Empirical Mathematical Model Research Articles

Advanced nanobubble flotation for enhanced removal of sub-10 µm microplastics from wastewater.

Sub-10 µm microplastics (MPs) in aquatic environments pose significant ecological and health risks due to their mobility and potential to carry harmful microcontaminants. Our effluent analysis from a Hong Kong Sewage Treatment Works shows that traditional treatment often fails to effectively remove these MPs. These small-sized MPs are commonly neglected due to challenges in accurate quantification, analysis, and removal. This study introduces a nanobubble-assisted flotation process that enhances the removal efficiency of both regular and irregular small-sized MPs from wastewater. The proposed process outperforms the traditional flotation process by fostering a more effective interaction between bubbles and MPs, increasing removal rates of MPs from 1 µm to 10 µm by up to 12% and providing a total efficiency boost of up to 17% for various particle sizes. Improvements are attributed to enhanced collision and adhesion probabilities, hydrophobic interactions, as well as better floc flotation. Supported by empirical evidence, mathematical models, and Molecular Dynamics simulations, this research elucidates the nanoscale mechanisms at play. The findings confirm the nanobubble-assisted flotation technique as an innovative and practical approach to removing sub-10 µm MPs in water treatment processes.

Quantitative Multi-Parametric MRI of the Prostate Reveals Racial Differences

Purpose: This study investigates whether quantitative MRI and histology of the prostate reveal differences between races, specifically African Americans (AAs) and Caucasian Americans (CAs), that can affect diagnosis. Materials and Methods: Patients (98 CAs, 47 AAs) with known or suspected prostate cancer (PCa) underwent 3T MRI (T2W, DWI, and DCE-MRI) prior to biopsy or prostatectomy. Quantitative mpMRI metrics: ADC, T2, and DCE empirical mathematical model parameters were calculated. Results: AAs had a greater percentage of higher Gleason-grade lesions compared to CAs. There were no significant differences in the quantitative ADC and T2 values between AAs and CAs. The cancer signal enhancement rate (α) on DCE-MRI was significantly higher for AAs compared to CAs (AAs: 13.3 ± 9.3 vs. CAs: 6.1 ± 4.7 s−1, p < 0.001). The DCE signal washout rate (β) was significantly lower in benign tissue of AAs (AAs: 0.01 ± 0.09 s−1 vs. CAs: 0.07 ± 0.07 s−1, p < 0.001) and significantly elevated in cancer tissue in AAs (AAs: 0.12 ± 0.07 s−1 vs. CAs: 0.07 ± 0.08 s−1, p = 0.02). DCE significantly improves the differentiation of PCa from benign in AAs (α: 52%, β: 62% more effective in AAs compared to CAs). Histologic analysis showed cancers have a greater proportion (p = 0.04) of epithelium (50.9 ± 12.3 vs. 44.7 ± 12.8%) and lower lumen (10.5 ± 6.9 vs. 16.2 ± 6.8%) in CAs compared to AAs. Conclusions: This study shows that AAs have different quantitative DCE-MRI values for benign prostate and prostate cancer and different histologic makeup in PCa compared to CAs. Quantitative DCE-MRI can significantly improve the performance of MRI for PCa diagnosis in African Americans but is much less effective for Caucasian Americans.

Hybrid CNC–MXene Nanolubricant for Tribological Application: Characterization, Prediction, and Optimization of Thermophysical Properties Evaluation

In the present work, hybrid Cellulose Nanocrystal–MXene (CNC–MXene) nanolubricants were prepared via a two-step method and investigated as potential heat-transfer hybrid nanofluids for the first time. CNC–MXene nanolubricants were synthesized via a two-step method by varying the weight percentage of CNC–MXene nanoparticles (ranging from 0.01 to 0.05 wt%) and characterized using Fourier-Transform Infrared Spectroscopy and TGA (Thermogravimetric Analysis). Response surface methodology (RSM) was used in conjunction with the miscellaneous design model to identify prediction models for the thermophysical properties of the hybrid CNC–MXene nanolubricant. Minitab 18 statistical analysis software and Response Surface Methodology (RSM) based on Central Composite Design (CCD) were utilized to generate an empirical mathematical model investigating the effect of concentration and temperature. The analysis of variance (ANOVA) results indicated significant contributions from the type of nanolubricant (p < 0.001) and the quadratic effect of temperature (p < 0.001), highlighting non-linear interactions that affect viscosity and thermal conductivity. The findings showed that the predicted values closely matched the experimental results, with a percentage of absolute error below 9%, confirming the reliability of the optimization models. Additionally, the models could predict more than 85% of the nanolubricant output variations, indicating high model accuracy. The optimization analysis identified optimal conditions for maximizing both dynamic viscosity and thermal conductivity. The predicted optimal values (17.0685 for dynamic viscosity and 0.3317 for thermal conductivity) were achieved at 30 °C and a 0.01% concentration, with a composite desirability of 1. The findings of the percentage of absolute error (POAE) reveal that the model can precisely predict the optimum experimental parameters. This study contributes to the growing field of advanced nanolubricants by providing insights into the synergistic effects of CNC and MXene in enhancing thermophysical properties. The developed models and optimization techniques offer valuable tools for tailoring nanolubricant formulations to specific tribological applications, potentially leading to improved efficiency and durability in various industrial settings.

Empirical mathematical model based on optimized parameter extraction from captured electrohydrodynamic inkjet memristor device with LTspice model

Empirical mathematical model based on optimized parameter extraction from captured electrohydrodynamic inkjet memristor device with LTspice model

Estimating community-wide indirect effects of influenza vaccination: triangulation using mathematical models and bias analysis.

Understanding whether influenza vaccine promotion strategies produce community-wide indirect effects is important for establishing vaccine coverage targets and optimizing vaccine delivery. Empirical epidemiologic studies and mathematical models have been used to estimate indirect effects of vaccines but rarely for the same estimand in the same dataset. Using these approaches together could be a powerful tool for triangulation in infectious disease epidemiology because each approach is subject to distinct sources of bias. We triangulated evidence about indirect effects from a school-located influenza vaccination program using two approaches: a difference-in-difference (DID) analysis, and an age-structured, deterministic, compartmental model. The estimated indirect effect was substantially lower in the mathematical model than in the DID analysis (2.1% (95% Bayesian credible intervals 0.4 - 4.4%) vs. 22.3% (95% CI 7.6% - 37.1%)). To explore reasons for differing estimates, we used sensitivity analyses and probabilistic bias analyses. When we constrained model parameters such that projections matched the DID analysis, results only aligned with the DID analysis with substantially lower pre-existing immunity among school-age children and older adults. Conversely, DID estimates corrected for potential bias only aligned with mathematical model estimates under differential outcome misclassification. We discuss how triangulation using empirical and mathematical modelling approaches could strengthen future studies.

Breakthrough curves of H2/CO2 adsorptions on CuBTC and MIL-125(Ti)_NH2 predicted by empirical correlations and deep neural networks

With the continuous emergence of new materials, efficiently screening suitable materials for hydrogen purification by pressure swing adsorption (PSA) technology has become a hot topic. Metal-organic frameworks (MOFs) hold significant promise in gas adsorption and separation due to their unique structure and versatility. Breakthrough curves depict the dynamic adsorption kinetics of multi-components in fixed-bed columns, offering a means to screen adsorbents. In this study, a deep neural network (DNN) model comprising 11 hidden layers is developed to predict the dynamic breakthrough behavior of MOF CuBTC and MIL-125(Ti)_NH2 adsorbents. The training data for the DNN were generated from a non-isothermal model established using Aspen Adsorption software. Results demonstrate that the DNN model effectively predicts the H2/CO2 breakthrough behavior on CuBTC and MIL-125(Ti)_NH2 adsorbents. Compared with empirical mathematical correlation models, the DNN can predict breakthrough profiles under varying operating conditions, exhibiting superior adaptability. Furthermore, parametric studies based on the DNN model reveal that initial temperature, adsorption pressure and feed flow rate play important roles in the dynamic adsorption process, significantly influencing the position and shape of the breakthrough curve. Decreasing the feed flow rate and initial temperature while increasing adsorption pressure can enhance breakthrough times and hydrogen purity. By comparing the breakthrough curves of the two adsorbents under different operating conditions for H2/CO2, the dimensionless breakthrough time of CO2 on the CuBTC adsorbent was longer. Additionally, simulation results of the PSA cycle suggest that CuBTC yields higher hydrogen purity than MIL-125(Ti)_NH2. Consequently, CuBTC is deemed more suitable for hydrogen purification of binary H2/CO2 mixtures than MIL-125(Ti)_NH2.

Economically optimized forage utilization choices in drylands for adapting to economic, ecological, and climate stress

Improving the economic performance of range forage in drylands internationally faces challenges from economic, ecological, and climate stress. Stakeholders in these drylands wish to protect range forage ecosystems while assuring economic viability of ranching. Despite several recent research achievements, little work to date has integrated relationships among precipitation, grazing pressure, animal performance, and forage production to protect ranching incomes faced with economic, ecological, and climate stress in dryland areas. This work addresses that gap by developing an empirical mathematical programming model for optimizing economic performance of livestock grazing on range forage ecosystems that adapt to several stressors. Its unique contribution is to formulate and apply a ranch income optimization model calibrated using positive mathematical programming. The model replicates observed economic, forage, and climate conditions while accounting for interacting relations among stocking rates, forage conditions, grazing pressure, animal performance, and ranch economic productivity. Results show ranch incomes ranging from about $5 to $88 per acre and marginal values of forage ranging from $0.01 to $0.12 per pound of forage, depending on economic, ecological, and climate conditions. Results reveal how all these stressors affect economically optimized choices of grazing levels, ranch income, and economic values of forage for a range of six biomes seen in the US west. Results help livestock ranchers to adjust stocking and forage choices as well as farm policymakers who seek flexible government programs to adapt to changes in economic, ecological, and climate conditions. The work's importance comes from applicability to forage management problems in dry regions internationally.

Análisis de mecanismos bioquímico-fisiológicos involucrados en las respuestas a sequía en soja

Water deficit limits soybean crop productivity and reduces yield stability. Many parameters have been associated with tolerance to water deficit, where the control of leaf water loss is by far the most important. Since most of the water loss occurs through the stomata, the objective of this thesis was to deepen the understanding of the response to water deficit in soybeans through the control of stomatal closure and to determine how this can affect the water consumption of soybeans and its tolerance to water deficit. To achieve this, we delved into the study of stomatal closure control. We focused on the role of nitric oxide (•NO) as a key molecule in the control of stomatal opening/closing. •NO kinetic accumulation was analyzed from the establishment of the hydric deficit, and its association with stomatal closure was assessed. Our work showed an endogenous •NO accumulation at the guard cell level before stomatal closure, which allowed us to postulate that in the early perception of stress there is an accumulation of •NO that inhibits stomatal closure, potentially through blocking responses to ABA. This initial fine control of the stomatal closure by •NO would be decisive to define the final responses of water loss/consumption during the establishment of the water deficit. Furthermore, we developed an empirical mathematical model in soybean that describes the kinetics of water consumption under water deficit conditions of a controlled plant-pot-substrate growth system. The model defined two parameters that determine the water consumption curve, t0.5 (time at which the system lost half of the maximum amount of potentially evapotranspirable water) and Gw(t0.5) (stomatal conductance at t0.5). A correspondence analysis between t0.5 and Gw(t0.5), and the genetic structure of two soybean populations, indicated the existence of genetic associations with consumption phenotypes based on these parameters. On the other hand, using data from the drought susceptibility index (DSI) in the field, generated by previous work on one of the populations of this thesis, and through a correspondence analysis, a grouping between the model parameter t0.5 and DSI is observed. This would indicate that the developed phenotyping strategy could also be useful in the characterization of genotypes at the field level.

Prediction of compressive strength of concrete under various curing conditions: a comparison of machine learning models and empirical mathematical models

Prediction of compressive strength of concrete under various curing conditions: a comparison of machine learning models and empirical mathematical models

Mathematical modeling of routine biological parameters kinetics in order to predict durable benefit for first-line immunotherapy in metastatic or unresectable melanoma.

e21549 Background: PD1, CTLA4 and LAG3 blockade have shown remarkable efficacy in melanoma patients. Predictive biomarkers are needed to predict response, prevent unneeded toxicity and reduce costs. Despite collective efforts, no biomarker is robust or accessible enough for routine use. Our objective was to evaluate mathematical modeling-based kinetic markers derived from routine biological parameters as early predictors of durable benefit for first-line immunotherapy in advanced melanoma. Our secondary objective was to assess if these modeling could predict progression-free survival (PFS). Methods: We retrospectively included all consecutive, treatment-naïve, metastatic or unresectable melanoma patients treated with PD1 blockade alone or in combination with CTLA4 or LAG3 blockade between April 2020 and 2022 in our department. Clinical, biological and radiological data were collected. The primary endpoint was durable clinical benefit (DCB) defined as partial or complete response at 6 months or stable disease of at least 6 months. 11 simple blood markers and their on-treatment kinetics were considered. 4 empirical mathematical models (constant, linear, double exponential and hyperbolic) were fitted to the data, allowing to reject the constant null hypothesis for all of them. The association of the best-models coefficients with DCB and PFS was assessed using logistic and Cox regression. To do so, the data was truncated at 1, 2 and 3 months and the model coefficients were retrieved using Bayesian estimation with a population prior identified on the full-kinetics dataset. This study was approved by our local IRB. Results: 61 patients were included with 24 months median follow-up. DCB was observed for 57% of them. A low model-based value at baseline using 1 month truncated data was significantly associated with DCB for neutrophils (OR = 4.54[1.69-12.5], p < 0.0001) and - neutrophils/lymphocytes ratio (NLR) (OR = 3.03 [1.47-6.67], p = 0.003). Model-based results increased AUC versus baseline raw data: 0.755 versus 0.699 for neutrophils and 0.76 versus 0.7 for NLR. An elevated model-based at baseline using 1 month truncated data was significantly associated with PFS for neutrophils (HR = 1.56 [1.25-1.96], p < 0.0001), AST (HR = 1.71 [1.24-2.35], p < 0.0001), LDH (HR = 2.0 [1.44-2.77], p < 0.0001), CPR (HR = 1.75 [1.14-2.67], p = 0.01) and ALT (HR = 1.37 [1.05-1.78], p = 0.02). At 1 month, the kinetics parameters on creatinine (HR = 1.38 [1.05-1.82], p = 0.02), albumin (HR = 0.68 [0.48-0.97], p = 0.03) and monocytes (HR = 1.49 [1.02-2.18], p = 0.04) were significantly associated with PFS. Conclusions: Modeling the kinetics of routine biological parameters shows potential ability to predict DCB. Perspectives include model improvement, kinetics machine learning integrative model development as well as a toxicity prediction.

Empirical mathematical model for absorption and evaporation phenomena of organic solvent in electrically-sensitive wood

Empirical mathematical model for absorption and evaporation phenomena of organic solvent in electrically-sensitive wood

An Ultrasonic Rock Bolt Sensing Technology (I): Methodology and Laboratory Studies

Rock bolts play a critical role in ground support in mining, tunneling and construction. Being able to obtain timely information on rock bolt load condition and deformation could help immensely in safeguarding workers’ safety, optimization of ground support system, and ensuring stability and longevity of underground structures. The objective of this work was to develop a practical ultrasonic rock bolt sensing technology for monitoring axial load and deformation of a full-bodied rock bolt in both elastic and plastic deformation regimes. To this end, empirical mathematical models involving simultaneous use of times of flight of longitudinal and shear ultrasonic waves propagating along the axial direction of the rock bolt were developed, sensors were designed and fabricated, and laboratory studies were conducted. The results showed that the technology was able to measure load change, provide early detection of yield, and measure both plastic and total elongations of the rock bolt undergoing a pull test. Additionally, sectional load and elongation information could be obtained by applying the technology to rock bolts divided into sections by drilled holes along their shanks, therefore, providing the capability to assess the condition of grouted bolts at different depths within a rock mass. This work has laid the groundwork for the deployment of the technology in the field.

Effect of Feed Mass, Reactor Temperature, and Time on the Yield of Waste Polypropylene Pyrolysis Oil Produced via a Fixed-Bed Reactor.

This paper presents the results of investigations into the pyrolysis of waste polypropylene in a laboratory fixed-bed batch reactor. The experiments were designed and verified in such a way as to allow the application of the response surface methodology (RSM) in the development of an empirical mathematical model that quantifies the impacts mentioned above. The influence of the mass of the raw material (50, 100, and 150 g) together with the reactor temperature (450, 475, and 500 °C) and the reaction time (45, 50 and 75 min) was examined. It has been shown that the mass of the raw material, i.e., the filling volume of the reactor, has a significant influence on the pyrolysis oil yield. This influence exceeds the influence of reactor temperature and reaction time. This was explained by observing the temperature change inside the reactor at three different spots at the bottom, middle, and top of the reactor. The recorded temperature diagrams show that, with greater masses of feedstock, local overheating occurs in the middle part of the reactor, which leads to the overcracking of volatile products and, from there, to an increased formation of non-condensable gases, i.e., a reduced yield of pyrolytic oil.

Synergistic epistasis among cancer drivers can rescue early tumors from the accumulation of deleterious passengers.

Epistasis among driver mutations is pervasive and explains relevant features of cancer, such as differential therapy response and convergence towards well-characterized molecular subtypes. Furthermore, a growing body of evidence suggests that tumor development could be hampered by the accumulation of slightly deleterious passenger mutations. In this work, we combined empirical epistasis networks, computer simulations, and mathematical models to explore how synergistic interactions among driver mutations affect cancer progression under the burden of slightly deleterious passengers. We found that epistasis plays a crucial role in tumor development by promoting the transformation of precancerous clones into rapidly growing tumors through a process that is analogous to evolutionary rescue. The triggering of epistasis-driven rescue is strongly dependent on the intensity of epistasis and could be a key rate-limiting step in many tumors, contributing to their unpredictability. As a result, central genes in cancer epistasis networks appear as key intervention targets for cancer therapy.

Navigation by magnetic signatures in a realistic model of Earth's magnetic field.

Certain animal species use the Earth's magnetic field (i.e. magnetoreception) alongside their other sensory modalities to navigate long distances that include continents and oceans. It is hypothesized that several animals use geomagnetic parameters, such as field intensity and inclination, to recognize specific locations or regions, potentially enabling migration without a pre-surveyed map. However, it is unknown how animals use geomagnetic information to generate guidance commands, or where in the world this type of strategy would maximize an animal's fitness. While animal experiments have been invaluable in advancing this area, the phenomenon is difficult to studyin vivoorin situ, especially on the global scale where the spatial layout of the geomagnetic field is not constant. Alongside empirical animal experiments, mathematical modeling and simulation are complementary tools that can be used to investigate animal navigation on a global scale, providing insights that can be informative across a number of species. In this study, we present a model in which a simulated animal (i.e. agent) navigates via an algorithm which determines travel heading based on local and goal magnetic signatures (here, combinations of geomagnetic intensity and inclination) in a realistic model of Earth's magnetic field. By varying parameters of the navigation algorithm, different regions of the world can be made more or less reliable to navigate. We present a mathematical analysis of the system. Our results show that certain regions can be navigated effectively using this strategy when these parameters are properly tuned, while other regions may require more complex navigational strategies. In a real animal, parameters such as these could be tuned by evolution for successful navigation in the animal's natural range. These results could also help with developing engineered navigation systems that are less reliant on satellite-based methods.

Urinary and fecal potassium excretion prediction in dairy cattle: A meta-analytic approach

Quantification of potassium (K) excretion in dairy cattle is important to understand the environmental impact of dairy farming. To improve and monitor the environmental impact of dairy cows, there is a need for a simple, inexpensive, and less laborious method to quantify K excretion on dairy farms. The adoption of empirical mathematical models has been shown to be a promising tool to address this issue. Thus, the current study aimed to develop empirical predictive models for K excretion in dairy cattle from urine and feces that can help evaluate efficiency and monitor the environmental impact of milk production. To develop urine K (KUr, g/d) and fecal K (KFa, g/d) excretion prediction models, published literature that involved 45 and 54 treatment means from 10 and 14 studies, respectively, were used. Some studies reported either urinary or fecal K excretion or both, but in total, treatment means used to develop the models were from 17 studies. The linear mixed models were fitted with the fixed effect of K intake, DMI, dietary K content, urine volume, milk yield, and water intake, and the random effect of study weighted according to the number of observations. Leave-one-study out cross-validation was used to evaluate the performance of the proposed models and the best model was based on the lowest root mean square prediction error as a percentage of the observed mean values (RMSPE%) and highest concordance correlation coefficient (CCC). As expected, most daily K excretion was through urine (202.5 ± 92.1 g/d) than through feces (43.5 ± 21.0 g/d), and among the proposed models, the model including dietary K concentration showed poor predictive ability for both KUr and KFa with the lowest CCC values (−0.15 and −0.02, respectively) and systematic bias. The model developed using DMI to predict KFa excretion showed reasonable accuracy, as indicated by RMSPE, CCC, and R2marginal of 46.6%, 0.42, and 48%, respectively. Among the proposed models for KUr and KFa, the model with K intake demonstrated better predictive performance, showing minimal systematic bias and random errors due to data variability of >92%. While these proposed models suggested that reducing K intake can lead to a decrease in K excretion, it is important to ensure that dairy cows receive adequate amounts of this nutrient to maintain optimal health and productivity, especially during periods of heat stress.

Efficient bioremediation of indigo-dye contaminated textile wastewater using native microorganisms and combined bioaugmentation-biostimulation techniques

In this work, the bioremediation of wastewater from the textile industry with indigo dye content was carried out using combined bioaugmentation, bioventilation, and biostimulation techniques. Initially, the inoculum was prepared by isolating the microorganisms from the textile wastewater in a 2 L bioreactor. Then, the respirometry technique was implemented to determine the affinity of the microorganisms and the substrate by measuring CO2 and allowed the formulation of an empirical mathematical model for the growth kinetics of the microorganism. Finally, the bioremediation was carried out in a 3 L bioreactor obtaining an indigo dye removal efficiency of 20.7 ± 1.2%, 24.0 ± 1.5%, and 29.7 ± 1.1% for equivalent wavelengths of 436 nm, 525 nm, and 620 nm. The chemical oxygen demand showed an average reduction of 88.9 ± 2.5%, going from 470.7 ± 15.6 to 52.3 ± 10.7 ppm after 30 days under constant agitation and aeration. A negative generalized exponential model was fitted to assess the affinity of the microorganism with the wastewater as a substrate by evaluating the production of CO2 during the bioremediation. Bioremediation techniques improve water discharge parameters compared to chemical treatments implemented in the industry, reducing the use of substances that can generate secondary pollution. Bioaugmentation, biostimulation, and bioventing of the textile wastewater in this study demonstrate the potential of these combined techniques to serve as an efficient alternative for indigo-contaminated wastewater in the textile industry.

SIGNIFICANT FACTORS IN CALIBRATION FOR 60 CALIPERS: A EXPERIMENTAL DATA

Caliper calibration is essential for accurate dimensional measurements, especially in precision- driven industries. This research investigates the significant factors affecting the calibration of 60 calipers through experimental data analysis. The study systematically examines environmental conditions, instrument design, operator techniques, and technological advances as potential contributors to measurement uncertainties. The temperature variations explored reveal environmental factor fluctuations in caliper dimensions and their influence on subsequent measurement uncertainties. It was also observed that analysis of caliper structural integrity, manufacturing tolerances and overall design explained their roles in measurement variability. Sources of variability were identified by tested operator techniques. Empirical data and mathematical modeling were used to quantify and understand the uncertainty factors identified in the study. The findings provide valuable insight into precision measurement and calibration, along with practical recommendations for improving caliper measurement reliability in industrial settings. The study informs calibration practices, advancing the pursuit of dimensional measurement accuracy. Key Words: significant factors, experimental data, calibration of callipers, dimensional measurement, environmental conditions

Compressive Behavior of Some Balls Manufactured by 3D Printing from Ceramic-Polymer Composite Materials.

It is known that ceramic-polymer composite materials can be used to manufacture spherical bodies in the category of balls. Since balls are frequently subjected to compression loads, the paper presents some research results on the compression behavior of balls made of ceramic composite materials with a polymer matrix. The mathematical model of the pressure variation inside the balls highlights the existence of maximum values in the areas of contact with other parts. Experimental research was carried out on balls with a diameter of 20 mm, manufactured by 3D printing from four ceramic-polymer composite materials with a polymer matrix: pottery clay, terracotta, concrete, and granite. The same ceramic-polymer composite material was used, but different dyes were added to it. A gravimetric analysis revealed similar behavior of the four materials upon controlled heating. Through the mathematical processing of the experimental results obtained by compression tests, empirical mathematical models of the power-type function type were determined. These models highlight the influence exerted by different factors on the force at which the initiation of cracks in the ball materials occurs. The decisive influence of the infill factor on the size of the force at which the cracking of the balls begins was found.

Experimental analysis of solar drying kinetic of Algerian bay leaves (Laurus nobilis L.)

In this work, we present an experimental study of thin layer solar drying kinetics of Algerian bay leaves. The experiments were carried out in an indirect solar dryer operating in forced convection fitted with an auxiliary heater with aero controlled conditions. Bay leaves were dried at a relative intervals of relative air humidity, the air temperatures and air velocities ranging from 21 to 40 %, 40 to 60 °C and 0.25 to 0.8 m/s, respectively. 95 % of the water content of the product was reduced for a temperature of 60 °C. The experimental curves obtained show the presence of a decreasing drying rate. This drying rate increases with the increase of air temperature and varies inversely with the drying time. Five empirical mathematical models were used to analyze experimental data of moisture ratio over time. The model of Wang and Singh was the best prediction of drying curves with a correlation coefficient, chi-square, and an average relative error ranging respectively from 0.993 to 0.999, from 0.011 to 0.042 and 2.748 to 16.472 %. The curves obtained for all drying conditions were used for the determination of the drying characteristic curve. This latter has allowed us to empirically determine the equation of bay leaves drying rate which has been interpreted by a three degree polynomial. In addition, the diffusivity of the moisture content of bay leaves was determined from the analytical solution of the Fick’s equation. The values range from 0.9×10-9 to 6.1×10-9 m2/s with an activation energy that varies from 47.015 to 64.957 kJ/mole.