ارزیابی سینتیک و برآورد ضرایب انتقال جرم وابسته به دمای استخراج پکتین از پوست هندوانه

Introduction
Pectin is one of the heteropolysaccharide components of plant cell walls. This polysaccharide is extensively used in the food industry for its ability to produce gels and stabilize fluid materials. The molecular backbone of this polymer consists primarily of galacturonic acid residues. Galacturonic acid in pectin is often partially esterified with methanol or acetic acid (Ridley et al., 2001). pectin is commonly extracted by treating apple and citrus byproducts with hot, acidic water. This process typically employs mineral acids like hydrochloric acid, and is carefully controlled at a low pH for a set time to maximize yield (Koubala et al., 2008). From this perspective, modeling the extraction process has become a proper tool for optimizing operational parameters (Xu et al., 2014). Therefore, researchers have developed various empirical kinetic models based on simplified system assumptions. Panchev et al. (1989) proposed a kinetic model for pectin extraction from apple pomace. They identified two critical stages: the initial solubilization of pectin from the insoluble protopectin in the cell wall, followed by degradation of the now-solubilized pectin chains. This model clarified how temperature and time directly influence the final yield of extraction, the mass transfer coefficient, and the overall dynamics of the process.
Materials and Methods
The testing procedure was carried out with care and attention to detail. The watermelon type (variety and species) was selected based on the most common watermelon variety in Isfahan. After separation the watermelon rinds, samples were dried using hot air dryer, milled using coffee grinder, and passed through a 60-mesh sieve to obtain a uniform powder. The ground powder was packaged in airtight bags and stored in a dry, controlled environment. Pectin extraction was conducted using aqueous hydrochloric acid (pH 1.5) with s: L 1:40 (w/v) under reflux conditions at time interval (15, 30, 45, 90, 120 min) according the one factor design. The extract was then cooled to 4 ℃ and filtered and centrifuged (5280 × g) for purification. Then, ethanol (96%) was added in an equal volume to the sample solution, and it was gently stirred before refrigeration overnight to precipitate the extracted pectin. The resulting gelatinous pectin was separated by centrifugation. After washing the samples three times with ethanol, the pectin was dried at 50 °C until to reach the constant sample weight. The galacturonic acid content of samples were determined using the carbazole–sulfuric acid assay (Taylor, 1993). To further characterize the extraction process, the mass transfer coefficient and effective diffusion coefficient were calculated using Fick's laws of diffusion and second order kinetics model (Rakotondramasy-Rabesiaka et al., 2010; Almohammed et al., 2017).
Results and Discussion
The findings of this study demonstrate a clear relationship between extraction temperature and pectin yield. As temperatures increased, so did extraction efficiency, primarily due to improved protopectin solubility and reduced solvent viscosity. Higher temperatures promote more effective breakdown of plant cell structures, facilitating better access for the acidic solvent to dissolve protopectin. The maximum pectin yield (17.45%) was achieved at 90°C after 90 minutes of extraction. However, the extraction yield was reduced as increasing the process time. This observation indicated that the thermal degradation of pectin polymers into shorter chains that are less likely to precipitate during ethanol purification. This highlights the critical balance between temperature and time - while higher temperatures enhance raw material solubilization, they also increase the risk of polymer breakdown, emphasizing the need to maintain structural integrity while maximizing yield. Ractondramasi et al. (2010) reported that the quadratic kinetic equation provides an acceptable fit index for modeling the extraction process. Table 1 and kinetic analysis revealed that a second-order model effectively described the extraction process, with high R² values confirming strong correlation between experimental data and theoretical predictions. Both the rate constant (k) and equilibrium concentration (Cₛ) increased with temperature, demonstrating temperature's profound influence on pectin release kinetics. In Figure 2- Part B, the performance of the second kinetic model in predicting pectin extraction at different temperatures and times has been showed. As can be seen, at the initial times (15 minutes), a greater difference is observed, which is probably due to the effects of the failure to reach stable conditions. At the final times (90 minutes), the model has a moderate performance in estimating the final yield, which could be affected by the saturation of the process or structural changes of the extracted pectin. Therefore, according to the data presented, this model was able to accurately simulate the overall extraction process, especially in the intermediate time intervals. Haruna et al. also reported that second kinetic models are a suitable model for the extraction process (Haruna et al. 2007). As shown in Figure 3, elevated temperatures improved transport phenomena, with both mass transfer coefficient (kₘ) and effective diffusion coefficient increasing progressively. At lower temperatures, limited thermal energy restricts acid hydrolysis of protopectin, resulting in poor solubilization and reduced yields. The enhanced mass transfer at higher temperatures stems from improved solvent-solute interactions, greater disruption of plant tissue structure, and reduced medium viscosity. Notably, the mass transfer coefficient (kₘ) significantly exceeded the effective diffusion coefficient, suggesting minimal external resistance to solute movement. Consequently, pectin diffusion within the plant matrix emerged as the rate-limiting step, confirming that internal diffusion governs the overall mass transfer process under these conditions. The Biot number analysis provided further insights, with values consistently exceeding 50 (Figure 4), confirming that internal resistance predominates over external resistance. This indicates that solute diffusion within the solid matrix controls extraction kinetics, while solid-liquid interface resistance plays a negligible role. The slower mass transfer rates within solid particles compared to solid-liquid phase transfer ultimately limit the overall extraction rate, reinforcing that internal transport phenomena are crucial for system design and optimization. For purity assessment, the galacturonic acid content was measured. Results showed high purity levels (79.0±1.6% to 84.7±1.8%) across all temperature conditions. Maximum and minimum galacturonic acid content was record at 80°C and 80°C respectively.
Conclusion: the results demonstrate that both temperature and extraction duration significantly influence the kinetics and yield of pectin extraction. The second-order kinetic model properly predicted the extraction yield (high R²) confirming its effectiveness in describing the extraction behavior. Both the rate constant (k) and the equilibrium pectin concentration (Cs) rose, as increasing temperature. Furthermore, temperature elevation resulted in increased mass transfer coefficients (km) and effective diffusion coefficients (Deff). In other words, as increasing temperature, improved solute mobility and extraction efficiency. Moreover, the effective diffusion coefficient values showed a positive correlation with temperature. The dominance of internal resistance, as indicated by the high Biot number, confirmed that intraparticle diffusion was the primary limiting factor of mass transfer in pectin extraction. In response to these insights, Fick’s laws were employed to mathematically estimate the effective diffusion coefficients and model the pectin transfer rate based on kinetic data.The high GalA content of samples across all temperature conditions highlighted the reliability and robustness of the extraction protocol.