**3. Results**

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**2. Methodology**

USA) as emulsifying agent.

**2.2 Microemulsion formation**

**2.1 Materials**

**2.3 Particle size**

bacteria related to common illness by food consumption.

formulated with 3% of Tween 80 and 5% of inulin.

**2.4 Release of encapsulated CEO and REO**

**2.5 Mathematical modeling for release profiles**

used to fit a second-order dynamic (Eq. (2)).

*C*(*t*) = *Cmax*[1 − *e*<sup>−</sup>*k*1*<sup>t</sup>*

*C*(*t*) = *Cmax*[1 − (*k*<sup>2</sup> *t* + 1) *e*<sup>−</sup>*k*2*<sup>t</sup>*

consequently, the development of mathematical models able to describe the release of these compounds establishes a very useful tool for the behavior prediction [6]. The objective of this study was to evaluate the release of CEO and REO encapsulated in microemulsions prepared by high-frequency ultrasound, setting a target concentration to be released, according to their antimicrobial activity against

The REO was purchased at Hersol (Mexico) and the CEO at TECNAAL (Mexico). For the preparation of the oil-in-water (O/W) microemulsions, inulin (Fructagave PR95, Mexico) was used as stabilizer and Tween 80 (Sigma-Aldrich,

The dispersed phase of CEO microemulsion was prepared with 10% (w/w) of CEO, while for REO microemulsion, it was prepared with 30% (w/w) of REO. The microemulsions were prepared using an ultrasound homogenizer (Cole Parmer, CP 505, USA). The continuous phase of the O/W CEO or REO microemulsions was

Particle size distributions of the microemulsions' droplets were measured using

The amount of microemulsion dispersed in water was defined according to values reported in other studies [8, 9] of minimum inhibitory concentration (MIC) and minimum bactericide concentration (MBC) against bacteria of the CEO and REO; maximum concentrations of 15 and 80 μL/mL, respectively, were adjusted in this study. The microemulsions were added in water, maintaining the system agitated at 60 rpm and 25°C. The quantification of the EOs' release was made by dissolving 1 mL of sample in 9 mL of n-hexane, determining their absorbance in a spectrophotometer at 310 nm for the CEO and 225 nm for the REO.

The concentration data of the released EOs at different times were recorded and fitted to dynamic kinetic models, by optimizing the minimal square error. Eq. (1) was applied to describe a first-order kinetic model. A kinetic with an initial zero slope and a maximum slope at the inflection point (typical *S* shape response) was

] (1)

] (2)

a particle analyzer by laser diffraction (Bluewave, Microtrac, USA).

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According to the release curves (**Figure 1**), the CEO release showed a constant rate in the first 90 min; followed by a plateau from 90 to 360 min. On the other hand, the REO release presented a delay release of 60 min, but then the release rate was constant until 420 min passed, presenting a decrease of the release rate until reaching a plateau at 600 min.

The antimicrobial activity of EOs depends on their availability, in certain food, to inhibit spoilage microorganisms [8]. In **Figure 1**, it can be observed that the encapsulated CEO release of 10 μL/mL was obtained after 60 min, and for REO release, the concentration of 60 μL/mL was obtained after 360 min.

Tomičić et al. [9] evaluated the antimicrobial activity of different EOs against *Listeria monocytogenes*. The authors reported that the MIC value with CEO was 2.56 μL EO/mL and with REO was 20.48 μL EO/mL. In addition, Kaskatepe et al. [8] reported MICs values of commercial and natural CEO between 0.39 and 12.5 μL EO/mL against *Escherichia coli*. For this study, these values were taken as a reference for the EOs release. In accordance with the release curve of CEO microemulsion (**Figure 1**), the MICs for both bacteria would be available in 30 min, whereas the MBC for *L. monocytogenes* will be released in 90 min and for *E. coli* in 60 min. Meanwhile, for the REO microemulsion, the MICs would be released after 120 min, for both bacteria. Finally, the concentration of MBC for *L. monocytogenes* and *E. coli* would be available after 210 and 420 min, respectively.

Different factors can influence the rate at which the EOs is released: first, the amount of EO in the microemulsion; and second, the lipid droplet size in the microemulsion. The droplet size D50 determined in CEO and REO microemulsions were 1.99 and 3.45 μm, respectively. Since the CEO microemulsion droplet size was smaller than in REO microemulsion, it enhanced its release in the aqueous solution. As shown in **Figure 1**, the release profile for CEO shows a monotonic response with a rapid raising at the beginning of the process, and after a lapse of time, the CEO concentration tends to achieve a stationary value, such behavior was described by a first-order kinetic model. For REO, a change in the slope of the release curve, describing a *S*-shape response, can be observed. This behavior was fitted to a second-order dynamic model, as discussed by Cardoso-Ugarte et al. [10].

For the CEO release, k1 was determined as 0.0166, while for REO liberation, the parameter k2 was calculated as 0.00708. To be dimensionally consistent, both

#### **Figure 1.**

*(a) Release of CEO microemulsion (*■*) and (b) REO microemulsion (•), both in water at 60 rpm and 25°C. Continuous lines represent mathematical model estimation.*

parameters have units of min<sup>−</sup><sup>1</sup> and are directly related to the release rate. The fits of the proposed models are shown in **Figure 1**; the correlation coefficient (R2 ) between experimental data and the model estimation ranged from 0.993 to 0.974.
