux was applied to all quadrilateral boundaries, the solid fraction under heat extraction and heat input conditions is reduced by 82% and enhanced by 138%, respectively, compared to the scenario with no boundary heat flux. Additionally, the maximum concentration of oxygen solute is found to be 197.6% and 69.5% of that without boundary heat flux, respectively. This study improves the understanding of the evolution of solid-air dendrite growth and can provide theoretical guidance for the safe use of liquid hydrogen systems.

Particle non-isothermality effect on the radiative thermal conductivity in dense particulate systems

Emerging high-temperature applications require a deeper understanding of radiative heat transfer in particulate systems, while existing theoretical tools are still limited in estimating the influence of the highly variable particle parameters (morphology, size, and optical properties) on heat transfer characteristics. In this work, a novel method is developed to determine radiative heat transfer in optically thick particulate media based on the radiation distribution factor. The important parameters of characterizing radiative heat transfer in particulate systems, i.e., transport coefficient and radiative thermal conductivity, are directly calculated by the Monte Carlo ray tracing method at particle scale. Two ideal cases of high and low thermal conductivity of solid particles, characterized by radiative Biot number Bi, are considered to investigate the effect of particle non-isothermality on the radiative thermal conductivity, which correspond to the cases of isothermal (Bi<<1) and non-isothermal particles (Bi>>1), respectively. The results show that radiative transfer is more intensive in isothermal particles due to the additional contribution of internal heat transfer in highly conductive particles. The difference between the limits of isothermal particles and non-isothermal particles is significant at high values of solid fraction and surface emissivity. In addition, the results are used to estimate the applicability domain of the analytic multiphase approach. This work brings new insights to the understanding of radiative heat transfer in particulate media.

Numerical Prediction of Turbulent Drag Reduction with Different Solid Fractions and Distribution Shapes over Superhydrophobic Surfaces

The exploration of superhydrophobic drag reduction has been and continues to be of significant interest to various industries. In the present work, direct numerical simulation (DNS) is utilized to investigate the effect of the parameters on the drag-reducing performance of superhydrophobic surfaces (SHS). Simulations with a friction Reynolds number of 180 were carried out at solid fraction values of ϕs=116,111, and 14, and three distribution shapes: aligned, staggered, and random. The top wall is the smooth one, and the bottom wall is a superhydrophobic surface (SHS). Drag reduction and Reynolds stress profiles are compared for all cases. The turbulent kinetic energy budget, including production, dissipation, and diffusion, is presented with respect to the solid fraction and type of distribution to investigate the drag reduction mechanism. The sizes of the longitudinal vortices and formation of hairpin vortices are investigated through the observation of coherent structures. The simulation of a post model is a useful method to study the drag reduction for different solid fraction values and distribution geometries. Our study demonstrates that the drag reduction could acquire 42% with the solid fraction value ϕs=116 and an aligned distribution shape for post superhydrophobic surface geometry. Our study also showed the relationship of the Reynolds stress component (R11, R22, and R33) to the drag reduction with the differences in the solid fraction values and distribution geometry. In which, the R11 component has the most change between an aligned distribution and a random one. The peak value of R11 tends to shift away from the SHS wall. In addition, the analysis of the TKE budget over the superhydrophobic surface was performed, which can be adopted as a useful resource in turbulence modeling based on RANS methodology.

Compression of amorphous solid dispersions prepared by hot-melt extrusion, spray drying and vacuum drum drying

The present study explored vacuum drum drying (VDD) as an alternative technology for amorphous solid dispersions (ASDs) manufacture compared to hot-melt extrusion (HME) and spray drying (SD) focusing on downstream processability (powder properties, compression behavior and tablet performance). Ritonavir (15% w/w) in a copovidone/sorbitan monolaurate matrix was used as ASD model system. The pure ASDs and respective tablet blends (TB) (addition of filler, glidant, lubricant) were investigated. Milled extrudate showed superior powder properties (e.g., flowability, bulk density) compared to VDD and SD, which could be compensated by the addition of 12.9% outer phase. Advantageously, the VDD intermediate was directly compressible, whereas the SD material was not, resulting in tablets with defects based on a high degree of elastic recovery. Compared to HME, the VDD material showed superior tabletability when formulated as TB, resulting in stronger compacts at even lower solid fraction values. Despite the differences in tablet processing, tablets showed similar tablet performance in terms of disintegration and dissolution independent of the ASD origin. In conclusion, VDD is a valid alternative to manufacture ASDs. VDD offered advantageous downstream processability compared to SD: less solvents and process steps required (no second drying), improved powder properties and suitable for direct compression.

Impact of gravity-induced and Fourier’s heat flux on the nano-film flow over thermal sensitive surface

This article investigates the phenomenon of gravity-driven flow of nanoliquid film along a vertical surface under the effects of nonlinear thermal radiations. The falling nanofluid film is subjected to a convectively heated surface along with slip condition. The flow and thermal properties are investigated considering four different nanoparticles namely Ag (silver), Cu (copper), $$\mathrm {TiO}_2$$ (Titania) and $$\mathrm {Al}_2\mathrm{O}_3$$ (alumina) with water as a acting base fluid. The physical model is presented in terms of nonlinear partial differential equations. These equations are reduced to a system of nonlinear ordinary differential equations through similarity transformations. The problem is solved numerically utilizing Bvp4c function in MATLAB. Multiple solutions are presented for unfavorable buoyancy or opposing flow ( $$\sigma <0$$ ) and favorable buoyancy or assisting flow ( $$\sigma >0$$ ). The impact of nanoparticle volume fraction is found to be useful in intensifying the temperature and dropping heat transfer rate because of dominant convection. It is worth mentioning that silver nanoparticles in the thin film of nanofluid lead to higher wall shear stress and heat transfer rate. The increasing nature of skin friction coefficient $$(C_f)$$ is examined in buoyancy assisting flow while in opposing buoyancy flow its behavior is noticed reduced for various values of solid fraction ( $$\phi $$ ) of $$\mathrm {Ag}$$ nanoparticles.

Development of Superhydrophilic 6061 Aluminum Alloy by Stepwise Anodization According to Pore-Widening Time

This study created alumina structures with the highest hydrophilic properties on 6061 aluminum alloy. The anodization process was applied to make various aluminum oxide structures. To create uniform alumina structures on top of a 6061 aluminum alloy surface, after conducting the first anodization in 0.3 M oxalic acid at 40 V at 0 &lt;sup&gt;o&lt;/sup&gt;C, the alumina was removed using a mixture of chromic acid and phosphoric acid. Then, secondary and tertiary anodization was performed using the same electrolyte conditions as the primary anodization for 30 minutes at 40 V, respectively. Pore-widening (PW) of oxide film formed after the secondary anodic oxidation was performed for 20, 30, and 40 minutes in 0.1 M phosphoric acid solution. The PW time control allowed various oxide structures to be created, and reduced the area of the outermost surface in contact with water droplets. The smaller the initial area of water droplets, the better the hydrophilic phenomenon. The surface area can be represented as a solid fractional value. Surfaces with solid fraction values of less than or equal to 0.5 were superhydrophilic. This well-controlled anodization process with a pore-widening step can be used to create excellent superhydrophilicity on various metallic substrates, expanding their usefulness and efficacy.

Developing thixo-extrusion process for additive manufacturing of metals in semi-solid state

This paper deals with a comprehensive study of the semi-solid metal extrusion and deposition (SSMED) process and influencing parameters. This process could be considered as a non-powder based metal Additive Manufacturing (AM) method. Unlike the common methods of metal AM, it utilizes the extrusion of a metallic filament in a semi-solid state (thixo-extrusion) to build the final product from a CAD file in a layer-wise fashion. A continuous wire thixo-extruder was designed and mounted on a 3 axis table to deposit semi-solid slurry layer by layer. This work seeks to provide a better understanding of the impact of the principle process variables on the quality of this layer-wise freeform fabrication method. The process parameters related to the production and pre-treatment of the metallic filament, its thixo-extrusion, rheological and microstructural aspects are included in this study. The results show that wire pre-treatment process variables have strong effect on the globular microstructure of metallic filament and this in turn has great role in the alloy’s thixo-extrudability. Proper design of a thixo-extruder and selecting accurate values for the influencing parameters is the key to a successful production. The quality of the fabricated part was influenced by several factors such as microstructural, geometrical and run time parameters. Semi-solid alloy's solid fraction was the most influential factor in the thixo-extrusion process. Alloys with solid fraction values in the range of 0.3-0.6 could be thixo-extruded. It was found that temperature distribution and feed rate had a great effect on the process performance. Also design guidelines for selecting the appropriate thixo-extrusion properties were presented for different operating conditions.

Geometrical properties of rigid frictionless granular packings as a function of particle size and shape.

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedra) achieve higher solid fraction values than amorphous packings of spherical or rounded particles, thus fulfilling the analog of Ulam's conjecture stated by Jiao and co-workers for random packings [Y. Jiao and S. Torquato, Phys. Rev. E 84, 041309 (2011)PLEEE81539-375510.1103/PhysRevE.84.041309]. This seeming discrepancy between experimental and numerical results is believed to result from difficulties in overcoming inter particle friction through experimental densification processes. Moreover, solid fraction is shown to increase further with bidispersity and peak when the volume proportion of small particles reaches 30%. Contrarily, substituting up to 50% of flat pinacoids for isometric ones yields solid fraction decrease, especially when flat particles are also elongated. Nevertheless, particle shape seems to play a minor role in packing solid fraction compared to polydispersity. Additional investigations focused on the packing microstructure confirm that pinacoid packings fulfill the isostatic conjecture and that they are free of order except beyond 30% to 50% of flat or flat-elongated polyhedra in the packing. This order increase progressively takes the form of a nematic phase caused by the reorientation of flat or flat-elongated particles to minimize the packing potential energy. Simultaneously, this reorientation seems to increase the solid fraction value slightly above the maximum achieved by monodisperse isometric pinacoids, as well as the coordination number. Finally, partial substitution of elongated pinacoids for isometric ones has limited effect on packing solid fraction or order.

Convective heat transfer characteristics of low Reynolds number nanofluid flow around a circular cylinder

Numerical investigation of heat transfer phenomena of low Reynolds number nano-fluid flow over an isothermal cylinder is presented in this paper. Steady state governing equations (continuity, N–S and energy equations) have been solved using finite volume method. Stationary heat transfer, and flow characteristics over the cylinder have been studied for water based copper nanofluid with different solid fraction values. The effect of volume fraction of nano- particles on the fluid flow and heat transfer were investigated numerically. It was found that at a given Nusselt number, drag coefficient, re-circulation length, and pressure coefficient increase by increasing the volume fraction of nano-particles.

Heat Transfer Characteristics of Low Reynolds Number Flow of Nanofluid Around a Heated Circular Cylinder

Numerical investigation of heat transfer phenomena over an isothermal cylinder, for low Reynolds number flow of nanofluid is presented. Conservation equation of mass, momentum and energy under steady state have been solved using finite volume method. Heat transfer characteristic and flow over the stationary cylinder has been studied for water based copper nano fluid with different solid fraction values. Local Nusselt number over the cylinder surface has been found to increase with increase in nano particle fraction as well as increase in flow strength, though, the physics behind the rise in two cases is entirely different. Local heat flux drops along the cylinder wall and increases with increase in nano particle fraction as well as Reynolds number. Neglecting buoyancy effect, flow separation angle is not affected by presence of nano particles in the base fluid.

Numerical Simulation and Experimental Investigation on Thixo-Backward Extrusion of 7075 Aluminium Alloy

The thixoextrusion process could become an important technique to extend the complexity of extruded profiles. However, the complex thixotropic flow behavior of semi-solid, during thixoextrusion is still partly characterized. The study described in this paper investigates thixoextrusion for 7075 aluminium alloy at different temperature conditions. A complete die filling and a good surface state of parts was obtained at high solid fraction (fS = 0.70), in heated dies, for an extrusion ram speed of 416 mm/s. The thixoextrusion process is simulated using the finite element code Forge2009©. The constitutive equation used for these simulations is based on a micro-macro model for the semi-solid evolution. The tendency of the experimental curves evolution, preserving the same parameters of the micro-macro constitutive model, for each values of solid fraction, was reproduced, except the last step of the ram displacement.

Mono-sized sphere packing algorithm development using optimized Monte Carlo technique

In this paper, fuel cell catalyst layer was developed using the optimized sphere packing algorithm. An optimization technique named adaptive random search technique (ARSET) was employed in this packing algorithm. The ARSET algorithm will generate the initial location of spheres and allow them to move in the random direction with the variable moving distance, randomly selected from the sampling range (α), based on the Lennard–Jones potential and Morse potential of the current and new configuration. The solid fraction values obtained from this developed algorithm are in the range of 0.610–0.624 while the actual processing time can significantly be reduced by 5.58–34% based on the number of spheres. The initial random number sampling range (α) was investigated and the appropriate α value is equal to 0.5.

Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

The influence of grain angularity on the properties of dense flows down a rough inclined plane are investigated. Three-dimensional numerical simulations using the nonsmooth contact dynamics method are carried out with both spherical (rounded) and polyhedral (angular) grain assemblies. Both sphere and polyhedra assemblies abide by the flow start and stop laws, although much higher tilt angle values are required to trigger polyhedral grain flow. In the dense permanent flow regime, both systems show similarities in the bulk of the material (away from the top free surface and the substrate), such as uniform values of the solid fraction, inertial number and coordination number, or linear dependency of the solid fraction and effective friction coefficient with the inertial number. However, discrepancies are also observed between spherical and polyhedral particle flows. A dead (or nearly arrested) zone appears in polyhedral grain flows close to the rough bottom surface, reflected by locally concave velocity profiles, locally larger coordination number and solid fraction values, smaller inertial number values. This dead zone disappears for smooth bottom surfaces. In addition, unlike sphere assemblies, polyhedral grain assemblies exhibit significant normal stress differences, which increase close to the substrate.

Experiments and simulations of gas–solid flow in an airlift loop reactor

The hydrodynamics in a gas–solid airlift loop reactor was investigated systematically using experimental measurements and CFD simulation. In the experiments, the time averaged parameters, such as solid fraction and particle velocity, were measured by optical fiber probe. In the simulation, the modified Gidaspow drag model accounting for the interparticles clustering was incorporated into the Eulerian–Eulerian CFD model with particulate-phase kinetic theory. Predicted values of solid fraction and particle velocity were compared with experimental results, validating the drag model and the simulation. The results show that the profiles of particle velocity and solid fraction are uniform in annulus. However, the core-annulus structure appears in other three regions (draft tube region, bottom region and particle diffluence region), which presents the similar heterogeneous feature of aggregative fluidization usually occurred in normal fluidized beds. Simulated profiles of particle residence time distribution indicate that the airlift loop reactor should be characterized by near perfect mixing.

Effect of solidification path and contraction on the cracking susceptibility of carbon peritectic steels

The solidification path and contraction generated during the solidification of three carbon steels were studied. Two of the carbon steels were of hypo-peritectic chemical composition, with 0.11 % C and 0.15 % C, while one of the carbon steels were hyper-peritectic with 0.16 % C. The steels with 0.11 % C and 0.16 % C solidified as expected due to their chemical composition. In contrast, the chemically hypo-peritectic steel with 0.15 % C solidified as hyper-peritectic steel, which was associated with the microsegregation of Mn. For the steel exhibiting a hypo-peritectic solidification path, peritectic transformation occurred at solid fraction values higher than 0.9, where it was assumed that the contraction generated in the mushy shell cannot be fed by the liquid. However, for steels exhibiting a hyper-peritectic solidification path, peritectic transformation began at solid fraction values lower than 0.9, where the contraction generated by the peritectic transformation was partly fed by the liquid. Hence, the highest cracking susceptibility was associated with the hypo-peritectic solidification mode.

Profiles of solid fraction and heterogeneous phase structure in a gas–solid airlift loop reactor

The time-averaged and transient local solid fractions in a gas–solid airlift loop reactor (ALR) were investigated systematically by experiments and CFD simulations. To demonstrate the macro-flow pattern, the time-averaged local solid fractions in four regions of the ALR were measured by optical fiber probe under the conditions of different superficial gas velocities and particle circulation fluxes. The experimental results show that the lateral distribution of time-averaged local solid fraction is a core-annulus or heterogeneous structure in the three regions (draft tube, bottom region, particle diffluence region), but a uniform lateral distribution in the annulus. The operating conditions have different effects on the lateral distribution of time-averaged local solid fraction in each region. In the CFD simulation, a modified Gidaspow drag model considering the formation of particle clusters was incorporated into the Eulerian–Eulerian CFD model with particulate phase kinetic theory to simulate and analyze the transient local solid fraction and the two-phase micro-structures in the gas–solid ALR. The predicted values of solid fraction were compared with the experimental results, validating the drag model. The contours of transient flow field indicate that the flow field of the ALR should be divided into five flow regions, i.e., draft tube, annulus, bottom region, particle diffluence region and constrained back-mixing region, which further improves the understanding of the airlift reactor where only four divisions were determined from the experiments. The transient local solid fraction and its probability density function profoundly reveal the two-phase micro-structures (dilute phase and emulsion phase or cluster phase in the constrained back-mixing region) and explain the heterogeneous phenomenon of solid fraction in the ALR. The dilute phase tends to exist in the center of bed, while the emulsion phase mainly appears in the wall region. The results also indicate that the gas–solid ALR has the common characteristic of aggregative fluidization similar to that in normal fluidized beds. The simulated two-phase transient micro-structures provide the appropriate explanations for the experimental core-annulus macro-structures of time-averaged local solid fraction.

Description of the Hypo-peritectic Steel Solidification under Continuous Cooling and Crack Susceptibility

This study describes the phase evolution during solidification under continuous cooling conditions of a hypo-peritectic multicomponent steel. Additionally, the mechanical behavior and dimensional variation of the solid–liquid skin were evaluated by using mathematical expressions reported in the literature as a function of the proportion of phases and solute distribution respectively. The crack susceptibility of the solid–liquid skin depended on the proportion of phases and it occurred in two solid fraction regions, independently of the cooling rate. For the region exhibiting the lowest solid fraction values this susceptibility was associated to γ phase, while at the highest solid fraction values it was related to δ phase.At the end of the peritectic transformation the highest contraction observed can be considered as an additional contribution to the crack susceptibility in the solid fraction range of 0.92–0.98. The significant microsegregation of Mn observed for high cooling rates promotes a change in the solidification mode, from a hypo-peritectic mode into a hyper-peritectic mode and the expansion of solid formed from the remaining liquid.

Implications of solid phase interaction mechanisms on momentum, heat and solute transport in semi-solid materials processing

In this work, the problem of mathematical modeling of transport phenomena during semi-solid metal processing is investigated from a fundamental approach. The phenomenon of solid phase interaction is modeled by an evolution equation of an internal state variable. The formation of an interconnected network of agglomerated solid fragments at high values of solid fraction is also accounted for, leading to a more realistic prediction of momentum transport in comparison to other standard models reported in the literature. Numerical simulations are performed based on two separate momentum transport models. One of the models essentially neglects solid phase interaction mechanisms, whereas the other one incorporates the associated transport features, in order to capture the implications of solid phase agglomeration in a semi-solid slurry processing. A detailed analysis of the results reveals a profound impact of agglomeration and break-up on the transport phenomena, which need to be effectively captured.