**1. Introduction**

Plants are a source of natural products that have several applications and are an important raw material for obtaining compounds of interest to the pharmaceutical and food industries [1,2]. Several species of *Acacia* have been studied and their secondary metabolites have anti-inflammatory [3–5], antifungal [6–8], antibacterial [9–12], antioxidant [13–15], anticancer [16,17], antidepressant [18], and antifeedant properties [19], among others. The extracts of different *Acacia* species, such as *A. catechu*, *A. concinna*, *A. dealbata*, *A. decurrens*, *A. farnesiana*, and *A. senegal* are used in cosmetics, according to the International Cosmetic Ingredient Dictionary and Handbook [20].

The *Acacia mearnsii* De Wild, a member of the Leguminosae family (subfamily Mimosoideae), is widely grown in Brazil and South Africa, with an estimated 540,000 hectares cultivated worldwide [21], representing the main source of vegetable tannins. Although the biological activities of other *Acacia* genus species have already been studied and the use of its bark and wood is already common, the *A. mearnsii* flowers have not yet been industrially explored.

**Citation:** da Silva, G.F.; de Souza Júnior, E.T.; Almeida, R.N.; Fianco, A.L.B.; do Espirito Santo, A.T.; Lucas, A.M.; Vargas, R.M.F.; Cassel, E. The Response Surface Optimization of Supercritical CO2 Modified with Ethanol Extraction of *p*-Anisic Acid from *Acacia mearnsii* Flowers and Mathematical Modeling of the Mass Transfer. *Molecules* **2022**, *27*, 970. https://doi.org/10.3390/ molecules27030970

Academic Editors: Reza Haghbakhsh, Sona Raeissi and Rita Craveiro

Received: 14 December 2021 Accepted: 18 January 2022 Published: 31 January 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Supercritical fluid extraction (SFE) is an important process used to obtain bioactive compounds [22] and it stands out in the food, pharmaceutical, and cosmetic industries due to its capacity to extract compounds with a high purity without thermal degradation, as well as its use of toxic solvents [23,24]. SFE is considered a clean technology when carbon dioxide, which is considered a green solvent, is used as a solvent, offering advantages over traditional methods, such as the extraction by steam distillation and hydrodistillation methods [25,26].

In SFE, operational conditions such as temperature, pressure, and particle size influence the process efficiency [22]. The design of experiments and response surface methodologies are commonly employed for the identification and optimization of variables [27–35]. The methodology allows evaluating the influence of several variables regarding one or more responses with a reduced number of experiments, therefore, reducing the time and cost [36]. After the extraction process has been optimized, the mathematical modeling of the extraction process dynamic is an important step for the prediction and process scale-up [37,38]. The mathematical modeling of the extraction is substantial, to evaluate the influence of the operational parameters in the technical and economic viability of an industrial process, with a reduced number of laboratory experiments [38–40].

In this work, supercritical carbon dioxide extraction was applied to the *Acacia mearnsii* flowers, a part of the plant with potential that is yet to be explored. The antibacterial activity of the extract was evaluated in the crude extract and the fractions obtained by column chromatography; *p*-anisic acid was identified in the fraction with the best antibacterial activity. *p*-anisic acid, also known as draconic acid or 4-methoxybenzoic acid.

(IUPAC), is an important substance that has digestive, diuretic, and expectorant properties and it is used as an aroma component in the food and cosmetic industries as a flavor, a preservative, and an antiseptic agent [41,42]. It also has importance in medical science for the treatment of Parkinson's disease, hepatitis B and C viruses, liver diseases, the post-radiation treatment of breast cancer, and skin desquamation [43]. Finally, it is an important substance in the production of pharmaceutical intermediates and pharmaceutical products, agrochemicals, and dyes [44]. The solubility of *p*-anisic acid in water is low, but it is highly soluble in alcohols and is soluble in ethers, as well as ethyl acetate [45].

The extraction evaluation can be carried out in terms of either the overall yield or the selectivity of a target component. The selectivity aspect is important since a high purity product for the desired analyte does not require subsequent purification operations. These purification steps make the process more expensive, in addition to exposing the extract to solvents that may not be compatible with the outcome of the product [46–48]. Thus, the response surface methodology was used for the optimization of *p*-anisic acid selectivity in the extract obtained by supercritical carbon dioxide extraction. The effects of pressure, temperature, and particle size were evaluated using a Box–Behnken design. For the optimized conditions within the framework investigated, the mass transfer parameters of three mathematical models were estimated to support the extraction process simulation.

#### **2. Results**
