Deposition Model Research Articles

DESIGN AND DEVELOPMENT OF GASTRO-RETENTIVE FLOATING TABLET CASE USING FDM 3D PRINTING TECHNOLOGY

The aim of this research was to examine a novel Fused Deposition Model (FDM) 3D Printing Method for creating a gastro-retentive floating tablet case containing metronidazole compressed tablet. Metronidazole was employed as a model drug and successfully integrated into floating tablet case composed of polyvinyl alcohol filament. The tablet design was made by AutoCAD software and the slicing of tablet design was carried out. To evaluate the formulation parameters for 3D printed tablet case, various orifice sizes were optimized. These 3D printed tablet cases were assessed for weight variation, friability, hardness, in vitro floating test and in vitro dissolution studies. All results met acceptable criteria. Notably, the 0.5 mm orifice case floated on 0.1 N HCI media surface for over 345 min, displaying zero - order drug release. Thus, this work demonstrates the potential of 3D Printing technology as an innovative platform for gastroretentive floating tablets to promote a modern era of personalized medicine.

Gamma-ray line emission from the Local Bubble

Deep-sea archives that include intermediate-lived radioactive 60Fe particles suggest the occurrence of several recent supernovae inside the present-day volume of the Local Bubble during the last ~10 Myr. The isotope 60Fe is mainly produced in massive stars and ejected in supernova explosions, which should always result in a sizeable yield of 26Al from the same objects. 60Fe and 26Al decay with lifetimes of 3.82 and 1.05 Myr, and emit γ rays at 1332 and 1809 keV, respectively. These γ rays have been measured as diffuse glow of the Milky Way, and would also be expected from inside the Local Bubble as foreground emission. Based on two scenarios, one employing a geometrical model and the other state-of-the-art hydrodynamics simulations, we estimated the expected fluxes of the 1332 and 1809 keV γ-ray lines, as well as the resulting 511 keV line from positron annihilation due to the 26Al β+ decay. We find fluxes in the range of 10−6–10−5 ph cm−2 s−1 for all three lines with isotropic contributions of 10–50%. We show that these fluxes are within reach for the upcoming COSI-SMEX γ-ray telescope over its nominal satellite mission duration of 2 yr. Given the Local Bubble models considered, we conclude that in the case of 10–20 Myr-old superbubbles, the distributions of 60Fe and26 Al are not co-spatial - an assumption usually made in γ-ray data analyses. In fact, this should be taken into account however when analysing individual nearby targets for their 60Fe to26 Al flux ratio as this gauges the stellar evolution models and the age of the superbubbles. A flux ratio measured for the Local Bubble could further constrain models of 60Fe deposition on Earth and its moon.

Analysis of Soot Deposition Effects on Exhaust Heat Exchanger for Waste Heat Recovery System

This study investigates the thermal–hydraulic behavior and deposition characteristics of a shell and tube exhaust heat exchanger using a CFD-based predictive model of soot deposition. Firstly, considering the influences of thermophoretic, wall shear stress, and other deposition and removal mechanisms, a predictive model is developed for long-term performance of heat exchangers under soot deposition. Then, the variations in exhaust heat exchanger performance during a 4 h deposition period are simulated based on the model. Subsequently, the variation of deposition distribution and different deposition velocities are also evaluated. Finally, an analysis of the long-term performance of the exhaust heat exchanger under varying gas velocities and temperature gradients is conducted, revealing the performance variations under all engine-operating conditions. Results show that the deterioration in normalized relative j/f1/2 varies from 5.26% to 24.91% under different work conditions, and the exhaust heat exchanger with high gas velocity and low temperature gradient exhibits optimal long-term performance.

A Critical Analysis of the CFD-DEM Simulation of Pharmaceutical Aerosols Deposition in Upper Intra-Thoracic Airways: Considerations on Aerosol Transport and Deposition.

The reliability and accuracy of numerical models and computer simulations to study aerosol deposition in the human respiratory system is investigated for a patient-specific tracheobronchial tree geometry. A computational fluid dynamics (CFD) model coupled with discrete elements methods (DEM) is used to predict the transport and deposition of the aerosol. The results are compared to experimental and numerical data available in the literature to study and quantify the impact of the modeling parameters and numerical assumptions. Even if the total deposition compares very well with the reference data, it is clear from the present work how local deposition results can depend significantly upon spatial discretization and boundary conditions adopted to represent the respiratory act. The modeling of turbulent fluctuations in the airflow is also found to impact the local deposition and, to a minor extent, the flow characteristics at the inlet of the computational domain. Using the CFD-DEM model, it was also possible to calculate the airflow and particles splitting at bifurcations, which were found to depart from the assumption of being equally distributed among branches adopted by some of the simplified deposition models. The results thus suggest the need for further studies towards improving the quantitative prediction of aerosol transport and deposition in the human airways.

OSL re-dating and paleoclimate of Laoya Cave in Guizhou Province, southwest China

Laoya Cave is a significant prehistoric human site in Guizhou Province, Southwest China, and optically stimulated luminescence (OSL) and a Bayesian depositional model were used to update the chronology of the cave. Six OSL samples were dated to 16.7 ± 1.2, 18.0 ± 1.1, 28.8 ± 2.3, 32.1 ± 2.8, 57.7 ± 6.5, and 74.0 ± 5.9 ka, respectively, and the Bayesian deposition model has provided a coherent chronological framework, revealing boundaries with median ages of 18.5, 25.0, 27.5, 28.6, 29.9, and 74.4 ka for Boundaries 1/2, 2/3, 3/4, 4/5, 5/6, and 6/9, respectively. By comparing the new chronological framework with the related records of paleoclimate and human activities, we gain insight into the relationship between the environment and Paleolithic hominins at different times. During relatively warmer periods, humans tend to spread, while in relative colder climates, they tend to rely more heavily on caves and employ hunting strategies with an equal age distribution. These survival strategies help humans prevent the threats of cold weather. Additionally, the analysis of OSL dating results uncovers a discrepancy between OSL and accelerator mass spectrometry radiocarbon (AMS 14C) dating methods, with AMS 14C dates generally appearing older at later ages (<∼30 ka). This phenomenon may be due to disturbances caused by human activity, and OSL dating may recognize this to some extent.

In Vitro Modeling of Fat Deposition in Metabolic Dysfunction-Associated Steatotic Liver Disease.

The prevalence of metabolic dysfunction-associated steatotic liver disease (MASLD) has surged due to changes in economic and lifestyle patterns, leading to significant health challenges. Previous reports have studied the establishment of animal and cellular models for MASLD, highlighting differences between them. In this study, a cellular model was created by inducing fat accumulation in MASLD. HepG2 cells were stimulated with the unsaturated fatty acid oleic acid at various concentrations (0.125 mM, 0.25 mM, 0.5 mM, 1 mM) to emulate MASLD. The model's efficacy was assessed using cell counting kit-8 assays, Oil Red O staining, and lipid content analysis. This study aimed to create a simple-to-operate cellular model for MASLD cells. Results from the cell counting kit-8 assays showed that the survival of HepG2 cells was dependent on the concentration of oleic acid, with a GI50 of 1.875 mM. Cell viability in the 0.5 mM and 1 mM groups were significantly lower than those in the control group (P < 0.05). Furthermore, Oil Red O staining and lipid content analysis examined fat deposition at varying oleic acid concentrations (0.125 mM, 0.25 mM, 0.5 mM, 1 mM) on HepG2 cells. The lipid content of the 0.25 mM, 0.5 mM, and 1 mM groups was significantly higher than that of the control group (P < 0.05). Additionally, triglyceride levels in the OA groups were significantly higher than those in the control group (P < 0.05).

Development and experimental validation of a thermo-metallurgical-mechanical model of the laser metal deposition (LMD) process

The current paper presents the development and experimental validation of a thermo-metallurgical-mechanical model for a multi-pass Laser Metal Deposition (LMD) process, with the objective of accurately predicting the resultant constituent phases and residual stresses. The thermal model is calibrated using temperature readings and is shown to accurately capture the transient temperature field and extent of the fusion zone associated with the multi-pass LMD process. The metallurgical model incorporates the kinetics of ongoing solid-state phase transformations (SSPTs) and tempering reactions. The predictions are validated via hardness measurements, demonstrating a very good agreement with the predictions. The developed mechanical model predicts the residual stress field, which is validated using X-ray diffraction measurements, and the comparison also shows a very good agreement between the predictions and measurements. The validated numerical model is then used to explore alternative LMD strategies showing that the choice of deposition strategy can significantly impact resultant constituent phases and residual stresses.

Automated toolpath planning with 3D implementation of a parabolic weld bead deposition model for wire arc additive manufacturing repair

To ensure sufficient repair of a metal structure damaged from, e.g., corrosion or wear by wire arc additive manufacturing (WAAM), appropriate toolpath planning and prediction of material deposition for the welding process are required. In the current work, a planner employing combined contour and raster pattern paths based on a sliced surface scan of the damage was developed. To extend existing empirical models for material deposition during welding to the two-dimensional paths used in WAAM, a paraboloid deposition function was used. Realistic deposition rates for uneven substrates were ensured by continuously adjusting the vertex height of the paraboloid in closely timed deposition events along the path. The deposition prediction can be used to assess if additional layers of repair welding are needed to fill a damage. For a repair with a build height of around 13 mm, the damage was sufficiently filled after following the generated toolpath plan, and a minimal amount of voids were observed. Errors in the material deposition prediction were within ±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm 1$$\\end{document} mm in most of the repair. Errors in the predicted deposition were higher in the start/stop regions of weld beads, presumably because the ignition procedure in the welding machine was not accounted for.

Machine learning method for roughness prediction

This work aims to employ machine-learning models, specifically neural networks, to predict the time evolution of the global surface roughness in a lattice model that represents a film growing on a d-dimensional substrate. We analyze the well-known ballistic deposition (BD) model for d=1, 2 since it presents strong corrections to the scaling, making it difficult to observe directly, via effective scaling exponents, its correspondence with the Kardar-Parisi-Zhang (KPZ) universality class. As an alternative to overcome this difficulty, we first intend to learn the time evolution of the global roughness for substrate sizes that are computationally viable to simulate. To test the learning, we apply two different methodologies for d = 1: the first one learns the Family-Vicsek scaling relation, and by doing the reverse transformation, we get the global roughness as a function of the time, and the second one learns the kinetic roughening directly from the time series data. For growth in d = 2 where applications arise and no exact KPZ scaling exponents are known, we apply the second methodology. However, we employ a more resilient learning model tailored for time series problems. Hence, the time required to generate the same amount of data, showing the evolution of global roughness, is reduced dramatically. Importantly, machine learning techniques capture the scaling corrections of the BD model, predicting an effective global roughness exponent, α, calculated from the learned data extracted from very large lateral sizes and times that cannot be simulated using lattice models. Our prediction is consistent with accurate estimates of the KPZ roughness exponent reported in the literature for d = 2.

Two-Parameter Probabilistic Model and Experimental Research on Micron Particle Deposition

The deposition of micron particles in gas pipelines has always been an important problem in ultra-clean ventilation technology in the modern laser fusion, precision electronics, aerospace, and biomedical fields. Combining the mathematical expression of the migration, collision, and deposition of micron particles in a gas pipeline with a simulation of flow fields, a two-parameter particle probability deposition model based on vinl, θcr and collision probability coefficient PP is established, and the distribution law of particle deposition, considering two deposition targets of the pipe wall and deposition layer, is given. Combined with an experiment on particle migration and deposition in a gas pipeline, an interpretation and verification of the particle deposition distribution law are given, and the difference between the model and experiment is discussed through particle deposition efficiency mass distribution. Studies have shown the following: Under the premise of two kinds of deposition targets, different particle sizes in the gas pipeline present different deposition laws; the deposit morphology is a spot deposit of 10 µm particles and a flake deposit of 40 µm particles; the deposit position shows a uniform distribution and a lower wall dominance; and the deposit concentration area of 40 µm shows a more significant distribution. The results are very important for the selection and optimization of gas pipelines for clean spaces.

Physics of microscale freeform 3D printing of ice

Ice is emerging as a promising sacrificial material in the rapidly expanding area of advanced manufacturing for creating precise 3D internal geometries. Freeform 3D printing of ice (3D-ICE) can produce microscale ice structures with smooth walls, hierarchical transitions, and curved and overhang features. However, controlling 3D-ICE is challenging due to an incomplete understanding of its complex physics involving heat transfer, fluid dynamics, and phase changes. This work aims to advance our understanding of 3D-ICE physics by combining numerical modeling and experimentation. We developed a 2D thermo-fluidic model to analyze the transition from layered to continuous printing and a 3D thermo-fluidic model for the oblique deposition, which enables curved and overhang geometries. Experiments are conducted and compared with model simulations. We found that high droplet deposition rates enable the continuous deposition mode with a sustained liquid cap on top of the ice, facilitating smooth geometries. The diameter of ice structures is controlled by the droplet deposition frequency. Oblique deposition causes unidirectional spillover of the liquid cap and asymmetric heat transfer at the freeze front, rotating the freeze front. These results provide valuable insights for reproducible 3D-ICE printing that could be applied across various fields, including tissue engineering, microfluidics, and soft robotics.

CFD Modeling of Aerosol Transport and Deposition Using a Drift-Flux Model

Aerosol transport and deposition are important processes in modeling of accident scenarios for a small modular reactor. An aerosol drift-flux model is attractive because it is computationally less expensive than Lagrangian particle tracking. It must be determined, however, how well it performs when implemented in a commercial computational fluid dynamics (CFD) code. This work presents results of modeling aerosol transport and deposition using a full Eulerian three-dimensional drift-flux model implemented in the commercial CFD code STAR-CCM+. The forces due to gravity and thermophoresis are included in the present drift-flux model along with Brownian motion and turbulent diffusion. The forces are added as a source term to a passive scalar transport equation. In addition, a drift velocity representing the forces is used in a built-in electrochemical species transport equation. The results of these two approaches are compared. An appropriate deposition velocity is used to calculate the aerosol concentration deposited on surfaces. The semiempirical relation proposed by Lai and Nazaroff (2000) is used to compute the deposition velocity due to gravitational settling, and the present results are compared with the experimental and numerical data obtained from the work of Chen et al. (2006). It was found that the concentration profile obtained from the present drift-flux model showed reasonable agreement with the literature data. A thermophoresis model showed good agreement when compared with the analytical solution of Nazaroff and Cass (1987). In addition to the particle concentration results, this work presents details of the drift-flux model implementation and the bulk flows. These extra details will enable comparisons by others developing similar models.

A CFD-DEM investigation into hydraulic transport and retardation response characteristics of drainage pipeline siltation using intelligent model

Siltation of drainage pipelines is a major disaster-causing factor in urban flooding. Owing to critical bed shear stress and the possibility of settlement at the bottom of pipes, there are significant nonlinear differences in the hydraulic transport and retardation response characteristics of siltation particles under different initial flow velocities, siltation degrees, and siltation lengths. Studies on siltation in drainage pipelines lack a comprehensive understanding of the intricate coupling dynamics between siltation particles and water flow, and the regularity governing the siltation transport behaviour under varying water flow conditions remains unclear. To solve these problems, this study constructs computational fluid dynamics and discrete element (CFD-DEM) coupling method and adaptive penalty model for pipeline deposition based on probabilistic settlement function, adaptive genetic algorithm, and bidirectional long short-term memory neural network (PSF-AGA-BLSTM). A three-dimensional transient hydraulic model of pipeline siltation was adopted to clarify the critical bed shear stress of the silt particles, after which an adaptive genetic algorithm with a probability settlement function as fitness was constructed to generate a numerous silt particle sample sets with settlement result labels. Adaptive genetic algorithms were combined with bidirectional long short-term memory neural networks to establish a spatiotemporal adaptive penalisation mechanism for pipeline silt particle transport. The simulation model based on PSF-AGA-BLSTM and CFD-DEM was analysed using simulation and scale tests and was found to have strong robustness and reliability. The results showed that the effects of siltation degree, flow rate, and siltation length on the transport of silt particles were all non-negligible; when the siltation degree exceeded 0.2, the siltation degree had a more significant effect on particle transport than siltation length and flow rate. The transport of silt particles occurred in two phases, rapid growth and steady growth under erosion by water flow. The rate of change in silt length accounted for up to 45% of the reason for silt nudging and silt spreading. The study clarified the hydraulic transport law of silt particles and analyzed the effect of different influencing factors. These efforts provide technical support for subsequent pipe cleaning and maintenance as well as flood prevention and mitigation.

Retinal hyperspectral imaging in mouse models of Parkinson’s disease and healthy aging

Retinal hyperspectral imaging (HSI) is a non-invasive in vivo approach that has shown promise in Alzheimer’s disease. Parkinson’s disease is another neurodegenerative disease where brain pathobiology such as alpha-synuclein and iron overaccumulation have been implicated in the retina. However, it remains unknown whether HSI is altered in in vivo models of Parkinson’s disease, whether it differs from healthy aging, and the mechanisms which drive these changes. To address this, we conducted HSI in two mouse models of Parkinson’s disease across different ages; an alpha-synuclein overaccumulation model (hA53T transgenic line M83, A53T) and an iron deposition model (Tau knock out, TauKO). In comparison to wild-type littermates the A53T and TauKO mice both demonstrated increased reflectivity at short wavelengths ~ 450 to 600 nm. In contrast, healthy aging in three background strains exhibited the opposite effect, a decreased reflectance in the short wavelength spectrum. We also demonstrate that the Parkinson’s hyperspectral signature is similar to that from an Alzheimer’s disease model, 5xFAD mice. Multivariate analyses of HSI were significant when plotted against age. Moreover, when alpha-synuclein, iron or retinal nerve fibre layer thickness were added as a cofactor this improved the R2 values of the correlations in certain groups. This study demonstrates an in vivo hyperspectral signature in Parkinson’s disease that is consistent in two mouse models and is distinct from healthy aging. There is also a suggestion that factors including retinal deposition of alpha-synuclein and iron may play a role in driving the Parkinson’s disease hyperspectral profile and retinal nerve fibre layer thickness in advanced aging. These findings suggest that HSI may be a promising translation tool in Parkinson’s disease.

Consideration of geomechanic effects during hydrodynamic model of weakly-cemented reservoir setting

The article offers an approach to tuning of heavy oil deposition model from weakly-cemented reservoir with geomechanic effects. This effects appear as changing permeability at the downhole zone near the injection well. Researchers think that the nature of low-density zones occurrence related to increasing of the resistance factor which is influenced with increasing of filtration velocity. High filtration velocity is caused by polymer flooding increasing. This work was made with basis on hydrodynamic model of the pilot area where are the experiments of displacement of heavy oil during polymer flooding. There are not only well history-matching but assessment of hydrodynamic model prediction ability. Keeping of geomechanic effects allows to achieve the adequate reproduction dynamic of fact bottom-hole pressure during polymer solution injection. Application of the given approach leads to uncertainty reduction and improved prediction reliability.

Mathematical Modeling of the Drug Particles Deposition in the Human Respiratory System—Part 1: Development of Virtual Models of the Upper and Lower Respiratory Tract

In order to carry out mathematical modeling of the drug particles or drop movement in the human respiratory system, an approach to reverse prototyping of the studied areas based on the medical data (computed tomography) results is presented. To adapt the computational grid, a mathematical model of airflow in channels of complex geometry (respiratory system) has been developed. Based on the data obtained, the results of computational experiments for a single-phase system are presented.

Application of fusion property calculations for Kazakhstani oil samples

This study thoroughly investigates the melting properties and solid-state transition temperatures of crude oil from Kazakhstan's oil field, which is critical for predicting wax precipitation. Utilizing advanced laboratory equipment such as gas chromatographs, differential scanning calorimeters (DSC), and pour point testers, we obtained comprehensive data on these parameters. Based on the results, we developed new correlations for the melting point and solid-state transition temperature of crude oil, which demonstrate closer alignment with the reference values for various hydrocarbons' melting points compared to standard prediction models. These findings provide more accurate models for wax deposition, essential for efficient crude oil transportation and processing. The results indicated that implementing these new correlations could lead to significant cost savings by reducing pipeline blockages and maintenance requirements, thereby improving overall operational efficiency.

Microscopic Mechanism and Percolation Model of Dynamic Deposition of Elemental Sulfur Particles in Acidic Gas Reservoirs.

The dissolution of elemental sulfur in acidic gas leads to its precipitation as gas pressure decreases, thereby causing potential damage to the formation due to the deposition of sulfur particles. Previous sulfur deposition prediction models often relied on the solubility of sulfur in acidic gas and the stress state of sulfur particles to determine the occurrence of deposition, thus establishing predictive models. However, in the presence of complex geological conditions, the multiphase flow through porous media and the adsorption of particles on pore throat walls can also influence sulfur particle deposition to some degree. It is well known that sulfur particle deposition during gas reservoir development exhibits instability, with multiple factors influencing the deposited sulfur particles. Particularly noteworthy is the influence of airflow velocity, which can resuspend sulfur particles that are physically adsorbed on pore throat surfaces, thereby reintegrating them into the gas phase. Additionally, the dynamic deposition of larger sulfur particles involves a dynamic process. This study elucidates the dynamic process of sulfur deposition by considering the diverse transport dynamics of sulfur particles. Physical adsorption and desorption behaviors of sulfur particles are determined based on variations in reservoir conditions. The desorption status of sulfur particles with different particle sizes within the formation is established by evaluating the equilibrium between the force exerted on the pore throat wall and the suspension force generated by gas flow. The critical conditions for sulfur deposition in Yuanba gas reservoir were obtained by substituting on-site parameters into calculations. Moreover, a mathematical model is proposed to describe the dynamic deposition and migration of sulfur particles, adopting principles from continuous porous media porous flow theory, fluid flow mass conservation, as well as sulfur particle desorption and migration. The formulated model is solved, and its resulting solution process and outcomes hold significant implications for numerical simulation and predictive assessment of the development impact on gas reservoirs, particularly in later stages.

Fiber bundle deposition model and variable speed printing strategy for in-situ impregnation 3D printing of continuous fiber reinforced thermoplastic composites

In the in-situ impregnation 3D printing of continuous fiber reinforced thermoplastic composites (CFRTPCs) at constant printing speed, in order to pursue higher printing efficiency, a higher speed for printing is adopted generally, which has no effect on the printing of the straight section, but at the same speed of printing at the corner, the printing speed will cause the fiber bundle to deviate from the printing path at the corner, which affects the accurate laying of fiber bundle along the printing path. Obviously, reducing the printing speed is an effective method to improve the print quality at the turn, but printing the entire part at the reduced speed will greatly limit the overall printing speed. However, the problem of different corner angles and shifting points from the straight section of high-speed printing to the corner section of low-speed printing has been puzzling researchers. In this paper, a fiber bundle deposition model has been proposed to reveal the deposition of fiber bundles, and the maximum offsets of fiber bundles were predicted under different turning angles. Compared with the measured results, the prediction error at different turning angles ranged from −1.07 % to 10.30 %. Then, combining with the finite element analysis method, the fiber bundle deposition model was adopted to study the effects of printing speeds, and the maximum printing speeds for different printing angles and the variable printing speed strategy have been put forward. The results have revealed that, by using the optimized variable printing speed strategy, the surface quality of the fabricated parts and the deposition of the fiber bundles along the designed printing path were significantly improved. The fiber bundle deposition model and the variable speed printing strategy could be helpful for the high-precision 3D printing of CFRTPCs.

Stochastic Lagrangian wall deposition model for RANS prediction of deposition in turbulent gas–solid flows

In industrial-scale Reynolds Averaged Navier–Stokes (RANS) simulations, a wall-modeled approach is often employed, specifically choosing a dimensionless wall-cell height much greater than one. However, in gas–solid flows, a coarse description of the boundary layer may lead to inaccurate results in terms of particle dispersion and deposition. In this study, we conducted an investigation on stochastic RANS dispersion models with deposition on smooth walls using a wall-modeled approach. These models were applied to turbulent channel flows in both vertical and horizontal orientations. The modeling approach involved the adoption of the Euler–Lagrange formalism and the RANS k−ϵ turbulence model in OpenFOAM®. To assess particle behavior first, a simple homogeneous isotropic stationary turbulence (HIST) case was examined. Fluid elements were also tracked in an inhomogeneous turbulence for dispersion analysis. These tests gave the good formulation for the dispersion model to be used for particle tracking coupled with turbulent channel flow simulation. However, the deposition results in turbulent channel using such stochastic dispersion model in the wall-cell were found to be consistently overestimated across various scenarios for low-inertia particles. To address these limitations arising from the coarse description of the boundary layer, we examined, implemented, and evaluated a Lagrangian stochastic wall deposition model. The activated deposition model demonstrated good agreement with experimental data.