Layer Thickness Ratio Research Articles

Study on the Kinetics of Shell Powder Intensified Drying Process of Sludge

Based on the problems of large yield of sludge, low degree of shell resource utilization and large mass transfer resistance of sludge drying process in China, the drying characteristics and water migration rules of shell powder quenched sludge are studied in this paper. Single-factor and orthogonal experiments of drying temperature, thin layer thickness and mixing ratio are performed, and the results are fitted to the drying kinetics model. The results show that the drying process is best when the mixing ratio is 10:1; The degree of influence of each factor is: thin layer thickness > mixing ratio > drying temperature, the optimal process is: mixing ratio of 10:1, drying temperature of 160°C and thin layer thickness of 6 mm; The Midilli and Kucuk model in the kinetic analysis can better describe the water migration in the sludge. According to Fick’s second law and Arrhenius equation, the fitting equations of pure sludge and mixed sludge at 100° C -160°C and 6 mm are obtained, shell powder quenched sludge has greater effective diffusion coefficient and smaller activation energy than pure sludge, which shows that the addition of shell powder can optimize the drying process of sludge.

The behavior of ball penetrometer in soft-over-stiff soil deposits

Proper understanding of the ball penetration behavior under centrifuge condition is important for accurate soil property determination. In this study, large deformation finite element (LDFE) analyses are conducted to investigate the scale effect of ball penetrometer on its behavior in clay-over-sand deposit in centrifuge tests. The finite element model of this study is validated against previous theoretical solutions and available centrifuge test data with good agreement. Parametric studies are then carried out to explore the effects of potential factors, including the layer thickness ratio, the shaft-ball area ratio, the undrained shear strength of clay, and the relative density of sand. The results indicate that the soil failure mechanisms can be divided into three stages: i) shallow embedment stage, ii) cavity evolution stage, and iii) full-flow stage. The penetration resistance profiles in centrifuge tests can be better quantified, which can provide more accurate shear strength interpretation for the top clay.

A combined inverse prediction and experimental analysis for the frozen ground heat transfer in a structure foundation

This paper takes the representative buried structure in permafrost regions, a transmission line tower foundation, as the research object. An inverse prediction is conducted in a scaled-down experimental system mimicking actual heat conduction of the frozen ground in a tower foundation. In permafrost regions, global warming and the heat transfer through the buried structures bring significantly adverse thermal effects on the stability of the infrastructures. In modeling the thermal effects, it has been a challenge to determine the ground surface boundary condition and heat source strength from the buried structures due to the complex climate and environmental conditions. In this work, based on the improved model predictive inverse method with an adaptive strategy, an inverse scheme is successfully implemented to simultaneously identify the time-varying surface temperature and the time-space-dependent heat source representing the buried structures. In this scheme, an adaptive time-varying predictive model is established by the rolling update of the sensitivity response coefficients according to the predicted temperature field to overcome the influence of nonlinear characteristics in the heat transfer process. The inverse method is verified by simulation and experimental data. According to the experimental inversion results, the reconstructed temperature distribution efficiently predicts the thermal state evolution of the permafrost foundation under seasonal freezing and thawing. It is found that, under the experimental conditions, the intensified thawing and freezing are significantly severe, e.g., the increased area ratio of active layer thickness is as high as 28% after building a tower, and the depth of permafrost table ranges from about 14 mm to about 38 mm, which could be detrimental to the stability and safety of the tower foundation. This study will provide valuable guidance for risk assessments or optimizing the design and maintenance of the real tower foundation and similar buried structures.

Experimental Verification of the Boundary Element Method for Adhesive Contacts of a Coated Elastic Half-Space

We consider analytical, numerical, and experimental approaches developed to describe the mechanical contact between a rigid indenter and an elastic half-space coated with an elastic layer. Numerical simulations of the indentation process were performed using the recently generalized boundary element method (BEM). Analytical approximation of the dependence of contact stiffness on the indenter diameter was used to verify the results of BEM simulations. Adhesive contacts of hard indenters of different shapes with soft rubber layers have been experimentally studied using specially designed laboratory equipment. The comparison of the results from all three implemented methods shows good agreement of the obtained data, thus supporting the generalized BEM simulation technique developed for the JKR limit of very small range of action of adhesive forces. It was shown that the half-space approximation is asymptotical at high ratios of layer thickness h to cylindrical indenter diameter D; however, it is very slowly. Thus, at the ratio h/D = 3.22, the half-space approximation leads to 20% lower contact stiffness compared with that obtained for finite thickness using both an experiment and simulation.

Topology optimization of bilayer thermal scattering cloak based on CMA-ES

A topology optimization method for the design of thermal cloak is proposed. The thermal scattering theory is introduced to pre-define the initial topology of the thermal invisible cloak as two layers to reduce the number of design variables. In bilayer concentric rings, insulating and high thermal conductivity materials are used to mask heat flow and correct thermal properties. Topology optimization based on the CMA-ES strategy is applied to quickly obtain the best configuration of available materials. The influence of the thermal properties of the material on the optimal configuration and the deflection angle of the thermal flux at the boundary surface has been investigated. Numerical simulations were performed to compare the function of the optimal cloak with that of the ideal metamaterial and the single insulating layer. The results show that despite its simple structure, the bilayer scattering cloak exhibits excellent cloaking performance under different thermal boundary conditions. In this work, the perfect scattering elimination is achieved by adjusting the layer thickness ratio of the cloak with the initial defined structure rather than seeking the optimal thermal conductivity of material, so as to avoid the problem of mismatch between the actual and ideal parameters. Compared to continuous optimization method, the pre-defined bilayer structure is easy to manufacture. Our scheme introduces thermal scattering theory to pre-set the initial structure of the topology optimization method, which provides a general, convenient, and efficient means for the design and application of thermally functional materials.

Enhanced dielectric and tunable performance in BCZT91/BCZT87 bilayer ceramics

The BCZT91/BCZT87 bilayer ceramics are prepared via solid-state reaction method to investigate the dielectric and tunable performance. The results indicate that the permittivity of bilayer ceramics is larger than that of monolayer ceramics due to the influence of space charge effect existing at interface. Meanwhile, a model evolving from the series equivalent circuit model and Landau-Devonshire theory is used to study the tunability of bilayer ceramics. The results indicate that the tunability of bilayer ceramics is obviously improved from ∼29% to ∼39% at ∼ -400 kV/m due to the influence of space charge effect when the thickness ratio of BCZT91 layer is 0.67. The similar result is also obtained when the thickness ratio is 0.50. The enhanced tunability accompanying with low loss tangent makes the figure of merit of bilayer ceramics precede monolayer ceramics. The results indicate that it is an effective method to improve the tunable performance of ceramics by introducing bilayer structure.

Effect of ECC layer thickness and reinforcement ratio on the load carrying capacity of steel‐reinforced composite beams

AbstractThe present study investigates the effect of Engineered Cementitious Composites (ECC) layer thickness against various reinforcement ratios on the flexural performance of reinforced ECC–concrete composite beams. In total, 20 reinforced composite beams are selected from the literature to predict their flexural response using Finite Element (FE) analysis. In addition to the FE analyses, a detailed analytical study is performed using the strain compatibility procedure to predict the flexural strength of ECC–concrete composite beams. The results from the FE analyses are compared against the experimental results and are found to show a close agreement. Using the validated FE models, detailed parametric studies are conducted to determine the effectiveness of different design parameters such as (a) ECC height replacement for a reinforcement ratio, (b) reinforcement ratio for an ECC height replacement, and (c) adequate reinforcement ratio for effective strengthening. The results of the parametric study show that the use of 0.4 ECC height replacement ratio and 1.70% steel reinforcement ratio exhibit better load‐carrying capacity in ECC–concrete composite beams. The effective tensile reinforcement ratio for the ECC–concrete composite beams from minimum to maximum varies in the range of 0.92%–1.85%, respectively. The moment capacities predicted from the section analysis is in good agreement with the experimental and numerical moment capacities.

Transition-Layer Implantation for Improving Magnetoelectric Response in Co-fired Laminated Composite

Magnetoelectric (ME) laminated composites with strong ME coupling are becoming increasingly prevalent in the electron device field. In this paper, an enhancement of the ME coupling effect via transition-layer implantation for co-fired lead-free laminated composite (80Bi0.5Na0.5TiO3-20Bi0.5K0.5TiO3)/(Ni0.8Zn0.2)Fe2O4 (BNKT/NZFO) was demonstrated. A transition layer composed of particulate ME composite 0.5BNKT-0.5NZFO was introduced between the BNKT piezoelectric layer and the NZFO magnetostrictive layer, effectively connecting the two-phase interface and strengthening interface stress transfer. In particular, an optimal ME voltage coefficients (αME) of 144 mV/(cm·Oe) at 1 kHz and 1.05 V/(cm·Oe) at the resonant frequency in the composite was achieved, with a layer thickness ratio (BNKT:0.5BNKT-0.5NZFO:NZFO) of 3:1:6. The static elastic model was used to determine strong interface coupling. A large magnetodielectric (MD) response of 3.95% was found under a magnetic field excitation of 4 kOe. These results demonstrate that transition-layer implantation provides a new path to enhance the ME response in co-fired laminated composite, which can play an important role in developing magnetic field-tuned electronic devices.

Scratch adhesion evaluation of diamond like carbon coatings with alternate hard and soft multilayers

A series of four diamond like carbon coatings comprising alternating soft and hard layers was prepared by closed field unbalanced magnetron sputtering. A constant bias voltage of −40 V was used for soft layer deposition, while the hard layers were deposited at different bias voltages for different coatings in series. A uniform hard-to-soft layer thickness ratio of approximately 1:1.33 was maintained for all four coatings. Cross-sectional transmission electron microscopy of the coatings confirmed that these diamond like carbon coatings indeed exhibited distinct soft and hard layers. Moreover, increasing bias voltage during hard layer deposition also increased the residual stress in these coatings. The coatings were also subjected to scratch testing to determine the effect of increasing bias voltage on the scratch toughness. Scratch cracking mechanism changed from chevron tensile cracking at low bias voltages to buckle spallation at higher bias voltages. All the coatings exhibited substrate exposure at high normal loads beyond the upper critical load. The scratch crack propagation resistance parameter was reduced by ∼1.5 times when the bias voltage was increased to −140 V. It was demonstrated that coatings deposited at a hard layer bias voltage of −100 V demonstrated the best combination of mechanical properties, including the plastic deformation resistance (H3/E2 ratio) and elastic strain to failure (H/E ratio).

Dynamic Instability of Hybrid Functionally Graded Porous Plate Under Arbitrary Pulsating Loads

In this paper, the dynamic instability of hybrid functionally graded porous (FGP) plates under arbitrary periodic load is studied. The FGP plate composes of ceramic, functionally graded material (FGM) and metal. Four FGM core layers discussed include a non-pore perfect FGM layer and three imperfect FGM layers with different porosity distribution patterns. FGM layer properties are described by constituent volume fraction, porosity volume fraction and porosity distribution pattern. The Galerkin method and eigenfunctions transforms are used to establish the Mathieu-type governing equations. The influences of the load parameter, layer thickness ratio, constituent volume fraction, porosity distribution pattern and porosity volume fraction on the dynamic instability of hybrid FGP plates are investigated and discussed.

Phase-Field Simulation of Temperature-Dependent Thermal Shock Fracture of Al2O3/ZrO2 Multilayer Ceramics with Phase Transition Residual Stress.

Compared with single-phase ceramics, the thermal shock crack propagation mechanism of multiphase layered ceramics is more complex. There is no experimental method and theoretical framework that can fully reveal the thermal shock damage mechanism of ceramic materials. Therefore, a multiphase phase-field fracture model including the temperature dependence of material for thermal shock-induced fracture of multilayer ceramics is established. In this study, the effects of residual stress on the crack propagation of ATZ (Al2O3-5%tZrO2)/AMZ (Al2O3-30%mZrO2) layered ceramics with different layer thickness ratios, layers, and initial temperatures under bending and thermal shock were investigated. Simulation results of the fracture phase field under four-point bending are in good agreement with the experimental results, and the crack propagation shows a step shape, which verifies the effectiveness of the proposed method. With constant thickness, high-strength compressive stress positively changes with the layer thickness ratio, which contributes to crack deflection. The cracks of the ceramic material under thermal shock have hierarchy and regularity. When the layer thickness ratio is constant, the compressive residual stress decreases with the increase in the layer number, and the degree of thermal shock crack deflection decreases.

Effects of myo-inositol plus folic acid on ovarian morphology and oocyte quality in PCOS mouse model.

Although the role of myo-inositol (MYO) in promoting the oocyte quality of PCOS patients has been documented in human studies; the cellular effects of this supplement on oocytes have not been directly examined due to ethical limitations. In the first phase of this study, MYO dosimetry was carried out simultaneously with the PCOS model development. An effective dose was obtained following the assessment of fasting insulin and testosterone levels using ELISA and ovarian morphology appraisal by histopathology. In the second phase, following the continuous administration of the effective dose of MYO and dehydroepiandrosterone (DHEA), cellular evaluation was performed. The quality of oocytes from superovulation was analyzed by examining maturity and normal morphology percentage using a stereomicroscope, intracellular reactive oxygen species (ROS) and glutathione (GSH) levels using fluorometry, and ATP count evaluation using ELISA. The results revealed that, among the four different MYO concentrations, the 0.36 mg/g dose compared with the DHEA group reduced testosterone levels and large atretic antral follicles (LAtAnF) diameter. This dose also increased the corpus luteum count and the granulosa:theca (G/T)layer thickness ratio in antral follicles. Furthermore, this dose increased mature oocytes and normal morphology percentage, ATP count, and GSH levels; however, it decreased ROS levels in mature oocytes. Our findings provide the grounds for further cellular and molecular studies on the PCOS mouse model, suggesting that the improvement in mitochondrial function and its antioxidant properties is probably one of the mechanisms by which MYO increases oocyte quality.

Development of an Artificial Neural Network-Based k-Value Prediction Model to Improve the Sensitivity of Base Layer on Rigid Pavement Performance

The performance of rigid pavement is greatly affected by the properties of the base/subbase and subgrade layer. However, the performance predicted by the AASHTOWare Pavement Mechanistic-Empirical (ME) Design shows low sensitivity to the properties of base and subgrade layers. In this study, a new set of modified models, that is, resilient modulus ( MR) and modulus of subgrade reaction ( k-value) are adopted to better reflect these layers’ influence on the overall performance. An artificial neural network (ANN) model is developed to predict the modified k-value based on finite element (FE) analysis. The training and validation data sets in the ANN model consist of 27,000 simulation cases with different combinations of pavement layer thickness, layer modulus, and slab-base interface bond ratio. Eight pavement section data are collected from the long-term pavement performance (LTPP) database and modeled using the FE software ISLAB2000 to evaluate the sensitivity of the modified MR model and k-values to pavement performance. The computational results indicate that the modified MR values have a higher sensitivity to water content in the base layer on fatigue cracking (bottom-up and top-down cracking) and the faulting performance of rigid pavements compared with the results using the Pavement ME design model. It is also observed that the k-values using the ANN model have a greater sensitivity to cracking and faulting performance as a result of changes in any bonded conditions (fully bonded, partially bonded, zero bonded), whereas the Pavement ME design model can only calculate at two extreme bonding conditions (i.e., fully bonded and zero bonded).

Influence of temperature and porosities on free vibration of a three-phase bidirectional functionally graded sandwich beam

Understanding the influence of practical factors on natural frequencies of beams play an important role in design of this structure. This article explores the influence of temperature and porosities on vibration characteristics of a sandwich beam made from a three-phase bidirectional functionally graded material (BFGSW beam) for the first time. The sandwich beam composed from a homogeneous core and two face layers made of a three-phase composite material. The material properties are graded in both the beam axis and thickness by power-law functions, and they are evaluated by using the Voigt model. Heat loading with uniform temperature rise and even distribution of porosities are also considered. The expressions of the elastic strain energy and the kinetic energy for the beam as well as the strain energy due to temperature are obtained in the framework of the hyperbolic shear deformation theory. A two-node beam element with eight degrees of freedom has been proposed and used to establish the discretized equation of motion for the beam. The proposed method is validated by comparing the fundamental frequency parameters with two previous works. The beam with simply supported ends are used in numerical studies. The convergence of the derived beam element is represented by evaluating the fundamental frequency parameters. The effects of the temperature rise, the porosity volume fraction, the material indexes, the length to height ratio as well as the beam layer thickness ratio on the vibration characteristics are investigated and discussed in detail. It is concluded that the BFGSW beam parameters, the temperature rise and porous parameter play an important role in the natural frequency, which is helpful for the design of beam – like structures with the desired natural frequency.

Coupled thermal-hydro model tests of double-layered buffer for nuclear waste repository

In the high-level radioactive waste disposal repository, bentonite is a preferred buffer material. As the buffer material, the hydraulic conductivity must be less than 10−13 m/s and the thermal conductivity should be higher than 0.8 W/(m·K) recommended by International Atomic Energy Agency (IAEA). Due to the decay heat of radionuclide and low thermal conductivity of bentonite, the released heat cannot be quickly transferred to the host rock through bentonite buffer layer and the repository may be in a high temperature state (>100 °C), which compromises both the hydro-mechanical performance of the bentonite and the anti-corrosion behavior of nuclear waste canister, therefore the barrier function of the buffer layer is severely damaged. Thus, a double-layered buffer concept which is based on the dual requirements of thermal conductivity and permeability was proposed for the nuclear waste disposal repository. In this paper, coupled thermal-hydro model tests of double-layered buffer with graphite-bentonite mixture layer and bentonite layer (the layer thickness ratio of graphite-bentonite to bentonite was 2:3) were carried out to investigate the temperature and relative humidity distribution laws and determine whether the physicochemical properties of double-layered buffer change after experiencing the coupled thermal-hydro process. In the model test, a heater simulating the decay heat generated by HLW was placed below the graphite-bentonite layer, and a hydration system simulating groundwater infiltration was installed above the bentonite layer, thus, the heat was transferred from the graphite-bentonite layer to the bentonite layer while water was permeated from the bentonite layer to the graphite-bentonite layer. The temperature and relative humidity distribution were synchronously measured by temperature-humidity sensors. After the model tests, the heater was switched off, and the tested bentonite/graphite-bentonite mixture samples were taken out for subsequent water content, scanning electron microscopy (SEM) and X-ray diffraction (XRD) tests. The main conclusions from the test results are as follows. The distributions of temperature and relative humidity in the buffers were mainly governed by the competition between the thermal effect and the water permeation effect, the results of water content at different distances also indirectly verify this conclusion. And SEM results showed that macropores of the bentonite close to the water inlet side were significantly reduced and the pore distribution tended to be uniform along the water injection direction during wetting. XRD results indicated that the mineral composition of the graphite-bentonite mixtures close to the heater changed while that of the bentonite away from the heater remained unchanged. Obviously, even if the high thermal conductivity graphite was added to the buffer layer near the heat source, the mineral composition of the bentonite at the heat source side cannot be avoided completely unaffected. Therefore, it is necessary to conduct heat from the inner layer to outer layer to reduce the overall temperature in the repository and reduce adverse effects of temperature and water synchronization on outer bentonite layer. The research results in this paper can serve as a guideline for the buffer layer design in the high-level radioactive waste repository.

Analysis of temperature regulation and heat storage effect of the combined phase change envelope in hot summer and cold winter zone

In order to study the character of heat storage and temperature regulation, a mathematical model of the thermal performance of an ideal passive energy storage building is established. Indoor thermal environment evaluation indexes of the passive buildings such as the temperature attenuation coefficient and supercooling degree/superheating degree are proposed. The PCM (phase change materials) layer numbers, the total thickness and the thickness ratio of PCM layers of the combined PCM envelope are analyzed based on the simulation. The result shows that the combined envelope with two-layer PCM has better temperature regulation and heat storage effect. When the total thickness of the combined PCM envelope is 40 mm, and the thickness ratio of the PCM layer from the inside to the outside is13.3:26.7, the annual thermal comfort hours are the longest.

The influence of novel beam shapes on melt pool shape and mechanical properties of LPBF produced Al-alloy

New generation of multi-core fiber laser sources provide in-source dynamic beam shaping. Such sources can switch between Gaussian and ring beams, providing new irradiance profiles. The new irradiance profiles add up to the process flexibility for controlling the temperature fields generated in the laser powder bed fusion (LPBF) process. On the other hand, they bring further complexity as new process parameters should be defined and their influence on the mechanical properties unveiled. Accordingly, this work studies the use of seven different beam shapes provided by a multi-core industrial fiber laser source with beam diameters varying between 47 μm to 144 μm during the LPBF of AlSi7Mg0.6 alloy. The beam spatial profiles were measured and descriptive irradiance parameters were defined. The Al-alloy constituted a challenging material type due to its high reflectivity and low melting point, hence, more prone to lack-of-fusion and keyhole defects. LPBF experiments were conducted at fixed energy density and peak irradiance levels investigating the influence of the beam shapes on the melt pool geometry in prismatic samples. The results showed that the peak irradiance and the ring intensity had a direct impact on the melt pool aspect ratio (AR) and melt pool depth to layer thickness ratio (h/z). With all the conditions providing adequately dense parts (>99.5 %), the mechanical properties were found to be correlated to the melt pool geometry. The results confirm that the beam shape can be tuned between the central peak and the ring to further manipulate the material properties in LPBF.

Strong and tough laminated ceramics prepared from ceramic foams

Here, we present a novel strategy to prepare laminated ceramics by combining the ceramic foams and hot-pressing sintering. Al2O3 and ZrO2 ceramic foams prepared by the particle-stabilized foaming method was cut into thin slices and then directly laminated and hot-pressing sintered. Al2O3/ZrO2 laminated ceramics with various structures were prepared. Compared with the slices prepared by conventional process, ceramic foams can easily regulate the thickness of laminate to resemble the nacre-like structure. In addition, the grain in the ceramic foams have lower activity and shrinkage rate, thereby weakening the residual tensile internal stress caused by grain coarsening and differences in coefficient of thermal expansion. The effects of layer number and thickness ratio on residual stress and the structure-activity relationship between mechanical properties and microstructure were investigated. The fracture toughness, flexural strength, and work of fracture of the optimal Al2O3/ZrO2 laminated ceramics are 8.2 ± 1.3 MPa·m1/2, 356 ± 59 MPa, and 216 J·m−2, respectively.

Flexural behavior of layered CTRC-ECC reinforced cementitious composite plates

In this paper, three-point flexural testing was used to study the flexural properties of polyvinyl alcohol fiber-reinforced engineered cementitious composites (PVA-ECC) and carbon textile-reinforced concrete (CTRC)-layered composite plates. Taking the layer thickness of the two materials and the material type of the tensile plate surface as factors, eight research conditions were established. The effects of these factors on the cracking mode, cracking load, ultimate load, deflection, and toughness of CTRC-ECC plates were discussed. The test results show that the ultimate load and toughness of the specimen with CTRC as the tensile face are significantly larger than those of the specimen with ECC as the tensile face. C–P12–C1 has an ultimate load of 2.04 times that of P–P12–C1, C–P9–C2 has an ultimate load of 1.19 times that of P–P9–C2, and C–P6–C3 has an ultimate load of 1.30 times that of P–P6–C3. The greater the thickness of the CTRC layer is, the greater the ultimate load and toughness of the CTRC-ECC layered composite plate are. The ultimate loads of P–P12–C1, P–P9–C2, and P–P6–C3 are 39%, 157%, and 369% higher than that of P–P18–C0, respectively. When the thickness ratio of the CTRC layer to the ECC layer is two, the composite plate shows much higher toughness. The formulas were derived to calculate the flexural strength of the layered composite plate with CTRC as the tensile face, which can be used to guide the design of flexural members of layered composites.

A practical framework for predicting conversion profiles in vat photopolymerizations

Monomer fractional conversion is an important indicator of critical physical and thermal properties of thermosetting polymers. Acrylic photo-resins are widely used in light-based 3D printing techniques. The green conversion of acrylate double bonds affects the performance of 3D printed parts before and after post-processing. This work describes a practical framework for predicting conversion profiles of green parts produced by digital light processing (DLP) vat photopolymerization, although the principle should be applicable to all light-based vat photopolymerization techniques. The practical model utilizes accumulated dose profiles and photopolymerization kinetics to make predictions of conversion profiles. Photopolymerization kinetics was determined by real-time photo-infrared spectroscopy, and a phenomenological model was employed to describe the cure kinetics which included oxygen inhibition period and dose rate dependency. A sub-linear dependence of cure kinetics on dose rate showed that effective dose rather than actual dose determined the degree of cure. A mathematical model for accumulated effective dose was developed, and the effects of the ratio of layer thickness to resin depth of penetration on accumulated effective dose profiles were discussed. Predicted conversion profiles from the model were compared to experimental z-direction conversion profiles measured by IR microscope. Further, a Matlab program was developed for predicting and tuning z-direction conversion profiles in DLP vat photopolymerizations with user-input printing parameters. Using the program, the model predicted a relatively flat conversion profile by over-exposing the last layer. The prediction was experimentally verified which showed the effectiveness of this simple model.