3.1. Material Plant
Aerial parts (leaves and flowers) of
Galphimia glauca Cav. (Malpighiaceae) were obtained from a controlled crop developed in the State of Morelos, Mexico. MSc Abigail Aguilar Contreras performed the identification of the plant, and a voucher sample (registration number IMSSM-11061) could be found at the Medicinal Herbarium of Mexico (IMSS, Mexico City, Mexico). The material and the procedure for preparing the sample were the same as used in previous works [
11,
12,
13]. Drying of the plant material was carried out by natural convection at room temperature and dark conditions for 14 days. Then, the dried material (leaves and flowers) was ground in an electric blender and was sieved in mesh strainers, obtaining several particle diameter fractions. Each interval (200–250, 250–425, 425–500, and 500–600 μm) consisted of 0.75 kg sample from plant material, and its particle diameter average was calculated according to ASAE S319.3 method [
44], obtaining the next values: 224, 326, 461, and 548 μm. The apparent and true density of each sample listed in
Table 5 was determined by a liquid displacement pycnometer [
45]. These samples of the raw material of
Galphimia glauca were stored at room temperature in sealed bags until SFE experiments.
3.3. Apparatus and Procedure
The experimental apparatus where extractions were carried out was based on the continuous method. The schematic diagram of the home-made apparatus is depicted in
Figure 6.
It was mainly constituted of the carbon dioxide supply tank (1) with a dip tube, a dual-piston pump (2, model SFT-10, SFT Inc., Newark, DE, USA) with an internal Peltier chiller, an electrical coil heating tape as preheater (3), a stainless steel extraction vessel (4, model TOC7-10-GP, HiP Co., Erie, PA, USA), which is thermally controlled, a thermometer (5, model F200, ASL, Redhill, UK) coupled to a calibrated platinum resistance thermometer (100–Ω, Thermo-Est, Maizières-les-Metz, France) with an expanded uncertainty of 0.04 K, a digital manometer (6, model XP2i, Crystal pressure, San Luis Obispo, CA, USA) calibrated with an expanded uncertainty of 0.008 MPa, two refrigerated circulating baths (7,8, model PD07R, Polyscience, Niles, IL, USA), a back pressure regulator (9, model 26-1700, Tescom, St. Louis, MO, USA) to control pressure in the extractor, two U-shaped tubes arranged in series (10) immersed in a heat exchanger, and a wet gas meter (11, model WNK0.5A, Shinagawa, Tokyo, Japan). The tubular extraction vessel had an internal diameter of 2.54 cm and a length of 25.4 cm and was coiled by silicone rubber tubing connected to the liquid bath. It was internally equipped with two stainless steel filters of 5 and 2 μm screwed in the top and bottom flanges, respectively. The upper flange had a well that held the thermometer. All supercritical extraction experiments were carried out in dynamic mode and downward flow. The preparation of the SFE for each experiment started with the loading of 20 g of Galphimia glauca as raw material inside the extractor; then, it was filled with a layer of glass spheres (3 mm of diameter). These packed spheres and the upper filter promoted a homogeneous solvent dispersion and the mass transfer. In the beginning, the desired temperature was fixed in the preheater and the extractor, and the temperature for the last device was controlled by the refrigerated circulating bath. Besides, the temperature of the U-shaped tubes was set to 273.15 K. The thermal control in all devices was monitored up to stable conditions.
Afterward, liquid carbon dioxide was pumped from the supply tank to the top of the extractor vessel. Carbon dioxide temperature was higher than its critical temperature in the preheater located before the extractor vessel. Meanwhile, the supercritical solvent filled the extractor vessel, and the pressure was attained by the back pressure regulator, which acted as a restrictor. The extraction process was considered to begin when the desired supercritical conditions were reached.
Once the back pressure regulator was controlling pressure, the supercritical fluid flowed downwards to leave the extractor. The outer filter prevented dragging out solid particles from the fluid phase. Then, this fluid was suddenly expanded at the outlet of the back pressure regulator and allowed phase separation. In consequence, solids were precipitated in the U-shaped glass submerged in the cold container. Carbon dioxide continued flowing to the wet gas meter in order to quantify the gas volume. It was measured by considering temperature and pressure from room conditions. The mass of the extract was determined gravimetrically in an electronic balance (12, EP 520A, Precisa Gravimetrics AG, Dietikon, Switzerland).
Conversion from volumetric (flow rate and total volume) to mass units for carbon dioxide was performed using the Equation of State published by Span and Wagner [
46]. The mass of the extract at each time was registered and added to the previous measurement, in order to obtain cumulative extract mass. Each tube was washed with methanol and placed in a single flask to analyze the total extract on the SFE condition. Samples were stored in sealed vials and kept cooled until further analysis. Every experiment was stopped when there was no significant variation of mass between each register. Most of the experiments took an extraction time of 240 min, with a range from 90 to 390 min.
3.4. Analyses
Quantification of galphimine B was performed by means of HPLC chromatography (model series 200, Perkin Elmer, Waltham, MA, USA), based on previous studies [
9]. The methanolic solutions previously filtered were injected throughout a 20 μL sampling loop. A gradient of acetonitrile:water (A:W) as a mobile phase was used for the separation of components at a constant flow rate of 0.9 mL/min in a Spheri-5 RP-18 5 μm column 250 × 4.6 mm equipped with a guard column with the same stationary phase. A volume ratio of 40:60 was fixed for the first 10 min, the ratio was changed to 52:48 after 1 min and kept for 4 min; then, it was changed to 70:30 at 16 min, 88:12 at 17 min, and 94:6 at 18 min maintained for 2 min; 100% acetonitrile was reached at 22 min and kept for 1 min. Finally, a ratio of 40:60 was fixed at 25 min, and the analysis was stopped at 35 min. The absorbance of galphimine B was set to 230 nm in the UV-Vis detector.
A purified extract of galphimines with the known composition of galphimine B (G-B) was used as a standard for the detector calibration, which was obtained with the procedure described by Romero-Cerecero et al. [
11]. This standard is constituted mainly by galphimines B and E, and the concentration of galphimine B is 0.2 mg·g
−1. From this standard, the unknown composition of galphimine E was also reported as a relative area. A calibration curve with galphimine B was attained using concentrations of 1, 5, 10, 15, 20, 25, 30, 35 μg G-B/mL methanol. Results were adjusted to a linear function:
CG-B = 42.3341
AUG-B – 0.6819, where
CG-B is the concentration of G-B in μg/mL, and
AUG-B is the response area of G-B. In the case of galphimine E, the quantification was limited to as the percentage of the relative area between galphimine E and galphimine B.
3.5. Mathematical Modeling
Modeling of supercritical fluid extraction curves was achieved based on models developed with mass balances in the fluid and solid phases, reported elsewhere [
24,
26]. One of the most applied models is the one proposed by Sovová, which was developed originally for representing the extraction of oils from milled seeds by rejecting the interactions between the solid and fluid phases. This model is expressed in Equation (1) [
47] as follows:
where the dimensionless variables
G,
Z,
Y,
Ψ,
Ψk, and
hk are defined by the next expressions:
G = 1 –
xk/
x0,
Z =
Nkfaρf/
Q(1 –
ε)
ρs,
Y =
Nksax0/
Q(1 –
ε)
yr,
Ψ =
tQyr/
Nx0,
Ψk =
G/
Z + (1/
Y) ln{1 –
G [1 – exp(
Y)]}, and
hk = (1/
Y) ln[1 + {exp[
Y(
Ψ –
G/
Z)] – 1}/
G]. The above expressions include additional variables, which comprise physical meaning.
E is referred to the mass of extracted solute,
N denotes the mass of the solid material,
x0 corresponds to the initial concentration of solute in the solid phase,
xk represents the interface concentration of solute,
t symbolizes the extraction time,
Q indicates the mass flow rate of the supercritical fluid,
ε expresses the bed porosity,
a is the interfacial area,
ρf represents the supercritical fluid density,
ρs is referred to the solid density,
kf describes the external mass transfer coefficient, which is optimized together with the interfacial area
a as the product
kfa,
ks denotes the internal mass transfer coefficient, and
yr corresponds to the solute solubility in the supercritical fluid as apparent parameter in multicomponent matrixes, which actually is the apparent solubility, as it was not experimentally determined. Apparent solubility was obtained on each experimental condition as the slope of a plot of the cumulative mass of extract versus the mass of CO
2 spent per mass of material charged in the extractor.
The model of Sovová is adequate for modeling the supercritical fluid extraction of vegetable oils that commonly produces high yields (
e > 10%). To the best of our knowledge on applications with low yields, the mass transfer equilibrium is usually controlled by the specific interactions between the solute (solid phase) and the supercritical solvent (fluid phase). This is the case for the results obtained in this work since the highest yield was reported to be less than 2.22%. Therefore, the approach proposed by Papamichail et al. [
20] was also applied. A remarkable characteristic of this model is the consideration of those specific interactions between the solute and solvent. The expressions for this model are summarized as follows:
where
e corresponds to the extraction yield,
y0 denotes the solute solubility in the supercritical fluid similar to
yr from Equation (1),
A is a variable that comprises the overall mass transfer coefficient in the fluid phase (
kfa) and is defined as
kfaρf/
ρs(1–
ε), and
B is quantified by
A/(
Q̇ +
A).
Q̇ is expressed as the specific mass flow rate of the supercritical fluid estimated with the
Q/
N ratio. These additional definitions can state that
A is equivalent to the product
ZQ̇, as well as
̅x is also equivalent to
xk reported in the equations proposed by Papamichail et al. and Sovová, in that order.
The model proposed by Papamichail et al. in Equation (2) states that the extraction is controlled by two stages, each one dominated by solubility and diffusion mechanisms. The first expression for yield is applied when
x ≥
̅x and indicates that the extraction is under the solubility controlled regime, while the second expression is utilized when
x <
̅x and signifies that the process is subjected to a diffusion-controlled regime. The boundary for each regime is given by either the solute concentration in the solid phase
̅x or the time
̅t. This latter variable is defined as (
x0 –
̅x)/[(
y0A(1 –
B)]. Moreover,
K is the equilibrium constant in Equation (3) that was considered from Perrut et al. [
48]:
Sovová defines Ψk as the dimensionless time that is the boundary between the easy and difficult extraction stages. Then, the time of the boundary tk can be obtained from Ψk. A comparable assumption with tk for the Papamichail et al. model is that ̅t has the equivalent meaning. In the same way, the grinding efficiency G is equivalent to 1 – ̅x/x0.
Parameters for both models were obtained by minimizing the objective function based on the yield in Equation (4):
The absolute average relative deviation (
AARD) was calculated with Equation (5):
In Equations (4) and (5), n denotes the number of data points, and ei refers to the yield for each experiment. Superscripts exp and calc correspond to the experimental and calculated data points, respectively.