Inter-tablet coating variability: Tablet residence time variability

This paper investigates inter-tablet coating variability, specifically, the variability of tablet residence times within the spray zone of a horizontal coating pan. Results from experiments, discrete element method (DEM) computer simulations, and an analytical model developed to describe the coating mass distribution are presented.The simulations indicate that the coefficient of variation of tablet residence times, and subsequently, of coating mass, decreases with time following a power law relation. The theoretical model demonstrates that the coefficient of variation of residence time for a randomly mixed tablet bed is inversely proportional to the square root of the number of coating “trials”. DEM simulations show that during each pan revolution, tablets in the spray zone remain in a quasi-segregated state from tablets located outside the spray zone for some time period termed Δt_seg. Increasing the pan's Froude number, the spray zone aspect ratio, and the tablet-tablet and tablet-pan friction coefficient all act to decrease Δt_seg, leading to more uniform residence times and less inter-tablet coating variability for a given operating time. The relationship between Δt_seg and tablet load is more complex due changes in bed dynamics. In addition to the variability studies, a model is developed that relates coating fraction, effective mass flow rate, Δt_seg, and the desired coating mass to the allowable fraction of tablets with a coating mass lying outside of a specified range of coating masses.     

Island dynamics on charged silver electrodes: Kinetic Monte-Carlo simulations

The fluctuations of steps and the shapes of islands on metal surfaces generally depend strongly on the electrode potential, an effect that has been attributed to the interaction of local surface dipole moments with the double-layer field. In order to understand the details of this effect, we have calculated the relevant energies and dipole moments for the diffusion processes that govern the fluctuations of steps and island shapes on Ag(1 0 0). The corresponding rates have been used in kinetic Monte-Carlo simulations to explore the dynamics of these structures. Due to the field-dipole interactions the mobility of the surface becomes larger with increasing electrode potential. Fourier analysis allows us to determine the step stiffness and the kink energy, and from the shape of the islands we have obtained the line tension. All three quantities decrease with increasing double-layer field.     

Dynamic Monte-Carlo simulations of diffusion limited reactions in rough nanopores

It has recently been demonstrated that self- (or tracer) diffusivities and transport diffusivities of gases in nanoporous materials may differ in the Knudsen regime, when the pore surface is rough on molecular scales. Self-diffusion is roughness dependent, while transport diffusion is not. The impact of this result on diffusion-controlled reactions, catalyzed by porous catalysts with a rough internal surface, is now investigated. We consider the steady-state problem of a species diffusing in a three-dimensional pore with a fractal surface, on which the species reacts. Dynamic Monte-Carlo simulations and analytical calculations show that the self-diffusivity plays the fundamental role in determining the effective catalytic efficiency of a rough pore. The transport diffusivity, on the other hand, is not the fundamental quantity of interest to surface phenomena such as heterogeneous catalysis, and can only be used for porous materials with a smooth internal surface, in which case the self- and transport diffusivities coincide.     

Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

A new procedure for estimating surface diffusivities and tortuosities within realistic models of complex porous structures is reported. Our approach uses Monte-Carlo tracer methods to monitor mean-square displacements for molecules restricted to wander on pore walls within model random mesoporous solids typical of those used as adsorbents, heterogeneous catalysts, and porous membranes. We consider model porous solids formed from initial packings of spheres with unimodal, Gaussian, or bimodal distributions of size; changes in pellet porosity are achieved by increasing microsphere radii and by randomly removing spheres from highly densified packings in order to simulate densification and coarsening, respectively. Geometric tortuosities for the surface phase reached large values at void fractions near 0.04 and 0.42 for densified solids; the surface tortuosity gave a minimum value of 1.9 at a void fraction of ∼0.26. These high tortuosities correspond to percolation thresholds for the void and solid phases, which in turn reflect packing densities at which each phase becomes discontinuous. Surface tortuosities for coarsened solids at low void fractions were similar to those in densified solids; however, at void fractions above ∼0.3, surface tortuosities of coarsened solids increased only gradually with void fraction, because coarsening retains significant overlap among spheres at void fractions above those giving disconnected solids in densified structures. Simulations of bulk diffusion within voids were used to compare the transport properties and connectivity of the void space with those of surfaces that define this void space. Surface and void tortuosities were similar, except for void fractions near the solid percolation threshold, because unconnected solid particles interrupt surface connectivity but not gas phase diffusion paths. Surface and void tortuosities were also similar for channels within linear chains of overlapping hollow spheres as both tortuosities increased with decreasing extent of sphere overlap. These simulations provide a basis for estimates of surface and void tortuosities, which are essential in the interpretation and extrapolation of diffusion rates in complex porous media. Surface and void diffusivity estimates differed significantly from those obtained from lattice and capillary models of complex porous structures.     

Dynamic Monte-Carlo simulations of binary self-diffusion in zeolites: effect of strong adsorption sites

Dynamic Monte-Carlo simulations are performed to examine binary self-diffusion on heterogeneous cubic lattices and in ZSM-5 (MFI), which includes both strong and weak adsorption sites due to the presence of Al atoms in addition to Si. It is observed that the diffusion behavior in such zeolites strongly depends on the pore network topology, the fraction of strong adsorption sites, and the differing relative adsorption strengths of the diffusing species on different types of sites. The Maxwell–Stefan approach previously proposed to predict diffusivities in silicalite-1, the all-Si version of MFI, is reexamined and generalized to include the effect of strong adsorption sites. It is concluded that this approach is qualitatively and quantitatively inaccurate when correlation effects are large, as a result of zeolite heterogeneity. An alternative theory based on an effective medium approximation and other mean-field arguments is more successful for the case where differences in relative adsorption strengths of the species are very high. This theory can be further refined to include intermolecular correlations.     

Numerical simulations of ultrafine powder coating systems

Numerical simulations for gas–solid two-phase flows were conducted for an experimental coating booth and an industrial coating booth to study the effect of the coating powder size on the performance of the coating process. To optimize coating parameters, simulations were conducted for different coating parameters, such as the size of the coating part, the distance between the coating part and the spray gun, the air flow rate and particle flow rate from the spray gun, the position of the pattern adjust sleeve of the spray gun, and the electrostatic field, in order to increase the coating process efficiency and coating quality.

In numerical simulations, the air flow field is obtained by solving three-dimensional Navier–Stokes equations with standard κ– turbulence model and non-equilibrium wall function. The second phase, the coating powder, consists of spherical particles and is dispersed in the continuous phase, the air. In addition to solving transport equations for the air, the trajectories of the particles are calculated by solving the particle motion equations using Lagrangian method. It is assumed that the particle–particle interaction can be neglected due to low particle volume fraction in coating systems. The electrostatic field is predicted by solving the Laplace equation.     

DEM simulation of continuous tablet coating: Effects of tablet shape and fill level on inter-tablet coating variability

Tablet coating is a common pharmaceutical technique of applying a thin polymer-based film to a tablet or a granule containing active pharmaceutical ingredients (APIs). Inter- and intra-tablet variability of film coating is a critical issue in the production of solid oral dosage forms. In fact, inhomogeneity in the coating thickness can lead to significant variations in the delivery rate of active pharmaceutical ingredients and compromise the functional attributes of the tablet film. Although attempts have been made to use numerical approaches to analyze this complex problem, at present the uniformity of coating thickness is difficult to predict without expensive experimental work.The aim of this work is to analyze and understand the effects of tablet form and fill volume on the intra-tablet coating variability in a semi-continuous coating device. To this end, the Discrete Element Method was used to numerically reproduce the tablet motion inside a chamber of the coating pan. First, the material attributes of a sample placebo tablet were experimentally quantified in detail. Thereafter, three different tablet shapes, namely bi-convex, oval, and round, were modeled by means of the “glued spheres” method. The effect of three different fill volumes was then analyzed in terms of RT of the tablets under the coating spray, leading to a quantification of the intra-tablet coating variability for each particle shape. A detailed analysis of the tablets' velocities, both translational and rotational, on top of the tablet bed is presented. These results help to understand the dynamical behavior of the tablets under a spray gun that is essential for a satisfactory intra-tablet coating homogeneity. Finally, the various behaviors observed during the numerical simulations were addressed through a detailed analysis of the tablets' flow on the bed in terms of mean velocities and granular temperatures. The aim of this work is to demonstrate how a numerical simulation may be used for the development and design of continuous pharmaceutical tablet coating processes.     

Monte-Carlo simulations of the phase transitions in the Rb2ZnCl4 crystal

The model of the order- disorder phase transitions in Rb₂ZnCl₄ is studied. In this model BX₄, group has a four equlibrium orientations in a disordered hexagonal phase. The constants of the interaction between orderinq BX₄ groups are calculated in the framework of the electrostatic model. It is shown that these constants have a competitive nature. The Monte-Carlo method is applied to study the successive phase transitions hexagonal ⇒ orthorombic ⇒ incommensurate ⇒ commensurate ferroelecrtic phases.     

Inter-tablet coating variability: Residence times in a horizontal pan coater

This paper investigates inter-tablet coating variability, specifically, tablet residence times within the spray zone. Discrete element method computer simulations, experiments, and analytical investigations are performed to measure the residence time per pass, the circulation time, and appearance frequency of spherical shaped tablets for a range of pan speeds and tablet loads. In addition, the fractional residence time, defined as the ratio of time spent by a tablet in the spray zone to the total coating time, is measured. The average fractional residence time (averaged over all the tablets in the bed) is found to be equal to the ratio of the time-averaged number of tablets exposed to the spray to the total number of tablets in the pan, a result that is consistent with analyses. The average fractional residence time is observed to be independent of pan speed and total coating time. Furthermore, the fractional residence time is shown to be related to the residence time per pass and circulation time per pass. Appearance frequency is defined as the number of appearances a tablet makes in the spray zone per pan rotation. Simulations and analyses show that appearance frequency decreases with increasing pan speed. Circulation time per pass for a tablet is defined as the average time between successive appearances in the spray zone and residence time per pass is defined as the average time spent in the spray zone per pass. These various measures are all related, but from the standpoint of developing an analytical model for coating variability, fractional residence time is a more useful and intuitive parameter as it determines the fraction of total run time that a tablet spends in the spray. This paper concentrates on determining average fractional residence times and residence time per pass, while the inter-tablet variability is more closely related to the standard deviation of the fractional residence time.     

Monte Carlo simulations to determine coating uniformity in a Wurster fluidized bed coating process

This paper presents a coating model to predict the mass coating uniformity in a Wurster fluid bed coater using a Monte Carlo method. The velocity and voidage data obtained using imaging techniques on the same Wurster coater are used as inputs to the model. The semi-circular Wurster fluid bed used in this work was 22.9 cm in diameter. A batch of 3.6 kg tablets was used to conduct coating experiments and the coating weight gain distribution results were compared to predictions from the simulation. The model rigorously considers the sheltering effect of particles as they move in the spray zone. Good agreement was obtained when comparing the results with an analytical model.Spray shape and orientation of discretization were found to play an important role in predicting the coating uniformity. A simple spray experiment in a particle-free bed showed that the direction of spray material, in general, was vertically upward. Simulation results confirmed that an upward cylindrical spray model gives better agreement with experimental results compared to a solid cone spray model. Finally, the model was used to predict the changes in coating uniformity with bed operating conditions such as gas velocity and gap height. A wider coating distribution was found for the case with the lower gas velocity and gap height.     

Intra-tablet coating variability for several pharmaceutical tablet shapes

A combined discrete element method (DEM)–Monte Carlo simulation algorithm is used to investigate intra-tablet coating thickness variability for six pharmaceutical tablet shapes. The DEM simulations are used to collect tablet orientations when the tablets enter a specified spray zone. The Monte Carlo simulations are used to “coat” the tablets assuming a uniform spray and orientations chosen randomly from the distribution generated by the DEM simulations. The simulations demonstrate that for the non-spherical tablet shapes investigated here, the coating thickness variability, defined using a coefficient of variation, decreases with the square root of the number of coating trials, then approaches an asymptotic value. The greater the degree of a tablet's preferred orientation, the larger the asymptotic coefficient of variation. In addition, the number of trials required to reach this asymptote decreases for larger asymptotic values. These findings are consistent with theoretical analyses. For the range of parameters investigated, increasing the pan speed decreases the asymptotic coefficient of variation, but increasing the fill level had no consistent effect. The asymptotic coefficients of variation did not correlate with tablet sphericity, aspect ratio, or band-to-tablet area ratio, but the results suggest that a measure of a tablet's symmetry may provide better results. Modifying the angle of the coating spray so that a larger portion of the band is coated during each coating trial results in smaller asymptotic coefficients of variation than when the spray is oriented normal to the tablet bed surface. In addition, the relative order of the tablets with the smallest asymptotic coefficients of variation changes when the spray orientation is changed.     

Understanding granular mixing to enhance coating performance in a pan coater: Experiments and simulations

The knowledge of the particle flow and mixing in a pan coater is critical to optimize the design and operation of coating equipment. Mixing is an important but poorly understood aspect of coating of pharmaceutical dosage forms (tablets). Our study focuses on the fundamental mechanisms of granular flow and mixing and their relationship to the coating performance. A quantitative method is developed and validated to characterize the mixing process throughout the mixing vessel. This method is used to establish a baseline determination of mixing homogeneity as a function of various mixing conditions. White and red non-pareils of 5–6 mesh size are loaded in the ellipsoid pan coater to check the effect of initial loading (side–side and front–back), fill level, orientation of the vessel and the vessel speed on granular mixing. Video-imaging and discrete-pocket samplers are used to quantify mixing and to finally estimate the optimal operating conditions. DEM (Discrete Element Method) based numerical model was also developed to study the effect of granular mixing in a pan coater. When the axis of rotation of the mixer is horizontal (no tilt), slower axial dispersion is observed in both the experiments and simulations, than the radial convection. However, tilt enhances axial mixing, and faster axial mixing is seen for higher tilt angles from the horizontal. The speed of the rotating vessel has a nominal effect on the rate of mixing in a coating pan, as observed from the experimental and simulation studies. Moreover, fill level has no significant effect on the rate of mixing. Coating experiments are performed in the pan coater where white non-pareils being coated by spraying Opadry II solution. DEM simulation of coating is performed with post processing particle dynamics data. The effects of various operational and spray parameters are determined on the coating performance. Optimal coating performance is attained at an optimal mixing condition.     

基于预期不可预见费的Monte-Carlo模拟分析及应用

举例说明了采用基于预期不可预见费的Monte-Carlo模拟分析方法预测炼化工程项目总费用及风险,可为决策者提供有效的科学依据。     

Evaluation of the elastic-plastic properties of SiCN coating system by finite element simulations

The elastic properties of SiCN coating on substrates can be evaluated by nano-indentation test, however, it is challenging for experiments to evaluate the plastic performance of SiCN coating. Finite element (FE) is a numerical method for investigating in-depth mechanical behavior of various structures. In this paper, a contact model between Berkovich indenter and SiCN/Si system is established by FE method. The stress-strain behavior of SiCN coating is obtained by comparing the calculated P-h curves with experimental results. The indentation depth dependent elastic modulus and hardness of the SiCN coating are calculated from the P-h curves and are close to the experimental data. When the indentation depth is in excess of 10% of the coating thickness, the mechanical properties of SiCN coating tend to be influenced by the Si substrate, which also consists with experiments. The proposed approach provides an efficient tool to predict the mechanical properties of SiCN coating.     

Scaling inter‐tablet coating variability in a horizontal rotating drum

This study investigates how the drum‐to‐particle diameter ratio (D/d) affects the surface speed and interparticle coating variability in geometrically similar coaters. Discrete element method simulations were used to model particle movement in different‐sized, cylindrical drums with identical particle diameters, Froude numbers, fill volume fractions, and spray characteristics. The dimensionless streamwise surface speed profiles become increasingly symmetric as D/d increases, with the maximum speed increasing with D/d. The relationship between the maximum dimensionless speed and D/d is fit well with a power‐law expression. Interparticle coating variability decreases with the square root of the number of drum revolutions after a sufficiently large number of drum revolutions. Increasing D/d increases, in a logarithmic manner, the number of drum revolutions required to reach a given degree of coating variability. A similar logarithmic coating variability trend was observed in simulations using almond‐shaped pharmaceutical tablets, suggesting that the trend is independent of tablet shape. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3743–3755, 2017     

Effect of speed, loading and spray pattern on coating variability in a pan coater

A computational study using the discrete element method was performed to study the effect of pan speed, fill level and the design of the spray pattern on the coating variability of tablets coated in a rotating pan. The method simulates the movement of tablets in the pan and calculates the residence time of each tablet inside the spray zone, which is directly related to the amount of coating received by the tablet. The computational method was experimentally validated using a Laser Induced Breakdown Spectroscopy based analytical method. The simulations showed that the axial mixing was the most critical parameter affecting the coating variability. Although axial mixing was found to be better at higher pan speed, it did not affect the coating variability significantly. Lower variability was obtained when a 100% fill level was used as compared to 67% fill. Four spray patterns were used, two idealized (full surface spray and a symmetric band spray) and two realistic (5-ellipse and 5-circular spray guns). The full and band spray showed similar results while the ellipse and circular patterns were similar to each other (and much worse than the other two patterns) at all speeds and fill levels.     

Degradation study of polymer coating: Improvement in coating weatherability testing and coating failure prediction

Increased awareness of the environmental impact of solvent-borne anticorrosive coatings has increased the focus on long-term performance of a coating in order to make maintenance less frequent. In this work, three anticorrosive coating systems were tested. All samples were exposed to different artificial weathering tests: a neutral salt spray test (NSS ISO 9227) and four cycles (QUV ASTM G53, ASTM D5894, ISO 20340 and a new laboratory cycle). Besides, the same samples were exposed to a 4 years field test in locations with corrosivity classified as C3 and C5M. The degradation of the individual coats of the coating system (topcoat, basecoat and primer) were studied by FTIR spectroscopy and Dynamical Mechanical Analysis. The impact of these physico-chemical changes on the corrosion protection properties of the whole system was discussed based on electrochemical impedance spectroscopy (EIS) in 3 wt% NaCl solution, SEM observations, pull-off test and measurements of delaminated areas from a scribe. On the basis of these results, the controlling parameters in coating degradation mechanism were identified. The relevance of various accelerated test cycles is discussed based on correlation between test results and field exposure.     

蒙特卡罗模拟法在油气藏开发方案风险分析中的应用

在进行油气藏开发方案风险分析时，传统的敏感性分析只能反映某一因素变化时对某项效益指标的影响程度。而油气藏实际开发过程中往往有两项以上的因素同时发生变化，致使预先按固定的计算模型预测的效益指标出现较大的误差。这就需要一种可以同时分析多个变量的随机模型来进行风险分析。本文结合实例并运用Crystal Ball软件包（一种蒙特卡罗模拟工具），来对油气藏开发方案的主要效益指标财务净现值进行蒙特卡罗模拟仿真运算，从而帮助经济评价人员做出更加符合实际的投资决策。     

离子膜极片涂层老化因素探析

简述了亿利化学电解槽6年来运行情况,通过对电解槽电压数据分析,提出了离子膜、极片涂层老化影响因素,并针对这些影响因素提出改进措施。     

一次涂装事故的原因分析

针对某次汽车热镀锌板电泳后出现漆膜附着力不良的问题进行了研究,通过试片模拟现场电泳试验,对电泳工艺和材料进行了检验,采用扫描电镜和能谱仪对正常板和异常板去掉电泳漆膜后的磷化膜及其热镀锌板基材进行观察和分析,并对正常板和异常板进行冲压和焊装试验前后的外观进行对比。确定了造成电泳漆膜附着力不良的原因是使用了钝化后的热镀锌板,并从质量管理层面上提出了解决方案。