Investigation of the Effects of Sodium Caseinate/Xanthan Gum Complexes on the Stability and Sustained Release of Acid Double Emulsions Using Box–Behnken Design

Abstract

This study investigates the formulation and optimization of acid-stable water-in-oil-in-water (W/O/W) double emulsions stabilized by sodium caseinate (NaCN)–xanthan gum (XG) complexes, with the aim of developing a natural biopolymer-based delivery system exhibiting controlled release behavior. The emulsions were prepared at pH 4, and the effects of NaCN concentration, XG concentration, and primary fraction (PF) on the encapsulation efficiency (EE) and droplet size (DS) were systematically evaluated using response surface methodology (RSM) based on a Box–Behnken design (BBD). Microscopic and rheological analyses confirmed the formation of a rigid interfacial film around the droplets, leading to improved emulsion stability over one month of storage at 4, 25, and 40 °C. The release kinetics of chlortetracycline (CTC), used as a model drug, followed a Fickian diffusion mechanism, indicating efficient control of the release rate by the NaCN/XG interfacial complex. The optimized formulation (NaCN = 0.652%, XG = 0.339%, PF = 10%) yielded an encapsulation efficiency of 87.7% and a mean droplet size of 24.83 µm, demonstrating excellent predictive accuracy of the statistical model. The results highlight the potential of NaCN/XG complexes to produce acid-stable, biopolymer-based double emulsions capable of sustained release of bioactive compounds, making this system promising for food and pharmaceutical delivery applications.

1. Introduction

Double emulsions (DEs) are complex colloidal systems in which the droplets of the dispersed phase encapsulate smaller internal droplets [1]. Two main configurations can be distinguished: water-in-oil-in-water (W/O/W) and oil-in-water-in-oil (O/W/O) emulsions [2]. Owing to their multi-compartmental architecture, these systems find wide application not only in the pharmaceutical, cosmetic, and food industries [3,4,5], but also in industrial processes such as petroleum production and flow assurance, where interface structure and adsorption phenomena strongly affect multiphase flow and phase interactions [6].

These emulsions are thermodynamically unstable [7], but they can exhibit kinetic stability over a prolonged storage period when stabilized by strong interfacial films and increased continuous-phase viscosity [8]. This stability is achieved using surfactant molecules. However, a current trend aims to replace the synthetic surfactants with natural species. Biopolymers, such as proteins and polysaccharides, represent excellent examples of biopolymeric surfactants commonly used in the food and pharmaceutical industries [1,2,7].

NaCN, a natural protein, can also form a complex with XG, an anionic polysaccharide, through electrostatic interactions [9,10]. In recent decades, studies on NaCN-XG stabilized emulsions have been limited to simple emulsions [11,12,13]. The ability of this complex to effectively stabilize DEs remains uncertain. It seems that the pH influences the stability of dispersed systems when these two components are present [14]. In a previous study [15], it was observed that it is possible to formulate stable DEs using NaCN and XG by adjusting the emulsion pH close to the isoelectric point of the protein. It was found that their droplet size (DS) strongly depends on the pH of the system and the relative concentrations of the two biopolymers. Moreover, Liu et al. [9] reported that the NaCN-XG complex formed under acidic conditions significantly affects the dynamic interfacial characteristics of the sodium caseinate adsorption film.

Therefore, DEs stabilized by a combination of NaCN and polysaccharides at acidic pH present several opportunities [16]. At the isoelectric point, NaCN loses its negative charge and tends to aggregate, which can lead to emulsion instability. This phenomenon leads to protein aggregation and emulsion flocculation, thus causing phase separation [17]. Moreover, instability at low pH is often caused by depletion flocculation, where casein molecules bridge between droplets, leading to aggregation [18]. However, recent research has focused on using specific protein–polysaccharide interactions to overcome this limitation and create stable DEs under acidic conditions [19,20]. These advances have important implications for the design and optimization of novel food and pharmaceutical delivery systems.

Although several studies have investigated the interfacial and stabilizing properties of NaCN/XG complexes in single emulsions or solid-oil-in-water (S/O/W) systems, little work has been carried out to stabilize water-in-oil-in-water (W/O/W) double emulsions using this complex, especially under acidic conditions (pH ≈ 4). The ability of NaCN/XG complexes to simultaneously stabilize both internal and external interfaces in a double emulsion and to control the release of encapsulated actives has not been comprehensively investigated. Furthermore, no systematic optimization of formulation parameters using statistical experimental design methods has yet been reported for this biopolymer system.

The present study addresses these gaps by formulating and characterizing acid-stable W/O/W double emulsions stabilized by NaCN/XG complexes at pH 4. The effects of NaCN concentration, XG concentration, and the primary fraction (PF) were evaluated on key response variables, namely encapsulation efficiency (EE) and droplet size (DS). RSM, based on a BBD, was employed to model and optimize these parameters statistically. In addition, the study investigates the release kinetics of CTC to elucidate the diffusion mechanism governing sustained release.

This research provides the first comprehensive demonstration that NaCN/XG complexes can effectively stabilize acidic double emulsions, achieving high encapsulation efficiency, controlled release, and long-term stability. The findings highlight the potential of this natural biopolymer system as a sustainable alternative to synthetic surfactants for the development of controlled delivery systems in food and pharmaceutical applications.

2. Materials and Methods

2.1. Materials

NaCN was purchased from Sigma Life Science (Wellington, New Zealand). Food-grade XG was purchased from Rhodia (Algiers, Algeria). Sodium azide, used as a preservative, and glucose D (used as an osmotic pressure regulator) were supplied by Sigma-Aldrich (Buchs, Switzerland). Hydrochloric acid (HCl) was supplied from Fujifilm Wako Pure Chemical Co., Ltd. (Osaka, Japan). Olive oil and coconut butter (purchased from a local supermarket) were used as organic phases. The lipophilic surfactant (Span 60, HLB 4.3) was supplied by Sigma-Aldrich (Buchs, Switzerland). CTC was kindly donated by the company Saidal (Medea, Algeria).

2.2. Preparation of NaCN/XG Complexes

NaCN/XG dispersions were prepared by the method used by Matsuyama et al. [21] with some modifications. A volume of 50 mL of NaCN was mixed with 50 mL of XG by adding HCl (0.1 M) at the same time. The agitation was carried out using a homogenizer (Ultra-turrax T-25, IKA, Staufen, Germany) at 9000 rpm for 3 min. The final pH of the dispersion was 4. In the formulation study, the mass ratios of NaCN (0.2–0.8 w/w %) and XG (0.3–0.6 w/w %) were varied as independent factors defined by the Box–Behnken design.

2.3. Preparation of Double Emulsions

DE samples were prepared by the indirect method. This process consists of making a simple water-in-oil (W/O) emulsion based on a lipophilic surfactant (Span 60), which will be encapsulated in an external aqueous phase containing NaCN/XG complex. The primary emulsion was prepared by gradually adding the aqueous phase (40% distilled water) to the organic phase (34.5% olive oil and 24% coconut butter) containing 1.5% of Span 60 under magnetic stirring. A mixture of olive and coconut oils was intentionally selected to balance the physicochemical properties of the dispersed phase. Both phases were previously brought to the same temperature (60 °C). The system was then soaked in an ice bath for 5 min and then kept under magnetic stirring until room temperature. Once the emulsion temperature reached 20 °C, the system was sheared using a homogenizer (Ultra-turrax T-25, Staufen, Germany) at 1500 rpm for 5 min. Then, the W/O/W emulsion was prepared by introducing the primary fraction (PF) of the simple emulsion prepared into the external aqueous phase containing NaCN/GX at pH 4 using a homogenizer at 10,000 rpm and room temperature. For CTC encapsulation, a 0.1 M CTC solution was prepared by dissolving the powder in a mixture containing distilled water and ethanol, and then introduced into the internal aqueous phase of the primary emulsion. A concentration gradient between the two aqueous phases can cause water transfer from the external aqueous phase to the internal one. This transfer produces swelling of the internal droplets, which increases the volume fraction of the globules that can produce a significant change in the rheological properties of the DE [22]. For this, an osmotic pressure regulator (0.2 M D-glucose) was added to the external aqueous phase. All formulations were prepared on a mass basis (w/w). The oil mixture was maintained at an olive/coconut ratio of 1.4/1 (w/w), and all percentages refer to the total weight of the emulsion (

Table 1. Composition of double emulsions.

Component	Phase	Function	Concentration/Ratio (w/w %)	Notes
Internal aqueous phase (W1)	Water	Solvent/dispersed phase	40.0	May contain 0.1 M chlortetracycline (CTC) for release tests
	Sodium azide	Preservative	0.02	—
Oil phase (O)	Olive oil	Continuous phase (liquid–lipid)	34.5	Mixed with coconut butter
	Coconut butter	Solid–lipid (structure enhancer)	24.0	Pre-melted at 60 °C
	Span 60	Lipophilic surfactant	1.5	HLB = 4.3
External aqueous phase (W2)	NaCN	Protein emulsifier	0.2–0.8	Variable (X1)
	XG	Polysaccharide stabilizer	0.3–0.6	Variable (X2)
	D-Glucose	Osmotic regulator	0.2 M	Prevents swelling
Primary fraction (PF)	—	W/O proportion dispersed in W2	10–30	Variable (X3)
Total emulsion	—	—	100% (w/w)	All mass ratios relative to the total emulsion mass

).

2.4. Evaluation of Double Emulsion Stability

The stability of the different emulsions formulated by using NaCN/XG complexes was monitored for 4 weeks. A sample of each formulation was transferred into a glass test tube immediately after preparation and sealed to prevent evaporation. The emulsions were visually inspected, and the creaming index (CI %) was measured at fixed intervals (days 0, 3, 7, 14, 21, and 28). The emulsions were separated into the upper cream and lower aqueous phase layers over time, and the total emulsion height (H_T) and aqueous phase height (H_aq) were measured. The creaming index (CI %) was calculated as usual, in a percentage of the ratio of the measured values:

CI (%) = (H_aq/H_T) × 100

(1)

2.5. Microscopic Observation and Droplet Size Measurement

Microscopic observations of DEs were performed using an Olympus^® BX-51 phase contrast microscope (Bremen, Germany), equipped with an oil immersion lens (×100). It was connected to a digital camera for image capture. A minimum of one hundred droplets is counted for each test. The sample was placed between the slide and coverslip, and observations were made immediately after formulation. ImageJ software (ImageJ 1.54g) (USA) was used to calculate the diameter of the emulsion droplets.

2.6. Apparent Viscosity

For the measurement of the apparent viscosity of DE, a Visco-Tester viscometer (Haake, VT, Madrid, Spain) with a rotating mobile was used. It consists of a rotating cylinder driven by a switchable speed motor. This device is equipped with four mobiles of different shapes and geometries, where each mobile must be used within a well-defined range of viscosity and rotation speed varying between 0.3 and 200 rpm.

2.7. Conductivity and pH Measurements

The conductivity of the emulsions was measured using an LF 191 conductimeter (WTW, Weilheim in Upper Bavaria, Germany). The pH was measured directly in the solutions and emulsions prepared using a microprocessor pH/ion meter pMX 2000 (WTW, Burladingen, Germany).

2.8. Release Kinetics Study

The EE of DEs was evaluated by determining the amount of CTC released into the external aqueous phase over time by the method used by Seddari et al. [7] with some modifications. For this, a sample of each formulation was placed in a centrifuge tube and then centrifuged at 6000 rpm for 60 min. The amount of separated aqueous layer (1 mL) was carefully removed every day from the recovery phase using a syringe and then diluted 50 times. The aliquots were not returned to the test tubes after measurement. The release rate was monitored over 16 days of storage at 25 °C. The amount of CTC released was determined using a UV spectrophotometer (Shimadzu UV-1800, Kyoto, Japan) at λ = 370 nm.

The released fraction (RF) of CTC in the external aqueous phase of the DE was defined as the ratio of the CTC rejected in the external aqueous phase at a given time (Mt) to the total amount present in the external aqueous phase of DE if all CTC were released (M∞) [23].

$$RF\left(\%\right)={\displaystyle \frac{Mt}{M\infty }}\times 100$$

(2)

The EE was defined as the percentage of CTC trapped in the internal aqueous phase directly after formulation:

$$EE\left(\%\right)=100-RF(\%)$$

(3)

Additionally, the parameters of the release kinetics were estimated using first-order, Higuchi, and Korsmeyer–Peppas models, as described by the following equations, respectively:

$$Q=\left[1-\exp \left(-\mathrm{K}t\right)\right] \times 100$$

(4)

$$Q=\mathrm{K}{t}^{0.5}$$

(5)

$$Q=\mathrm{K}{t}^n$$

(6)

where Q is the fraction released of CTC at time t, K is the release rate constant, and n is the release exponent indicating the drug release mechanism [24,25].

2.9. Experimental Design

The effects of three independent variables (%NaCN, %XG, and %PF) on the encapsulation efficiency (EE) and droplet sizes (DS) of DEs were evaluated using RSM, and in a particular Box–Behnken design (

Table 2. Variables used and observed responses from runs in the BBD.

Factor	Specification		Experimental Field		Unity
X1	%NaCN		0.2–0.8		w/w %
X2	%XG		0.3–0.6		w/w %
X3	%PF		10–30		w/w %
Y1	EE		−66.90–92.56		%
Y2	DS		−25.36–38.45		µm
Run	Independent variables				Dependent variables
	X1	X2		X3	Y1	Y2
1	0.2	0.30		20	69.42	38.45
2	0.8	0.30		20	92.56	33.89
5	0.2	0.45		10	83.18	27.71
6	0.8	0.45		10	82.56	27.91
7	0.2	0.45		30	74.84	28.33
8	0.8	0.45		30	72.65	27.55
9	0.5	0.30		10	89.94	25.96
10	0.5	0.60		10	69.03	27.25
11	0.5	0.30		30	78.51	26.39
12	0.5	0.60		30	66.90	25.36
13	0.5	0.45		20	81.05	28.87
14	0.5	0.45		20	79.32	27.17
15	0.5	0.45		20	79.39	27.76

). For this, mathematical prediction models were established. The construction of the experimental plan and the statistical analysis were performed using Modde 6 software.

2.10. Statistical Analysis

All measurements were repeated three times, and data are presented as mean ± standard deviation (SD). Data were examined by one-way analysis of variance (ANOVA), followed by Tukey’s test with significance set at p < 0.05, to confirm the difference in mean value between samples using OriginPro.8 software (2019).

3. Results

3.1. Characterization of the Double Emulsions

3.1.1. Macroscopic Aspects

All formulated samples have a milky and homogeneous appearance with different consistencies depending on the concentration of biopolymers. The measured values of electrical conductivity directly after formulation vary between 332 ± 0.158 and 634 ± 0.098 µS/cm, indicating that the external phase is aqueous and that the obtained DE are of the type W/O/W.

3.1.2. Microscopic Analysis and Particle Size Distribution

The variation in the average diameter of the oil droplets for different formulations is illustrated in Figure 1. The obtained results showed that all emulsions exhibit a unimodal particle size distribution. However, it was found that for all samples, the average diameters (d_3,2) vary between 25.3565 ± 0.0093 and 38.4507 ± 1.5221 µm. Additionally, the variation in the NaCN:XG ratio has a remarkable effect on the size of DE globules. For example, for the same PF of 20%, the diameter decreases from 38.4507 ± 1.5221 to 25.974 ± 0.1394 µm for a NaCN:XG ratio of 0.5:0.75 and 0.5:1.5, respectively. Likewise, the DS decreases from 38.4507 ± 1.5221 to 33.8939 ± 0.0867 µm for a NaCN:XG ratio of 0.5:0.75 and 2:0.75. As a result, the DS of a DE stabilized by the NaCN/XG complex is influenced by the concentrations of biopolymers.

According to the quantity of water droplets trapped within the multiple droplets, three morphologies can be distinguished: types A, B, and C [26]. Type A is characterized by the presence of multiple droplets containing large internal droplets, type B with multiple droplets containing several small internal droplets, and type C, with multiple droplets containing a large number of small internal droplets [27,28]. As shown in Figure 2, the morphology of emulsions prepared with NaCN/XG complex is of type B, characterized by a rigid interfacial film that separates the three phases: internal aqueous phase, oily phase, and external aqueous phase. The internal droplets are small (not measured) and show no coalescence phenomena. Similarly, the oil droplets exhibited a predominantly spherical morphology with a continuous and rigid interfacial film, within which multiple internal water droplets were uniformly entrapped. The micrographs revealed well-defined W/O/W structures with negligible coalescence or phase separation.

3.1.3. Stability at Different Storage Temperatures

The crystallizable DEs stabilized by NaCN/XG complexes have a homogeneous appearance immediately after formulation. However, when they were submitted to temperature change and time storage, their appearances were modified. Macroscopic images of samples after 28 days of storage at 4, 25, and 40 °C were realized, and for each sample, the corresponding CI was calculated (Figure 3).

The analysis of these results revealed that the PF and concentration of the complex in the external aqueous phase have a remarkable effect on the stability of the prepared emulsions. Formulations F9 and F11, prepared with the same NaCN:XG ratio of 1.25:0.75 and increasing PF (from 10% to 30%), exhibited creaming at different storage temperatures (4, 25, and 40 °C). For all other emulsions, no instability phenomena were observed during the 4 weeks of storage at 4 °C. The instability of F9 and F11 (CI = 100%) may likely be due to the excess of protein that was not linked to polysaccharide. This instability has already been observed for solutions containing both biopolymers. At 25 °C, for the same PF (20%) and increasing concentrations of NaCN, F1 and F2 prepared with NaCN:XG ratios of 0.5:0.75 and 2:0.75, showed slight values of CI (3.03% and 0.99%, respectively). At 40 °C, for the same NaCN:XG ratio (1.25:1.5) and increasing PF, the CI increases from 0% to 90.43%. This can be explained by the fact that the amount of the complex necessary to stabilize the oil/water interface is insufficient. Consequently, the weight ratios between the two biopolymers and the PF have a significant influence on the stability of DEs. In a Previous work using a mixture of NaCN and k-carrageenan [29], it was found that the concentration of both biopolymers directly affects the stability of DEs. Also, Benichou et al. [30] successfully created stable multiple emulsions for 28 days using whey protein isolate (WPI) and XG as emulsifiers in the external interface. They noticed an increase in the stability of the system when the pH was below the isoelectric point of the mixture. They attributed this improvement to strong electrostatic interactions between the protein and polysaccharide molecules at that pH level.

The stability of multiple emulsions is not only governed by interfacial phenomena but also by the rheological properties of the continuous phase. The presence of XG and NaCN markedly increases the apparent viscosity of the external aqueous phase, thereby reducing droplet movement and delaying gravitational separation. XG exhibits viscosities of approximately 1400–1600 mPa·s at 1 wt.%, while NaCN solutions typically range from 1000 to 3000 mPa·s, depending on concentration and pH. Consequently, varying the NaCN:XG ratio alters the viscosity of the medium, which in turn influences the rate of creaming and coalescence. This suggests that the enhanced stability observed for formulations with intermediate NaCN:XG ratios (e.g., 0.65:0.35) may arise from a synergistic balance between interfacial film strength and bulk viscosity. Similar correlations between polymer concentration, viscosity, and emulsion stability have been reported in previous studies [31].

3.2. Apparent Viscosity of Double Emulsions

To study the effect of the concentration of the biopolymer complex in the external aqueous phase, as well as the oily fraction PF, on the rheological properties of DEs, measurements of the apparent viscosity of the different formulated systems were conducted. The results obtained are represented in Figure 4. It was noticed that the apparent viscosity for all formulations decreases with increasing shear rate, which indicates that the emulsions are non-Newtonian fluids. In addition, the viscosity of the different formulations varies with the NaCN:XG ratio. For example, F3 prepared with a ratio of 0.5:1.5 has a higher viscosity than F1 prepared with a ratio of 0.5:0.75 for the same PE (20%). The increase in viscosity is due to the rigidity of the interfacial film formed by the complex between XG and NaCN.

An excess of protein compared to the polysaccharide decreases the viscosity. For instance, F7, prepared with a ratio of 0.5:1.125, has a higher viscosity than F8, prepared with a ratio of 2:1.15 for the same PE (30%). This can likely be attributed to the amount of protein that is not adsorbed at the O/W interface. The formation of a complex between NaCN and XG due to electrostatic interactions can influence the adsorption rate of the protein, thus primarily the diffusion rate of NaCN at the O/W interface [32]. Additionally, a low viscosity of a DE may indicate the weakness of the film at the interface [33].

In conclusion, the NaCN/XG complex directly influences the viscosity of the external phase and consequently the stability of DEs. The higher the concentration of the complex, the greater the viscosity of emulsions, but this is valid for a certain ratio between NaCN and XG. These results demonstrate that it is possible to formulate stable DEs using a mixture of NaCN/XG at pH 4 and at a certain ratio between the two biopolymers.

Previous work has shown that NaCN solutions experience a marked increase in viscosity and aggregation around pH 4.3–4.6, due to approaching the protein’s isoelectric point and formation of large aggregates [34]. In the present study, the NaCN/XG complexes were prepared at pH 4.0, designed to exploit this region of enhanced protein aggregation and film formation. The higher aggregate size and viscosity at this pH likely contribute to the formation of a more rigid interfacial film around W/O/W droplets and reduce their mobility in the continuous phase, improving kinetic stability. Although the viscosity of the biopolymer solutions was not systematically measured across a broad pH range, the observed emulsion stability (low creaming index, minimal coalescence) is consistent with the enhanced viscosity/aggregation behavior of NaCN near its isoelectric point.

3.3. Release Kinetics of CTC

The effect of the NaCN:XG ratio and PF on the release kinetics was evaluated by determining the concentration of CTC released in the external aqueous phase over time during 16 days of storage at 25 °C and pH 4. Analysis of the obtained results (Figure 5) showed a release of half of CTC from the DE during the first two days for all formulations, followed by a gradual increase towards a plateau, except for F8, F10, and F12 (NaCN:XG = 2:1.125, 1.25:1.5, 1.25:1.5, and PF = 30%, 10%, 30%) where the release of CTC reached 75% on the first day. While F5, F9, and F11 (NaCN:XG = 0.5:1.25, 1.25:0.75, 1.25:0.75, and PF = 10%, 10%, 30%) reached half release by the fifth day. Thus, for the same PF, the rate of CTC release in the external aqueous phase heavily depends on the complex concentrations.

Among all the formulations tested, the values of t_50% ranged between 1 and 5 days. In the second step of emulsification, the hydrophilic emulsifier (NaCN/XG complex) adsorbs at the interface and forms a rigid interfacial film around the droplets containing CTC, slowing its release, which confirms that it is possible to control the release from CTC-loaded DEs by using an appropriate complex in the external phase.

According to the results illustrated in Figure 6, F2 represents the best EE (92.56%) for a NaCN:XG = 2:0.75 and a PF = 20%. F3 represents the lowest EE value (65.14%) for a NaCN:XG = 0.5:1.5 and a PF = 20%. This can be explained by the nature of the complex formed between the two biopolymers and its capacity to adsorb at the interface, as previously explained. The release in the external aqueous phase of encapsulated substances occurs through coalescence and/or diffusion/permeation phenomena [35]. To determine the nature of the CTC release mechanism, the experimental data were analyzed using first-order, Higuchi, and Korsmeyer–Peppas models. Fitted dissolution profiles were obtained using the experimental results (

Table 3. Release model parameters for CTC from double emulsion formulations.

Number	First Order		Higuchi		Korsmeyer–Peppas
	k (Day−1)	R2	k (Day−1)	R2	k (Day−1)	n	R2
1	0.303 ± 0.036	0.781	27.476 ± 1.120	0.675	52.744 ± 1.354	0.212 ± 0.011	0.989
2	0.2919 ± 0.027	0.865	27.381 ± 1.017	0.755	48.676 ± 2.023	0.247 ± 0.018	0.977
3	0.400 ± 0.053	0.848	28.511 ± 1.458	0.598	52.611 ± 6.452	0.230 ± 0.055	0.795
4	0.392 ± 0.038	0.897	28.917 ± 1.371	0.622	55.426 ± 3.205	0.205 ± 0.026	0.953
5	0.109 ± 0.010	0.613	20.187 ± 0.657	0.837	28.389 ± 3.306	0.361 ± 0.049	0.893
6	0.449 ± 0.054	0.855	29.017 ± 1.329	0.569	59.363 ± 1.417	0.184 ± 0.011	0.990
7	0.224 ± 0.029	0.583	25.401 ± 1.112	0.615	50.706 ± 1.637	0.194 ± 0.014	0.982
8	0.499 ± 0.095	0.626	28.293 ± 1.535	0.333	65.504 ± 1.728	0.127 ± 0.012	0.984
9	0.151 ± 0.011	0.849	23.528 ± 0.486	0.942	30.096 ± 2.117	0.392 ± 0.030	0.965
10	0.513 ± 0.102	0.604	28.386 ± 1.559	0.319	66.182 ± 2.183	0.124 ± 0.015	0.975
11	0.129 ± 0.007	0.884	21.774 ± 0.377	0.960	27.350 ± 1.440	0.400 ± 0.022	0.981
12	0.873 ± 0.179	0.778	30.238 ± 1.866	0.196	73.179 ± 1.110	0.096 ± 0.007	0.994
13	0.1961 ± 0.025	0.574	24.967 ± 1.020	0.698	46.046 ± 3.183	0.230 ± 0.031	0.935
14	0.151 ± 0.021	0.314	22.950 ± 1.117	0.574	45.501 ± 4.296	0.197 ± 0.042	0.868
15	0.196 ± 0.025	0.523	24.835 ± 1.056	0.650	48.226 ± 2.541	0.206 ± 0.023	0.957

k: Kinetic constant (day⁻¹), n: Diffusional exponent, R²: Correlation coefficient.

).

For all samples based on their correlation coefficients, the best model was that of Korsmeyer–Peppas with a minimum R²-value of 0.80 compared to Higuchi’s model with an R²-value of 0.20 and first-order with an R²-value of 0.31. The release was also explained by the value of the diffusional exponent n (Equation (6)). For all formulations, the value of n was found to be less than 0.45, indicating that the release mechanism is diffusion type [36]. Based on the release models and R²-values, the release of CTC depends on the NaCN/XG ratio in the external phase, and the PF value, which is another important parameter [15].

3.4. Evaluation of Effect Factors and Optimization

3.4.1. Statistical Analysis of the RSM Model

The statistical quality of the RSM model is conditioned by the determination of the statistical parameters. The first parameter is R², which measures the percentage of total variation that can be explained by the model. The second is the prediction coefficient (Q²), which measures the predictive strength of the model. In addition, the statistical significance of the models was also tested by the Fisher test.

From the results of the ANOVA (

Table 4. Analysis of variance (ANOVA) for the RSM responses.

Source	Sum of Squares	Degree of Freedom	Mean Square	F-Value	P	SD
%EE, Y1 (a)
Model (regression)	728.734	9	80.425	49.180	0.004	8.968
Residual	4.905	3	1.635			1.278
Lack of fit	2.749	1	2.749	2.549	0.251	1.658
Pure error	2.156	2	1.078			1.038
DS (µm), Y2 (b)
Model (regression)	151.995	9	16.888	26.578	0.010	4.109
Residual	1.906	3	0.635			0.797
Lack of fit	0.369	1	0.369	0.481	0.560	0.608
Pure error	1.536	2	0.768			0.876

^(a) R² = 0.993, Q² = 0.752; ^(b) R² = 0.988, Q² = 0.824.

), it was found that the quality of the EE (Y₁) model is satisfactory (R² = 0.993, and Q² = 0.752). Also, the quality of the DS (Y₂) model is satisfactory (R² = 0.988, and Q² = 0.824). Consequently, it seems that the models are potentially exploitable in terms of prediction. Moreover, it was deduced that they are statistically significant, considering the values of F (49.180 for EE and 26.578 for DS). Also, the values of the probability p were found to be less than 0.05 (0.04 for EE and 0.010 for DS).

The mathematical prediction equations were established by using second-order polynomial models. These models take into account all double interactions between the factors and non-monotonic effects; they were determined by the MLR method.

Y₁ = 79.853 − 0.702X₁ − 8.130X₂ − 3.976X₃ − 12.272X₁X₂ −0.392X₁X₃ + 2.325X₂X₃ − 2.390X₁² −
4.602X₂² + 0.844X₃²

(7)

Y₂ = 27.923 − 0.145X₁ + 0.065X₂ − 0.149X₃ + 2.119X₁X₂ − 0.245X₁X₃ − 0.580X₂X₃ + 4.965X₁² +
3.330X₂² − 5.014X₃²

(8)

3.4.2. Effect of Factors

The most important property of a multiple emulsion is its good encapsulation efficiency and adequate globule sizes of the internal phases. This is influenced by several parameters, including the composition of emulsions at all levels, especially at the interfaces, where emulsifiers play a dominant role. Understanding their influence allows predicting the mechanisms involved in the release of encapsulated substances. So, the individual effects of factors and their interactions on the responses can be deduced by simulation. These effects represent the coefficients in the response surface models. A positive value represents an effect that favors optimization, while a negative value indicates an inverse relationship between the factor and response. Also, the results obtained (Equation (8)) revealed that the factors XG and PF have a negative effect on EE, while NaCN has a negligible effect on the response. The interactions between NaCN and XG seem to have a negligible effect, while the quadratic effect of the factors is negative. On the other hand, it was noticed from Equation (8) that the interactions NaCN-XG, NaCN-NaCN and XG-XG have a great effect on the DS. However, the other factors and their interactions seem to have a negligible effect.

Figure 7 and Figure 8 illustrate the iso-EE contours and iso-DS contours as a function of NaCN and XG at different values of PF, respectively. It was noticed firstly that an increase of NaCN in the external phase, along with XG, leads to a significant decrease in EE (Figure 7). However, increasing XG with a minimal value of NaCN results in a slight increase in EE, reaching a maximum value (around 75% for NaCN = 0.2% and XG = 0.6%). While increasing NaCN with a minimal value of XG results in a significant increase in EE, reaching a maximum (around 95% for NaCN = 0.8% and XG = 0.3%). Nevertheless, when both values are at their maximum (NaCN = 0.8% and XG = 0.6%), EE is very low (about 55%). Furthermore, PF has virtually no effect on EE. The concentration of biopolymer has a considerable effect on EE. This can be explained by the nature of the interfacial film formed around the oil droplets by the NaCN/XG complex and its rigidity. This has a direct effect on the release of CTC.

On the other hand, examination of Figure 8 shows that an increase in the concentration of NaCN from 0.35% to 0.65% in the external phase, along with the concentration of XG from 0.37% to 0.52%, leads to a significant decrease in DS. It was also observed that PF has a negligible effect on DS. This can be explained by the fact that as NaCN increases, the amount of XG that interacts with NaCN also increases. The formed complex is then positioned at the interface of the oil droplets, and the aqueous phase is depleted of XG. Similar results were obtained for modified pectin–protein isolate complexes used to stabilize multiple emulsions. These complexes yield stable multiple emulsions with small droplet sizes and significant encapsulation yields [33].

In conclusion, the EE and DS of DEs prepared with NaCN/XG complexes (pH4) are largely influenced by the NaCN:XG ratio. It directly affects the nature of interactions between proteins and polysaccharides and thus the nature of the complex that constitutes the interfacial film covering the oil droplets.

3.5. Optimization of Double Emulsion Formulation

A crystallizable DE was prepared and characterized using the optimal parameters: NaCN = 0.637 (w/w %), XG = 0.331 (w/w %) and PF = 10 (w/w %). The characterization results of this emulsion, as well as the experimentally prepared one, are represented in

Table 5. Characteristics of the optimal double emulsion obtained experimentally and from the RSM model.

Characteristics	pH	Electrical Conductivity (µs/cm)	EE (%)	DS (µm)
Experimental	4.18	590	87.70	24.830
Predicted	-	-	93.67	24.915

. From the analysis of the particle size distribution of the optimal emulsion, directly after preparation, it was found that the optimal emulsion is monodisperse with a d_3,2 of 24.915 µm. In addition, it was also noticed that the experimental results are very close to the responses obtained through optimization, which demonstrated that the established RSM model is valid.

4. Conclusions

This study focused on the optimization of the formulation of a double emulsion stabilized by the NaCN/XG complex using an experimental design, as well as the study of the release kinetics of an active ingredient encapsulated in such systems. The maximum EE was found equal to 87.7% under optimal concentrations of NaCN (0.6522%), XG (0.3399%), and PF (10%). A lower EE was observed when the concentrations of NaCN and XG were high, probably due to excessive electrostatic interactions. The mean DS under these conditions was 24.83 µm. Consequently, the interactions between NaCN and XG directly influence the DS through the formation of a rigid interfacial film.

In addition, DEs formulated using these complexes demonstrated excellent stability during one month of storage at different temperatures (4, 25, and 40 °C). It was observed that the emulsion stability is strongly influenced by the NaCN:XG weight ratio and the total biopolymer concentration. The optimal ratio was 1.6:0.9, while the optimal biopolymer concentration was 0.99%. On the other hand, all formulated emulsions exhibited non-Newtonian behavior. Higher viscosity was observed for formulations containing specific NaCN:XG ratios, reflecting a higher rigidity of the interfacial film.

Based on the release models and correlation coefficients, it was noticed that the release of CTC is strongly influenced by the NaCN:XG ratio in the external phase and follows a Fickian diffusion mechanism. An efficient release control of CTC over a period of 16 days was obtained using the optimal formulations. These results underscore the ability of NaCN/XG complexes to create mechanically robust, acid-stable interfacial layers suitable for controlled delivery of hydrophilic actives.

Overall, this work provides a scientifically validated approach for developing natural, biopolymer-based multiple emulsions as sustainable alternatives to synthetic surfactant systems. The formulation strategy and statistical optimization framework described herein can be extended to encapsulate other bioactive ingredients for pharmaceutical, nutraceutical, and functional food applications. Future studies will focus on providing a full pH–viscosity profile, in vitro bioaccessibility testing, storage shelf-life under variable pH conditions, and scalability assessment for industrial application.