Open Access Article
Peyman
Ebrahimi
*a,
Alberto
De Iseppi
a,
Zeynep
Gülbeş
a,
Elisa
Canazza
a,
Jacopo
Nava
b,
Barbara
Simonato
c,
Corrado
Rizzi
c,
Dasha
Mihaylova
d and
Anna
Lante
*a
aDepartment of Agronomy, Food, Natural Resources, Animals, and Environment—DAFNAE, University of Padova, Viale dell’Università, 16, 35020 Legnaro, Italy. E-mail: anna.lante@unipd.it; peyman.ebrahimi@unipd.it; alberto.deiseppi@unipd.it; zeynep.guelbes@studenti.unipd.it; elisa.canazza.3@studenti.unipd.it
bDepartment of Geosciences, University of Padova, Via Giovanni Gradenigo 6, 35131 Padova, Italy. E-mail: Jacopo.nava@unipd.it
cDepartment of Biotechnology, Università Di Verona, Strada Le Grazie 15, Verona, 37134, Italy. E-mail: barbara.simonato@univr.it
dDepartment of Microbiology and Biotechnology, University of Food Technologies, 26 Maritza Blvd., 4002 Plovdiv, Bulgaria. E-mail: dashamihaylova@yahoo.com
First published on 4th February 2026
Encapsulating polyphenols in Ca(II)-alginate beads requires suitable co-carriers, such as inulin, to reduce bead porosity and enhance protective efficiency. However, the real impact of inulin remains unknown, with some studies showing improved encapsulation efficiency (EE) and others indicating a decline. This study investigated the actual effect of inulin on the EE, physical properties, and release behaviour of Ca(II)-alginate beads loaded with spent sour cherry pomace extracts. EE based on total phenolic content (TPC) determined from bead dissolution in sodium citrate increased significantly with inulin addition, exceeding 90%. In contrast, TPC-based EE calculated from unloaded compounds in the residual calcium chloride solution decreased with inulin, dropping below 40%. This inconsistency was attributed to interference from inulin in the Folin–Ciocalteu assay, as its incorporation into the bead matrix may lead to overestimated TPC values. Supporting this, pure inulin exhibited a measurable TPC of 74.79 ± 2.28 µg GAE per g and notable reducing activity in the ferric-reducing antioxidant assay. Moreover, beads containing inulin exhibited reduced hardness, due to increased viscosity of the feed solution, which likely hindered alginate-calcium cross-linking. However, inulin significantly enhanced anthocyanin-based EE from 47.18 ± 2.54% to 53.26 ± 0.91% (p ≤ 0.05). It also increased the beads' diameter, filling the pores within the Ca(II)-alginate matrix, as confirmed by SEM imaging. Release kinetics of TPC and anthocyanins followed the Korsmeyer–Peppas model (R2 > 0.9), with n values indicating Fickian diffusion. Although inulin reduced apparent TPC-based EE and bead rigidity, its functional advantages warrant further optimization of formulation parameters.
Sustainability spotlightThe increasing emphasis on sustainable food systems necessitates the valorization of agri-food by-products and the substitution of synthetic additives with natural alternatives. This study utilizes spent sour cherry pomace, a by-product of liqueur manufacturing, as a renewable source of polyphenols. Moreover, it develops a clean-label delivery system using inulin and alginate, which are both food-grade and biodegradable polysaccharides. The research addresses analytical challenges in measuring encapsulation efficiency and offers new perspectives on the design of environmentally friendly polysaccharide matrices for the stabilization and controlled release of natural antioxidants. This approach supports United Nations Sustainable Development Goals 12 (Responsible Consumption and Production) and 9 (Industry, Innovation, and Infrastructure) by promoting waste valorization and sustainable formulation strategies. |
Encapsulation of phenolic extracts can be performed using various techniques and wall materials, each offering distinct advantages and limitations.6 Due to the health concerns arising from the use of synthetic wall materials, greater emphasis has been placed on the use of natural alternatives.7 Alginate is a natural wall material isolated from brown algae, which is a polymer composed of D-mannuronic acid and L-guluronic acid linked by the α-1–4 glycosidic bond.8,9 It exhibits unique colloidal properties and can form versatile, biocompatible, and food-grade Ca(II)-alginate hydrogels through cross-linking with calcium ions.10 The ability of alginate to form hydrogels under mild conditions, without the use of organic solvents or elevated temperatures, makes it particularly suitable for encapsulating sensitive compounds such as polyphenols. However, Ca(II)-alginate beads often exhibit high surface porosity, allowing bioactive compounds to come into contact with oxygen.11 Therefore, it is necessary to identify an appropriate co-carrier or filler to reduce the porosity of these beads and enhance their protective efficiency.
Inulin is a linear polydisperse polysaccharide consisting mainly of β-(2 → 1) fructosyl-fructose linkages.12 It has potential applications in functional foods and pharmaceutical formulations as a dietary fiber with well-documented health benefits, including immune system modulation through stimulation of intestinal microflora.13 In addition to its physiological effects, inulin exhibits valuable technological properties, serving as a bulking agent and stabilizer in various food systems. Owing to these characteristics, inulin may provide structural reinforcement to Ca(II)-alginate beads by acting as a pore-filling co-carrier.12 While some studies have observed a positive correlation between inulin concentration and encapsulation efficiency (EE) in the ionic gelation method,13 others have reported a decrease in efficiency when higher concentrations of inulin were used.14 Building on these findings, the present study seeks to clarify the actual effect of inulin as a co-carrier in Ca(II)-alginate beads, determining whether its addition enhances or compromises encapsulation performance.
Both inulin and alginate possess a favorable regulatory status worldwide, being classified as Generally Recognized as Safe (GRAS) in the United States and approved by the European Food Safety Authority (EFSA) for food applications.15,16 The use of aqueous SSCP extracts, inulin derived from chicory roots, and sodium alginate for bead preparation in this study aligns with a fully clean-label formulation strategy, promoting the use of natural ingredients. This approach supports the development of functional encapsulated products that meet consumer demand for safe, sustainable, and transparent food ingredients.
Although several studies have focused on encapsulating SSCPs derived from juice processing,17,18 none have focused on encapsulating SSCP extracts obtained from residues of liquor production. In brief, the present work focuses on the encapsulation of these SSCP extracts while clarifying the actual effect of inulin as a co-carrier in Ca(II)-alginate beads. Specifically, the study aims to elucidate how the combination of inulin and alginate influences EE, bead physical characteristics, and the release behavior of phenolic compounds.
![]() | (1) |
The first method (EE based on unloaded compounds) provides an estimation of the actual encapsulated fraction by accounting for the non-entrapped components remaining in the residual CaCl2 solution. In this case, the inulin content, TPC, and TMAC in the CaCl2 solution were analyzed using the methods described in Sections 2.6, 2.7, and 2.8, respectively. The EE based on unloaded compounds (%) was calculated using eqn (2).
![]() | (2) |
The second method (EE based on loaded compounds) was included for comparative purposes, as it is commonly used in the literature. In this approach, 0.1 g of freeze-dried beads was completely dissolved in 5 mL of 5% (w/v) sodium citrate solution at 100 rpm for 2 h, and the resulting solution was used to quantify the loaded fraction. The EE based on loaded compounds (%) was then calculated according to eqn (3).
![]() | (3) |
The process yield was calculated as the ratio of the total mass of obtained beads to the total mass of the feed solution (i.e., the mixture of the extract, sodium alginate, and inulin). The process yield is expressed as a percentage, as shown in eqn (4).
![]() | (4) |
![]() | (5) |
| Components | Values | CV (%) |
|---|---|---|
| a Results are reported as mean ± standard deviation (n = 3). The coefficient of variation (CV) for all results is approximately ≤10%. | ||
| Vanillic acid (mg L−1) | 3.06 ± 0.18 | 5.88 |
| Syringic acid (mg L−1) | 0.94 ± 0.05 | 5.32 |
| Chlorogenic acid (mg L−1) | 13.37 ± 1.34 | 10.02 |
| Caffeic acid (mg L−1) | 3.04 ± 0.23 | 7.56 |
| TPC (mg GAE per L) | 249.11 ± 3.65 | 1.46 |
| TMAC (mg L−1) | 18.53 ± 0.23 | 1.24 |
| FRAP (mg TE per L) | 521.29 ± 12.25 | 2.35 |
| Inulin level in the feed solution (% w/w) | EE (%) based on bead dissolution in sodium citrate solution | EE (%) based on unloaded compounds found in residual calcium chloride solution | Process yield (%) | ||
|---|---|---|---|---|---|
| TPC | TPC | TMAC | Inulin | ||
| a Results are reported as mean ± standard deviation (n = 3). Different letters in each column show a significant difference (p ≤ 0.05) among the samples, as assessed by one-way ANOVA and Tukey's Honestly Significant Difference (HSD) tests. | |||||
| 0 | 54.17 ± 5.67a | 44.65 ± 0.49d | 47.18 ± 2.54 ab | — | 81.00 ± 0.44a |
| 2.5 | 71.54 ± 1.21b | 39.40 ± 0.65c | 42.52 ± 1.09a | 97.06 ± 0.09e | 83.02 ± 0.28b |
| 5 | 78.07 ± 2.99b | 35.20 ± 0.57a | 42.85 ± 0.98a | 94.89 ± 0.04d | 85.62 ± 0.50c |
| 7.5 | 88.58 ± 4.16c | 37.47 ± 0.35b | 47.20 ± 1.48 ab | 92.99 ± 0.04c | 86.07 ± 0.36c |
| 10 | 98.17 ± 1.98d | 37.31 ± 1.04b | 50.57 ± 3.50bc | 91.42 ± 0.13b | 90.27 ± 0.25d |
| 15 | 97.89 ± 1.06d | 36.07 ± 0.08 ab | 53.26 ± 0.91c | 87.32 ± 0.08a | 93.33 ± 0.28e |
When EE for TPC was calculated from the loaded compounds in the beads, a significant increase was observed with increasing inulin concentration. However, when EE was determined from the unloaded compounds, the opposite trend emerged, with higher inulin levels reducing the encapsulation of phenolic compounds. This inconsistency likely arises from interference by inulin in the Folin-Ciocalteu assay when the content of loaded phenolic compounds is considered for EE calculation. Indeed, the inulin employed in the bead formulation exhibited a measurable TPC of 74.79 ± 2.28 µg GAE per g when analyzed independently. Since the majority of inulin is incorporated into the beads, as indicated by inulin-based EE values, its presence may artificially inflate the measured TPC of beads dissolved in sodium citrate, leading to an overestimation of the loaded phenolic compounds. Thus, in systems containing other reducing agents, such as inulin and its hydrolysis products, determination of TPC-based EE via bead dissolution in sodium citrate is not recommended, as it may yield misleading results.
This overestimation could be further exacerbated by the acidic environment of the feed solution, which promotes partial hydrolysis of inulin into reducing sugars (e.g., fructose and D-glucose).12 Indeed, the SSCP extract used in the present study had a notably acidic pH (3.59 ± 0.10), which may participate in the hydrolysis of inulin. Moreover, the inulin exhibited significant ferric-reducing capacity in the FRAP assay (97.46 ± 1.29 µg TE per g), further supporting its reducing potential and contribution to overestimated TPC readings. Therefore, based on EE calculations derived from the quantification of unloaded compounds remaining in the calcium chloride solution, it can be inferred that the addition of inulin actually reduces the TPC-based EE in Ca(II)-alginate beads. This effect is likely due to competitive interactions between inulin and phenolic compounds, with inulin occupying a greater proportion of the bead matrix and consequently limiting the incorporation of bioactive molecules.
Table 3 summarizes previous studies on the encapsulation of phenolic extracts using calcium alginate and inulin. As shown, all those studies dissolved the beads in sodium citrate to measure TPC for EE estimation, and they mostly reported that inulin increased the EE of TPC. However, such increases are likely overestimated due to the interference of inulin and its monomers with the Folin–Ciocalteu assay. Future studies are therefore advised to quantify EE based on the unloaded compounds or, preferably, to determine individual phenolic compounds using chromatographic techniques for more reliable results. For example, Li et al. (2021)14 analyzed individual phenolic compounds in Ca(II)-alginate-inulin beads using HPLC and found that the EE of certain compounds increased, whereas others decreased or remained unchanged.
| Phenolic extract | Sodium alginate concentration (%) | Feed solution preparation | EE determination method | EE | References |
|---|---|---|---|---|---|
| Amazonian berry extracts | 1.5 | Sodium alginate and inulin solutions were prepared directly in the extract | EE measured after bead dissolution in sodium citrate; antioxidant activity (ABTS) compared before and after encapsulation | EE without inulin: 89.1 ± 1% | Moreira Mar et al. (2021)11 |
| EE with 2.5% inulin: 94.7 ± 2% | |||||
| Chokeberry (Aronia melanocarpa L.) extract | 1.5 | Sodium alginate and inulin solutions were prepared directly in the extract | EE measured after bead dissolution in sodium citrate; TPC compared before and after encapsulation | They reported an increase in the TPC of the beads after adding 5% w/v inulin | Ćujić et al. (2016)13 |
| Carqueja extract | 1.5 | The extract at 2 mg mL−1 was added to a 1.5% sodium alginate solution, and then inulin was mixed | EE measured after bead dissolution in sodium citrate; TPC compared before and after encapsulation | EE without inulin: 49.0 ± 3.1% | Balanč et al. (2015)31 |
| EE with 20% inulin: 73.8 ± 2.8% | |||||
| Thyme (Thymus serpyllum L.) aqueous extract | 1.5 | Sodium alginate and inulin solutions were prepared directly in the extract | EE measured after bead dissolution in sodium citrate; TPC compared before and after encapsulation | EE without inulin: 51 ± 3% | Stojanovic et al. (2012)32 |
| EE with 5% inulin: 79 ± 5% | |||||
| Tea polyphenols | 2 | Sodium alginate and inulin solution were added separately to 3 mg mL−1 tea polyphenol solution and then mixed in a proportion of 80 : 20 (w/w) |
EE measured after bead dissolution in sodium citrate; TPC compared before and after encapsulation | EE without inulin: 38.51 ± 1.96 | Li et al. (2021)14 |
| EE with 2% inulin: 36.48 ± 1.57 |
On the other hand, the beads with the highest inulin concentration exhibited the highest TMAC-based EE. Anthocyanins, which represent a specific subclass of phenolic compounds, may be preferentially stabilized by inulin; thus, their EE increased with higher inulin content. This trend suggests that elevated inulin concentrations enhance the entrapment of anthocyanins within the bead matrix, likely due to favorable hydrogen bonding or other molecular interactions between inulin and anthocyanins. A plausible explanation for this effect lies in the polarity of anthocyanins, which are highly hydrophilic and structurally suited to interact with hydrophilic carriers such as inulin.33 These interactions may help reduce anthocyanin diffusion from the matrix during gelation, thereby improving retention and stability. However, due to their hydrophilic nature, some anthocyanins may still leach into the CaCl2 cross-linking solution during bead formation, resulting in a reduction of EE.11
Moreover, inulin incorporation markedly improved the process yield, which is likely attributable to the increased solid content of the feed solution. The overall results in this section revealed that the formulation of inulin-enriched matrices should be optimized to balance the EE of TMAC and TPC with the prevention of leaching during encapsulation. Moreover, pretreating the feed solution before the encapsulation process may significantly enhance the loading of different compounds into the beads. For instance, recent studies have reported that ultrasound treatment can promote the formation of inulin-polyphenol complexes, which enhance the antioxidant activity and stability of polyphenols and expand their potential applications in food systems.34 Therefore, applying ultrasound-assisted complexation prior to encapsulation could be a promising strategy to improve the interaction between inulin and phenolic compounds, potentially increasing EE, and the functional performance of the resulting beads.
| Parameter | Inulin concentration (% w/w) | |||||
|---|---|---|---|---|---|---|
| 0 | 2.5 | 5 | 7.5 | 10 | 15 | |
| a Results are reported as mean ± standard deviation (n = 3). Different characters in each row show a significant difference (p ≤ 0.05) among the samples, as assessed by one-way ANOVA and Tukey's honestly significant difference tests. | ||||||
| Hardness | 11.20 ± 2.01b | 9.39 ± 0.37 ab | 6.70 ± 0.26a | 8.48 ± 0.49 ab | 7.07 ± 1.48a | 8.23 ± 1.02 ab |
| Springiness | 2.41 ± 1.07a | 3.48 ± 0.65a | 2.41 ± 0.23a | 2.67 ± 0.27a | 2.77 ± 0.31a | 2.74 ± 0.90a |
| Cohesiveness | 0.54 ± 0.01a | 0.51 ± 0.02a | 0.52 ± 0.05a | 0.48 ± 0.05a | 0.51 ± 0.01a | 0.49 ± 0.02a |
| Elasticity index | 0.58 ± 0.19a | 0.43 ± 0.04a | 0.56 ± 0.03a | 0.49 ± 0.05a | 0.52 ± 0.01a | 0.53 ± 0.12a |
| Gumminess | 6.02 ± 1.23b | 4.77 ± 0.20 ab | 3.46 ± 0.19a | 4.06 ± 0.23a | 3.62 ± 0.82a | 4.03 ± 0.45a |
| Resilience | 0.79 ± 0.05a | 0.78 ± 0.04a | 0.72 ± 0.03a | 0.69 ± 0.05a | 0.74 ± 0.05a | 0.78 ± 0.02a |
| Diameter (mm) | 3.47 ± 0.27a | 3.92 ± 0.13 ab | 4.41 ± 0.29bc | 4.34 ± 0.14c | 4.62 ± 0.19c | 4.68 ± 0.12c |
However, the inclusion of inulin in the feed solution led to a noticeable increase in the diameter of the hydrogel beads (Table 4), and this trend persisted even after freeze-drying (Fig. 3). This enlargement could be attributed to the higher viscosity and reduced surface tension of the inulin-alginate mixture (i.e., the feed solution), which may lead to larger beads. As shown in Fig. 2(a and b), the viscosity of the feed solutions increased significantly with inulin addition (p ≤ 0.05), reaching its maximum at the highest inulin concentration.
Moreover, the combination of sodium alginate with other materials can fill pores and impact the bead size.11 Particularly, the filling capacity of inulin in Ca(II)-alginate has been proven in previous studies.36 Similarly to our findings, Moreira Mar et al. (2021) showed that increasing the inulin concentration can contribute to an increase in the diameter of beads. Fig. 3 shows the secondary electron microscopy (SEM) images and diameter of the freeze-dried beads with varying inulin concentrations (0–15%) at low (a) and high (b) magnification. The images clearly show that when inulin is added at higher concentrations, it occupies space within the gel matrix of Ca(II)-alginate, thereby contributing to a bigger diameter of the beads.
Overall, the effect of inulin on the physical properties of the feed solution and the beads may be responsible for the lower EE of the extract in the beads. While inulin increased the viscosity of the feed solution (Fig. 2a and b), which could limit phenolic diffusion during droplet formation, it may simultaneously act as a non-gelling polysaccharide within the Ca(II)-alginate network. As reported by Toprakçı et al. (2022),37 an increase in feed solution viscosity can lead to greater occupation of internal bead volume by the wall material, ultimately resulting in lower EE due to reduced space available for the active compounds. Consequently, inulin incorporation increases internal volume occupancy in the beads (Fig. 3) without contributing to network formation, yielding softer beads (Table 4) with diminished entrapment capacity. This softening, together with competitive space occupancy by inulin, facilitates phenolic leakage into the external medium during gelation, leading to higher phenolic content in the unloaded fraction and lower EE. Therefore, the denser alginate structure formed without inulin may better trap the active compounds, preventing their loss during preparation or handling. However, adding inulin to the beads is preferred as it may enhance the functional properties of the beads, such as their prebiotic activity and potential health benefits, making them more suitable for targeted use in food or pharmaceutical formulations. Therefore, Ca(II)-alginate beads without inulin and those containing 2.5% (w/w) inulin were selected for the next step of the project to study the release of bioactive compounds.
To conduct the release study in the subsequent stage, a drying step was applied to improve the physical properties of the beads, as dried microbeads generally exhibit greater stability and mechanical strength compared to their hydrogel counterparts. In addition, drying helps to prevent microbial growth during storage. However, dehydration during the drying process can disrupt the structural integrity of the Ca(II)-alginate matrix, resulting in reduced bead sphericity. To mitigate this issue, some researchers have proposed incorporating inulin as a filler.13Table 5 presents the moisture content, water activity, and hygroscopicity of the hydrogel and freeze-dried beads prepared with varying inulin concentrations. Drying significantly reduced both the moisture content and water activity across all formulations. Notably, beads containing inulin exhibited significantly lower water activity after drying, which is advantageous for storage stability. Since hydrogel beads showed no hygroscopic behavior, hygroscopicity results are reported only for the freeze-dried samples. Similarly, Moreira Mar et al. (2021)11 reported a reduction in bead moisture following the incorporation of inulin into the bead formulation.
| Inulin concentration (% w/w) | Moisture content (%) | Water activity | Hygroscopicity (%) | ||
|---|---|---|---|---|---|
| Hydrogel beads | Freeze-dried beads | Hydrogel beads | Freeze-dried beads | Freeze-dried beads | |
| a Results are reported as mean ± standard deviation (n = 3). Different letters in each column show a significant difference (p ≤ 0.05) among the samples, as assessed by one-way ANOVA and Tukey's Honestly Significant Difference (HSD) tests. | |||||
| 0 | 94.07 ± 0.15d | 5.97 ± 0.34a | 0.909 ± 0.002a | 0.160 ± 0.002d | 4.98 ± 0.26c |
| 2.5 | 93.65 ± 0.51 cd | 8.05 ± 1.61a | 0.909 ± 0.003a | 0.143 ± 0.002c | 5.32 ± 0.11c |
| 5 | 93.43 ± 0.12bc | 8.24 ± 0.59a | 0.911 ± 0.004a | 0.136 ± 0.002b | 4.71 ± 0.06bc |
| 7.5 | 92.84 ± 0.13b | 8.69 ± 0.42a | 0.912 ± 0.004a | 0.135 ± 0.002 ab | 4.02 ± 0.17 ab |
| 10 | 91.11 ± 0.07a | 7.94 ± 1.09a | 0.911 ± 0.002a | 0.130 ± 0.001a | 3.43 ± 0.11a |
| 15 | 91.61 ± 0.08a | 8.51 ± 1.35a | 0.911 ± 0.001a | 0.131 ± 0.003 ab | 3.26 ± 0.32a |
![]() | ||
Fig. 4 Release profiles of (a) TPC and (b) TMAC from freeze-dried beads without (■) and with ( ) inulin (2.5% w/w) over 30 minutes. | ||
In the present study, the inulin-containing beads exhibited a higher release of both TPC and TMAC compared to the plain Ca(II)-alginate beads. During the rapid release phase, beads with inulin released 67.16 ± 2.46% of TPC and 54.48 ± 0.66% of TMAC, whereas the inulin-free beads showed lower release rates, with 54.98 ± 0.78% for TPC and 49.28 ± 0.17% for TMAC. This difference in release behavior suggests that inulin may significantly influence the matrix structure and interactions between compounds. Consistent with our findings, in a study in which chokeberry extract was encapsulated in Ca(II)-alginate-inulin beads, significantly higher phenolic release was observed from freeze-dried sodium alginate beads containing inulin than from those without inulin.13 However, other studies also reported a decrease in the release rate when inulin was added to alginate-inulin beads.11,31 These contradictions may be related to the bead formulation, the type and source of inulin used, the polymer's physicochemical properties, or the pH and phenolic profile of the extract, all of which may lead to distinct release behaviors.
The release mechanisms were investigated by fitting the experimental data into five different kinetic models: zero-order, first-order, Korsmeyer–Peppas, Higuchi, and Hixson–Crowell (Table 6). The release kinetics of TPC and TMAC from bead formulations, with and without inulin, were best described by the Korsmeyer–Peppas model, as evidenced by the highest determination coefficients (R2 = 0.968 for TPC and 0.964 for TMAC). This indicates that the release mechanism is primarily diffusion-driven, as evidenced by n values below 0.5, consistent with Fickian diffusion. The Higuchi model also exhibited a good fit for both compounds (R2 > 0.91), reinforcing the predominance of diffusion-controlled release from the matrix. Conversely, zero-order and first-order models showed lower R2 values, particularly for TPC with inulin, indicating that constant-rate or concentration-dependent release may not fully describe the system. The Hixson–Crowell model provided a moderate fit, suggesting a limited contribution of surface-area changes to the release process.
| Models | Inulin concentration (% w/w) | TPC | TMAC | ||||
|---|---|---|---|---|---|---|---|
| n | k | R 2 | n | k | R 2 | ||
| a Note: k values are not comparable across models and are model-specific; R2 is used to assess the best fit. n: release exponent, k: release rate constant, and R2: coefficient of determination. | |||||||
| Zero-order | 0 | — | 0.428 | 0.878 | — | 0.428 | 0.842 |
| 2.5 | — | 0.347 | 0.753 | — | 0.424 | 0.857 | |
| First order | 0 | — | 0.005 | 0.906 | — | 0.004 | 0.866 |
| 2.5 | — | 0.005 | 0.786 | — | 0.005 | 0.885 | |
| Korsmeyer–Peppas | 0 | 0.105 | 47.054 | 0.968 | 0.117 | 41.650 | 0.958 |
| 2.5 | 0.075 | 60.190 | 0.910 | 0.106 | 46.420 | 0.964 | |
| Higuchi | 0 | — | 3.433 | 0.935 | — | 3.460 | 0.914 |
| 2.5 | — | 2.852 | 0.841 | — | 3.419 | 0.923 | |
| Hixson–Crowell | 0 | — | 0.013 | 0.897 | — | 0.011 | 0.858 |
| 2.5 | — | 0.013 | 0.775 | — | 0.012 | 0.876 | |
In parallel, inulin significantly influenced the physical characteristics of the beads, producing larger, softer Ca(II)-alginate particles. These structural changes were associated with enhanced diffusion-controlled release, characterized by a more pronounced release during the later phase and higher overall release of both phenolics and anthocyanins. Despite a reduction in apparent TPC-based EE when interference-free calculations were applied, inulin enhanced anthocyanin-based EE, underscoring its selective benefit across bioactive compound classes.
This research addressed the limitations of spectrophotometric assays for measuring EE, which are susceptible to pH changes and interference from reducing agents, such as inulin. While chromatographic methods can provide more precise quantification, the proposed approach based on unloaded compounds offers a rapid, cost-effective alternative. Moreover, the use of the residual cross-linking solution enables the assessment of anthocyanin-based EE through spectrophotometric methods that cannot be applied to bead-dissolution approaches due to pH changes. Future studies should focus on optimizing formulation parameters, such as inulin molecular weight, concentration, and alginate-to-calcium ratios, and on integrating chromatographic assays to further elucidate encapsulation mechanisms. Overall, despite the dual effects of inulin, employing it as a dietary fiber co-carrier remains promising for clean-label encapsulation systems, provided that formulation and analytical strategies are carefully optimized.
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