2.4. Preliminary Screening Study and RSM-Based Experimental Design

A preliminary screening study was carried out for determining the appropriate ranges of independent UAE process variables: ethanol concentration (X₁), sonication time (X₂), and leaf–solvent ratio (X₃) on the basis of a literature review [13,22,23]. X₁ was varied from 0 to 100% by keeping X₂ and X₃ fixed at 32 min and 0.23 g·mL⁻¹, respectively. Similarly, X₂ was changed within a range of 10–54 min, while both X₁ and X₃ were kept fixed at 50% and 0.23 g·mL⁻¹, respectively. Similarly, X₃ was varied from 0.148 to 0.313 g·mL⁻¹, while X₁ and X₂ were subjected to fixing at defined levels of 50% and 32 min, respectively. The preliminary experimental results that are shown in Figure 1 revealed increases in the response variables (Y₁: TEY, Y₂: ST yield, and Y₃: Reb-A yield) with corresponding rises in the input variables, and hence, were selected as the most influential parameters. All the UAE experimental runs were carried out in accordance with the specifications that were laid down by a 3–factor–5–level CCD. Moreover, all the independent process parameters were varied over 5 levels (−α, −1, 0, +1, +α) with the variables coding according to Equation (1):

Effect of X₁ (ethanol concentration) on TEY (%) target response, (a) the effect of X₁ (ethanol concentration) on ST and Reb-A yields (mg/g), (b) ST yield: sonication time effect on TEY (%) target response, (c) sonication time effect on ST and Reb-A yields (mg/g), (d) Leaf-to-solvent ratio effect on the TEY (%) response, (e) Leaf-to-solvent ratio effect on ST and Reb-A yields (mg/g) responses (f).

In Table 1, the description of the input UAE process variables with their particular experimental ranges is given, along with their units and coded notations (Equation (2))

where Y designates the target responses, whereas β₀ denotes the constant coefficient. β_i, β_ii, and β_ij are indicative of the regression coefficients pertaining to the UAE process variables corresponding to linear, quadratic, and interaction effects, respectively. The independent UAE process variables are presented by X_i and X_j, respectively, and ε depicts the error.

UAE process parameters with their particular experimental ranges and levels.