Geometry-aware Analysis of Wheat Grain Hydration Prior to Milling

101 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ Geometry-aware Analysis of Wheat Grain Hydration Prior to Milling А.Urinboev, Fergana State Technical University, Fergana, Uzbekistan [email protected] B. Ismailov, M.Auezov South Kazakhstan University, Shymkent, Kazakhstan [email protected] Abstract. This study presents an analysis of the geometry and short-time hydration of two wheat varieties widely cultivated in the Fergana Valley of Uzbekistan “Asr” and “Alekseevich”. Linear dimensions (length, width, thickness) were measured with a digital caliper (precision 0.001 mm); microstructure was examined by optical microscopy; and surface/volume characteristics were reconstructed from 3D scans. Hydration kinetics were assessed gravimetrically at 5 min intervals up to 30 min under cold (20–25 °C) and warm (40–50 °C) conditions. “Asr” grains were found to be larger across all axes (length 5.6 ± 0.3 mm; width 2.45 ± 0.2 mm; thickness 2.05 ± 0.2 mm) than “Alekseevich” (5.3 ± 0.2, 2.2 ± 0.2, 1.9 ± 0.2 mm; p < 0.05). Mass gain at 30 min was higher in warm compared with cold conditions (9.1% vs. 4.2% for Asr; 8.5% vs. 3.9% for Alekseevich). Box-plot analysis confirmed significantly faster water uptake for “Asr” under both regimes. An ellipsoidal multi-layer diffusion framework was applied to link grain geometry with predicted moisturepenetration times (𝑡50,𝑡95). The results demonstrate that geometry-aware conditioning can improve millability and flour quality while reducing repeated wetting–drying cycles. Kalit so‘zlar: Wheat, geometric parameters, 3D modeling, hydration kinetics, conditioning, diffusion. INTRODUCTION In Uzbekistan, wheat plays a central role in agricultural production, serving as the primary raw material for the milling, cereal, baking, and pasta industries. The quality of both winter and spring wheat is determined by a range of characteristics that significantly affect the final properties of processed products. Grain quality assessment is based on a combination of parameters that must conform to regulatory and technical documentation standards. Modern approaches to grain processing are aimed at improving the quality of finished products, reducing losses, and optimizing technological processes. One of the most critical stages in preparing grain for milling is hydration, which significantly alters the physical, mechanical, and geometric properties of the grain. This process affects the size, shape, and structure of the grain, directly influencing milling efficiency and flour quality. Modeling the geometric parameters of wheat grains during hydration allows for the identification of patterns essential for optimizing technological processes and developing advanced processing methods. In recent years, numerous studies have been conducted on the hydration and milling of wheat grains under varying moisture levels. Studies [1-4] have investigated various aspects related to the characteristics of wheat and flour, as well as processing technologies. Particular attention has been given to the influence of wheat variety on flour quality, along with the relationships between grain hardness, endosperm structure, and physicochemical properties. A significant focus has also been placed on crop management methods and their effects on yield and grain quality, contributing to more efficient production and process optimization. The physicochemical properties of grain are influenced by various factors, including climatic conditions and technological practices. Research [5-6] highlights the effects of temperature regimes, precipitation levels, and other 102 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ natural factors on yield and grain quality. Studies have also explored the consequences of heat stress, its impact on pathogen viability, and the preservation of grain during storage. Furthermore, it is important to examine the effects of various treatment methods on maintaining and enhancing grain quality, which is critical for the effective operation of agriculture and food security. Modern grain pre-processing methods, including the introduction of innovative technical solutions such as compact multifunctional machines and mobile grain dryers, contribute to increased productivity and reduced raw material losses. Research in developing and optimizing processing conditions in specialized equipment enables significant improvements in product quality with minimal energy input. These approaches greatly enhance the efficiency of post-harvest grain processing, fostering sustainability and economic benefits in agriculture. In the context of this study, the analysis of grain geometry and hydration processes prior to milling represents a vital area of research that supports the optimization of cereal processing technologies. Studies [9-12] emphasize the importance of morphological changes in grains during hydration, which directly influence their behavior during milling. Analyzing the geometric parameters of grains and how they change during hydration helps identify key patterns that can improve grain processing efficiency and lead to the production of higher-quality flour. Hydration plays a crucial role in ensuring the quality of final products such as flour. The process enhances the physical and mechanical properties of the grain, facilitating processing and increasing milling efficiency. Hydration ensures the uniform distribution of moisture within the grain, minimizing raw material loss and maximizing product yield. Given the growing demand for high-quality food products, optimizing hydration has become a vital objective in modern grain processing. Hydrothermal treatment, involving the combined action of water and heat, is implemented using two primary methods: cold and rapid conditioning. In cold conditioning, grains are moistened with water at room temperature and left to rest for a certain period. Rapid conditioning involves treating the grain with moist steam, increasing its moisture content by 1.5-2.0% and raising its temperature to 45-55°C in a short time (20-40 seconds). The choice of method depends on grain characteristics such as variety, gluten quality, and kernel translucency. For wheat cultivated in the Fergana Valley of the Republic of Uzbekistan-characterized by a translucency range of 40-60% and suboptimal gluten quality-cold conditioning is preferable. Due to local geographical and climatic conditions, the dominant wheat varieties grown in the region include “Asr” and “Alekseevich”. One promising direction for improving the hydration process is the modeling of grain shape and its influence on moisture absorption and distribution within the grain structure. Modern 3D modeling techniques enable detailed investigations of hydration kinetics, taking into account the geometric and morphological properties of the grain. These advancements create opportunities for automation and process control, as well as the development of innovative technologies and equipment. 3D modeling enhances the accuracy of experimental data, reduces the cost of data acquisition, and minimizes energy consumption by preventing the need for repeated moistening and drying before milling. Integrating mathematical and computer modeling into the automated control systems (ACS TP) of milling enterprises increases process efficiency and reduces environmental impact by promoting resource-efficient practices. According to studies [11-21], the shape of a wheat grain can be considered an irregular geometric figure (see figure 1). However, for mathematical modeling and numerical analysis of moisture distribution within the grain, its shape is often approximated as a regular body, such as an ellipsoid or a paraboloid of revolution. In our view, the most effective approach combines experimental and theoretical modeling techniques. Using modern computational tools (including 3D modeling), it is possible to determine quantitative characteristics of the grain’s geometric parameters, such as length, thickness, and porosity. These geometric parameters 103 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ are then used in moisture distribution simulations during hydration. A well-structured hydration process not only improves flour quality but can also enhance energy efficiency by avoiding repeated moistening or drying steps. Thus, modeling the geometric parameters of grains is a relevant task that contributes to more accurate predictions of key characteristics. Figure 1. A) Schematic representation of wheat: whole grain; B) grain cross-section. The objective of this study is to analyze the characteristics of the most widely cultivated wheat varieties in the Fergana Valley of the Republic of Uzbekistan and to develop computer models of their grains. The developed computational model enables the determination of optimal moisture penetration times for different grain layers, which is crucial for improving the efficiency of the hydration process and overall flour production. 2. METHODS AND MATERIALS This study focuses on analyzing the geometric parameters of two wheat varieties “Asr” and “Alekseevich” and their influence on moisture absorption during the hydration process. A combination of modern experimental techniques, including microscopic analysis and digital 3D modeling, was employed to obtain comprehensive data. To investigate the relationship between grain size and hydration behavior prior to milling, two wheat varieties were selected based on their prevalence within the agro-industrial sector of the Fergana Valley, Republic of Uzbekistan. The choice of “Asr” and “Alekseevich” varieties is justified by their widespread cultivation in the region and the distinctive physicochemical and geometric characteristics that significantly impact the hydration process. The “Asr” variety is indigenous to Uzbekistan, whereas “Alekseevich” was introduced from the Russian Federation. The geometric parameters obtained through these investigations serve as valuable inputs for mathematical models used in processing operations such as drying of overly moist grains or rehydrating excessively dry ones. 2.1. Selection of wheat varieties and their characteristics The geometric parameters of wheat grainincluding linear dimensions, shape, surface area, and surface area-to-volume ratio-have a significant impact on hydration processes. Wheat grains can vary in shape from oval and ovoid to elongated, with the following dimensional ranges: thickness - 1.4 to 2.7 mm, width - 1.4 to 3.6 mm, and length - 4.3 to 6.4 mm. The “Asr” and “Alekseevich” wheat varieties were developed by local breeders and are well-adapted to the climatic conditions of Uzbekistan, including the Fergana Valley. Their characteristics are summarized in Table 1. Table 1. Agronomic and quality characteristics of the wheat varieties “Asr” and “Alekseevich”. As shown in Table 1, the “Asr” and “Alekseevich” varieties exhibit stable adaptation to arid and hot climatic conditions, making them particularly suitable for regions characterized by high temperatures and limited humidity. These varieties fall into IDK (Individual Quality Group (classification based on gluten content and grain translucency)) Group 2, indicating compliance with specific quality standards, including gluten content and grain transparency. These traits make both varieties suitable for studies aimed at optimizing hydration processes. According to their physical structure, anatomical composition, and geometric characteristics, the mass ratio of grain components varies within certain ranges. For flour production, a high endosperm percentage is a 104 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ crucial indicator of quality, as the endosperm contains the majority of the starch and protein that determine the texture, nutritional value, and baking properties of flour. The “Asr” and “Alekseevich” varieties exhibit higher endosperm content, contributing to the production of high-quality white flour. Depending on processing goals, different types of flour are chosen: for bread baking, flour with a high endosperm content is preferred, while whole-grain flour with a balanced composition is recommended for healthier nutrition. Figure 2 presents a comparative diagram of the distribution of key grain components for the “Asr” and “Alekseevich” varieties. Figure 2. Comparative Diagram of the Main Grain Components of the “Asr” and “Alekseevich” Varieties. A) “Asr” variety; B) “Alekseevich” variety; (1-germ, 2-endosperm, 3-bran) In Figure 2a, the main grain components of the “Asr” variety are shown, consisting of three layers: the germ, endosperm, and bran. Each layer is characterized by a specific percentage that reflects its share in the total grain composition. - In Figure 2A-1, the germ-the vital reproductive part of the grain-accounts for 1.4% to 3.8% of the total grain mass. It provides the nutrients and energy required for sprouting. - In Figure 2A-2, the endosperm, the main component, serves as a nutrient reservoir (primarily starch) for the developing seedling. It constitutes 83% to 85% of the grain mass, making it the most significant component in the “Asr” variety. - In Figure 2A-3, the bran, or outer protective layer, plays a crucial role in shielding internal tissues from external factors. It makes up 1.1% to 1.8% of the grain mass-a relatively small share, yet important for protection and preservation. Figure 2B depicts the grain structure of the “Alekseevich” variety, which also consists of the germ, endosperm, and bran, though with slight differences in their proportional compositions: - In Figure 2B-1, the germ constitutes 1.2% to 3.4% of the grain mass, slightly less than that of the “Asr” variety, though still essential for sprouting. - In Figure 2B-2, the endosperm makes up 81% to 85% of the grain mass-similar to “Asr”, indicating comparable nutrient content supporting seed development. - In Figure 2B-3, the bran accounts for 1.1% to 1.2%, slightly lower than in the “Asr” variety. Despite its modest share, it plays a protective role in preserving internal grain tissues. In summary, both “Asr” and “Alekseevich” varieties share similar anatomical structures with minor percentage differences, which may influence their resistance to external stressors and nutritional value. To analyze the geometric parameters of the grain, computer modeling, microscopy, and experimental techniques were used. The physicochemical properties of the grain were determined in accordance with the national standard (GOST) [23] and international quality standards [24]. Hydration parameters were assessed by measuring changes in grain mass after immersion in water at various temperatures and time intervals. Thus, the selection of the “Asr” and “Alekseevich” varieties is justified by their characteristics and widespread cultivation, allowing the results to be effectively applied in real-world production for optimizing technological processes. 2.2. Methodology for measuring grain dimensions To ensure the precise measurement of the geometric parameters of wheat grains, a comprehensive methodology was employed in this study, incorporating modern instruments that provide a high degree of accuracy and reproducibility. In 105 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ particular, the digital caliper Mitutoyo 500-196-30 from the Mitutoyo Absolute Digimatic Caliper series was utilized to determine the linear dimensions of the grains (length, width, and thickness). This instrument offers measurement precision up to 0.001 mm, making it especially effective for applications where even the slightest dimensional variations are of scientific significance. For more detailed analysis and highresolution visual observation of the wheat grains, an optical microscope Motic BA310E was used. This device is capable of magnification up to 1000x and offers excellent optical resolution. It enabled thorough examination of the microstructure of the grains and accurate measurements of their dimensions at the micrometer scale. The superior optical capabilities of the microscope were essential for studying the anatomical and structural features of the grains in the context of hydration processes. In addition, to construct three-dimensional models of the grains and to investigate their surface morphology in detail, a 3D scanner EinScan Pro 2X Plus was employed. This device is capable of generating highly accurate 3D representations of objects, enabling not only the assessment of linear dimensions but also the calculation of grain volume and surface area with high precision. This approach allows for a more comprehensive analysis of the grain’s geometric parameters, which is particularly important in studies of hydration, where surface area and volume directly influence the rate and efficiency of water absorption. Figure 3. Geometric representations of wheat grain of the “Asr” variety: A) Optical micrograph of cross-section (scale bar=200 µm); B) 3D scanner image of intact grain. Using the aforementioned instruments, precise geometric characteristics of wheat grains were obtained and subsequently analyzed within the framework of this research. Figure 3 presents the images of the wheat grains acquired via the optical microscope and 3D scanner, clearly demonstrating the high quality and reliability of the collected data, as well as their compliance with the methodological requirements of the study. Table 1 presents the results of the geometric measurements of wheat grains of the “Asr” and “Alekseevich” varieties, obtained using the digital caliper. These results confirm the high precision of the measurements and their alignment with the research objectives. 2.3. 3d Modeling of wheat grain To investigate the geometric characteristics of wheat grains and analyze their shape, volume, and surface area, this study employed 3D modeling techniques. This approach enhanced measurement accuracy and facilitated a deeper understanding of the hydration processes of the grain. This section outlines the tools and software used, the steps involved in constructing 3D models, and the analysis of the resulting models. A 3D model of the wheat grain variety “Asr” was developed using Autodesk 3ds Max software. In the initial stage, the wheat grain was scanned using the EinScan Pro 2X Plus 3D scanner. Figure 4. 3D models of “Asr” wheat grain: A) Initial scan model; B) Mesh construction; C) Parameterized model prepared for analysis; D) 3D visualization of the wheat grain’s shape. This procedure yielded detailed digital images with high precision. Scanning was conducted in two modes: High-Resolution Mode for capturing detailed 106 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ geometric features, and Rapid Scan Mode for preliminary shape analysis. The obtained digital models were then imported into 3ds Max, where noise artifacts introduced during scanning were removed, and the grain dimensions were parameterized. Parameterization involved identifying key metrics (length, width, thickness) and generating a mesh model composed of numerous triangles, which enabled accurate reproduction of the grain surface. In the final stage, the 3D models were verified using SolidWorks. This verification involved comparing the 3D model dimensions to those obtained earlier using the digital caliper. Surface area and volume calculated from the models were cross-validated with experimental data, and mesh adjustments were made to minimize discrepancies. The 3D models created served as a foundation for the precise determination of geometric properties, including surface area, volume, and shape. These data were then analyzed to establish correlations between the grain’s geometric parameters and its hydration behavior. Figure 4 presents examples of 3D models of the “Asr” wheat grain developed using the described methodology. The application of 3D modeling significantly improved the accuracy of geometric analysis, which is essential for optimizing hydration processes and enhancing wheat processing quality under real-world industrial conditions. Based on the analysis shown in Figure 4, it was observed that the grain surface exhibits grooves or indentations. During hydration, the rate of moisture penetration through these grooves significantly exceeds the diffusion rate through other surface areas. This effect must be considered when comparing mathematical modeling results with experimental data that reflect the temporal and spatial distribution of moisture content. The research findings support the selection of “Asr” and “Alekseevich” wheat varieties based on their geometric properties and the analytical methods applied. The use of modern measurement tools-such as the digital caliper, optical microscope, and 3D scanner-ensured high data accuracy and allowed for detailed examination of critical grain parameters and their impact on hydration processes. The integration of 3D modeling techniques enabled a more comprehensive analysis by providing precise data on shape, surface area, and volume. The combined use of these tools and methods not only enhanced the reliability of the results but also confirmed their practical relevance for optimizing hydration and wheat processing technologies. These conclusions are particularly valuable for improving the quality of agro-industrial production in the Fergana Valley and other regions with similar climatic conditions. The results obtained can be integrated into technological workflows, thereby increasing the efficiency and productivity of grain processing operations. 2.4. Hydration protocol and statistical analysis. Hydration experiments were conducted on n = 50 individual grains per variety (“Asr” and “Alekseevich”), with three independent replicates at each temperature condition. Prior to hydration, grains were cleaned, sorted by size to remove outliers, and equilibrated at laboratory room temperature (22 ± 1 °C). Each replicate was immersed in distilled water at a fixed grain-to-water ratio of 1:20 (w/v) to ensure excess water availability. Two temperature regimes were tested: cold hydration (20–25 °C) and warm hydration (40–50 °C). Water baths (±0.5 °C precision) were used to maintain constant temperature, and no agitation was applied during the experiments. Hydration time points were set at 5, 10, 15, 20, 25, and 30 minutes. At each interval, grains were removed, gently blotted with filter paper to eliminate surface moisture, and immediately weighed using an analytical balance (±0.001 g). The relative change in grain mass was calculated using the following equation: ∆𝑚(%)=100×𝑚𝑡−𝑚0 𝑚0 where 𝑚𝑡 is the grain mass at time t, and 𝑚0 is the initial dry mass. All measurements are reported as mean ± standard deviation (SD). Statistical analysis was performed using one-way ANOVA, followed by Tukey’s HSD post-hoc test to assess pairwise 107 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ differences between varieties and temperature regimes. The significance threshold was set at α = 0.05. Effect sizes were estimated using Cohen’s d, and 95% confidence intervals (CI) were calculated for all mean values. Boxplots (Figure 6) display the distribution of grain dimensions and hydration data. In each plot, the central line indicates the median, boxes represent the interquartile range (IQR), whiskers extend to 1.5 × IQR, and individual points beyond the whiskers are considered outliers. 2.5. Data analysis Pre-processing and quality control. All raw measurements (length, width, thickness, and hydration mass over time) were screened for entry errors and biologically implausible values. Outliers were identified as points beyond 1.5×IQR in preliminary boxplots and were inspected against experimental notes (e.g., chipped kernels, incomplete blotting). Unless a procedural error was documented, values were retained to preserve natural variability; summary plots (Fig. 6–7) display these points transparently. Descriptive statistics. For geometric parameters and hydration outcomes, mean ± standard deviation (SD) and 95% confidence intervals (CI) were reported, with CIs computed as 𝑥±𝑡0.975,𝑑𝑓𝑠/√𝑡. Distributional summaries were visualized using boxplots (Fig. 6) and time-course curves (Fig. 7). Assumption checks. Prior to parametric inference, normality of residuals was assessed using Shapiro–Wilk tests and Q–Q plots, and homogeneity of variances across groups was evaluated by Levene’s test. When assumptions were not fully met, robust CIs (bias-corrected and accelerated, BCa) were obtained via nonparametric bootstrap (10,000 resamples), and pvalues were complemented by effect sizes. Inferential comparisons. - Geometry (Table 2; Fig. 6): Between-variety differences in length, width, and thickness were tested with one-way ANOVA (factor: Variety) for each dimension, followed by Tukey’s HSD for pairwise contrasts. Effect sizes were expressed as Cohen’s d with 95% CI. - Hydration endpoint (30 min): Mass gain (%) at 30 min was analyzed using two-way ANOVA with fixed factors Variety (Asr, Alekseevich) and Temperature (20–25 °C, 40–50 °C), including the interaction term. Tukey’s HSD controlled the family-wise error rate for simple effects. Partial η2 was reported to indicate factor importance. - Full time-course: Because repeated measurements were taken across time within replicates, mass-gain trajectories were modeled using a linear mixed-effects framework: 𝑦𝑖𝑗𝑘𝑙=𝛽0+𝛽1𝑉𝑎𝑟𝑖𝑒𝑡𝑦𝑖+𝛽2𝑇𝑒𝑚𝑝𝑗+𝛽3𝑡𝑘 +𝛽4(𝑉𝑎𝑟𝑖𝑒𝑡𝑦×𝑇𝑒𝑚𝑝)𝑖𝑗 +𝛽5(𝑉𝑎𝑟𝑖𝑒𝑡𝑦×𝑡)𝑖𝑘 +𝛽6(𝑇𝑒𝑚𝑝×𝑡)𝑗𝑘+𝑢𝑙+𝜖𝑖𝑗𝑘 where a random intercept 𝑢𝑙 accounted for replicate (and for grain, when tracked), and ∈𝑖𝑗𝑘𝑙 denoted the residual. Time t (min) was treated as continuous and was represented with a restricted cubic spline (3 knots) to capture curvature. Significance was determined by likelihood-ratio tests (nested models) with Satterthwaite degrees of freedom. Model adequacy was checked through residual diagnostics (homoscedasticity and independence across time). Empirical kinetics and characteristic times. For each condition (Variety×Temperature), hydration kinetics were summarized by fitting a Weibull-type uptake model to the mean curve (replicate-level fits were used in sensitivity analysis): 𝑋(𝑡)=𝑋∞[1−𝑒𝑥𝑝{−(𝑡/𝜏)𝛽}] where 𝑋∞ denotes the asymptotic gain, τ a scale parameter, and β a shape parameter. Characteristic times were computed analytically: 𝑡50=𝜏(𝑙𝑛2)1/𝛽, 𝑡95=𝜏(𝑙𝑛20)1/𝛽 Uncertainty (95% CI) for t50 and t95 was estimated by nonparametric bootstrap (10,000 resamples). The resulting values are reported in Table 4 alongside diffusion-model predictions. 108 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ Physics-based model validation. Agreement between experimental data and diffusion simulations (Section 3.3) was quantified using the root-meansquare error (RMSE) of the time courses and absolute/relative errors in t50 and t95: 𝑅𝑀𝑆𝐸=√1𝑁∑(𝑋𝑒𝑥𝑝(𝑡𝑘)−𝑋𝑚𝑜𝑑𝑒𝑙(𝑡𝑘))2 𝑁 𝑘=1 Mean absolute percentage error (MAPE) was additionally reported for interpretability. Parameter sensitivity (±20% around baselines in Table 3) was propagated to t50 and t95 and summarized using partial rank correlation coefficients (PRCC). Multiple testing and reporting. The overall significance threshold was set at α=0.05. Post-hoc comparisons used Tukey’s HSD. Alongside p-values, effect sizes (Cohen’s d, partial η2) and 95% CIs were presented to emphasize practical significance. Software and reproducibility. Statistical analyses were conducted in R (lme4, emmeans, car) or Python (statsmodels, pingouin, scikit-posthocs), and figures were generated with ggplot2 or matplotlib. Diffusion simulations were run in COMSOL Multiphysics 6.1. Analysis scripts and data are available from the corresponding author upon reasonable request. 3.RESULTS This study presents the results of the analysis of geometric parameters of wheat grains from the “Asr” and “Alekseevich” varieties, as well as an investigation into the hydration process and its effect on changes in grain mass. The measurements revealed significant differences in the size and shape of the grains, which directly influence the rate and extent of moisture absorption. Particular emphasis was placed on the effect of water temperature on the intensity of hydration, as well as on the modeling of moisture distribution within the grain using advanced 3D techniques. The findings provide valuable insights into the dynamics of water uptake and highlight the critical role of grain morphology in hydration efficiency. The obtained data serve as a foundation for the optimization of hydration and milling processes. Such optimization is expected to significantly improve flour quality and reduce raw material losses during industrial processing. 3.1. Measurement of geometric parameters of wheat grain An essential aspect of the wheat grain hydration process is the consideration of its geometric characteristics, as the shape and size of the grains significantly influence the rate and extent of moisture absorption. In this study, linear dimensions of wheat grains from the “Asr” and “Alekseevich” varieties were measured, revealing substantial differences in their geometric parameters. Figure 5 illustrates the principal geometric parameters of wheat grains, including length, width, and thickness. The main diagram presents a top view of a grain, clearly indicating its length and width, while an enlarged segment highlights the thickness measurement. These parameters are critical for analyzing the physical properties of the grain, which plays a significant role in optimizing storage, processing, and transportation processes in the agricultural and food industries. Figure 5. Geometric parameters of wheat grain: length, width, and thickness. Table 2 summarizes the average geometric characteristics of wheat grains from the “Asr” and “Alekseevich” varieties. As shown, the average length of “Asr” grains (5.6 mm) slightly exceeds that of “Alekseevich” grains (5.3 mm). Similarly, differences are observed in width and thickness: the average width of “Asr” grains is 2.45 mm compared to 2.2 mm for “Alekseevich”, and the thickness is 2.05 mm versus 1.7 109 “Al-Farg‘oniy avlodlari” elektron ilmiy jurnali ISSN 2181-4252. Tom: 1 | Son: 3 | 2025-yil "Descendants of Al-Farghani" electronic scientific journal. ISSN 2181-4252. Vol: 1 | Iss: 3 | 2025 year Электронный научный журнал "Потомки АльФаргани" ISSN 2181-4252. Том: 1 | Выпуск: 3 | 2025 год https://al-fargoniy.uz/ mm, respectively. These variations in linear dimensions may be attributed to the genetic traits of the varieties and the conditions under which they were cultivated. Understanding these geometric differences is important for predicting grain behavior during hydration, as size influences both the speed and uniformity of moisture penetration. Thus, the data presented in Table 2 provide a basis for further analysis and modeling of processes related to grain hydration and processing. Table 2. Average geometric characteristics of wheat grain varieties Parameter Asr (mm) Alekseevich (mm) Length 5.6 5.3 Width 2.45 2.2 Thickness 2.05 1.9 Figure 6 presents an analysis of the variations in geometric parameters of “Asr” and “Alekseevich” wheat grains. This visualization clearly depicts the range of changes in grain length, width, and thickness, as well as the median values for each parameter. Figure 6A in shows that “Asr” grain length varies from 5.0 to 6.2 mm, with a median closer to the upper bound, whereas “Alekseevich” grain length ranges from 4.8 to 5.6 mm, with a median near the center of the range. This indicates that, on average, “Asr” grains are longer than “Alekseevich” grains. Figure 6B demonstrates that “Asr” grain width ranges from 1.8 to 3.1 mm, while “Alekseevich” grains vary between 1.6 and 2.3 mm. The wider value range and higher median confirm that “Asr” grains are generally broader. Figure 6C shows the thickness distribution: “Asr” grains range from 1.7 to 2.4 mm, while “Alekseevich” grains fall within 1.4 to 2.0 mm. The median thickness for “Asr” grains is greater than that for “Alekseevich”, further affirming “Asr”'s superiority in this dimension. Figure 6. Comparison of geometric parameters of wheat grains from “Asr” and “Alekseevich” varieties: A) length. B) width. C) thickness. Boxplots show median (center line), interquartile range (box), whiskers to 1.5×IQR; points beyond whiskers are outliers. The diagram analysis confirms that the “Asr” variety has advantages across all three geometric parameters-length, width, and thickness-compared to the “Alekseevich” variety. These differences are likely due to varietal genetic traits and should be considered when selecting a variety for specific growing conditions or processing purposes. The results can also be used to optimize technological processes associated with grain handling and treatment. 3.2. The hydration process and mass change of wheat grain The hydration process of wheat grains was investigated under varying water temperatures and time intervals. Changes in grain mass indirectly indicate the rate of moisture diffusion and the quantity of water absorbed by the grain. Experimental results revealed that the most significant mass increase occurred when the grains were treated with warm water (40-50°C), whereas hydration in cold water (20-25°C) proceeded at a slower rate. Figure 7 illustrates the changes in grain mass as a function of water temperature and processing time. Grain mass was measured every 5 minutes, beginning at the 5th minute and concluding at the 30th minute of treatment. Figure 7 presents the graphs depicting the change in mass of wheat grains from two