## 4 Extraction Methods
### Extraction in Supercritical Fluids
#### 4.1.1 Solvent Selection--Efficiency  
Supercritical fluids provide advantages regarding mass transport between a solid and a solvent, which is crucial for extraction. High density increases the extraction yield, while low viscosity enhances penetration of the biomass matrix. However, along with temperature and pressure modulation, other properties of the solvent are changed, such as the dielectric constant and ionization coefficient. As a result, these changes affect the solvents' ability to dissolve various compounds. The SFE tannins extraction is mainly conducted with water, ethanol, methanol, and carbon dioxide, used as a co-solvent. As shown in Table 2, the dielectric constant determining the polar or non-polar nature of the solvating properties decreases when the conditions approach a critical point. The most widely used solvent for supercritical extraction of tannins, carbon dioxide (SC-CO\({}_{2}\)), is already non-polar under standard conditions. Its dielectric constant changes from 1.6 [73] to below 1.1 [74] under supercritical conditions. In the case of water, as the temperature increases, its dielectric constant decreases from a higher value of 78 [75] to only 5.35 [76]. This means that, at temperatures above 200 \({}^{\circ}\)C, the ability to extract hydrophobic compounds increases. Similar changes are observed for ethanol and methanol, the most frequently used solvents under standard pressure. SC-CO\({}_{2}\) is the most widely used method for extracting different biomass components in various studies [7; 83]. However, its nonpolar characteristics limit its ability to extract tannins, which are hydrophylic. Co-solvents like ethanol, methanol, or water are often used to enhance extraction, modifying the polarity of the supercritical fluid and improving tannin solubility. The high diffusivity and tunable solvating power of SC-CO\({}_{2}\) allow selective extraction of certain fractions of tannins. Depending on pressure and temperature settings, different molecular weight fractions of tannins may be extracted, leading to changes in composition. The extracted tannins often exhibit enhanced antioxidant activity due to the selective removal of lower-molecular-weight compounds while preserving bioactive polyphenols. SFE can alter the balance between hydrolyzable and condensed tannins in an extract, leading to different functional properties in food and pharmaceutical applications [84; 85]. Despite the low efficiency of SC-CO\({}_{2}\) in total tannin extraction, its application is justified by technical and economic factors. Due to its low critical parameters, the use of carbon dioxide as a co-solvent with polar solvents reduces the energy demand for the process [86]. As reported by [PERSON] et al., the extraction of jatoba bark (_Hymenaae courbari_ L.) yielded different results depending on the solvent system used. CO\({}_{2}\) alone and CO\({}_{2}\) with ethanol resulted in the lowest extraction yield (0.28% d.b. and 0.58% d.b.). Supercritical CO\({}_{2}\) with water as a co-solvent significantly outperformed the previous two examples (24% d.b.) [47]. Studies by [PERSON] and [PERSON] on _Phylanthus niruri_ showed similar effectiveness, depending on the solvents used. The yield was lowest with pure CO\({}_{2}\) (1.09%) and increased when ethanol (1.57%) or methanol (1.73%) were used as co-solvents. Still, the highest yield (19.83%) was achieved using 50% ethanol-water with CO\({}_{2}\) as an extraction mixture under supercritical conditions [87]. SFE of tannins from _Acacia mearnsii_ by [PERSON] and lob showed that supercritical CO\({}_{2}\) alone was ineffective, but the yield increased to 9.5% with ethanol and methanol mixtures [23]. The most effective co-solvent, yielding 25%