Modern Techniques for Flavonoid Extraction—To Optimize or Not to Optimize?

Abstract

Flavonoids, specialized metabolites found in plants, have a number of beneficial properties and are important for maintaining good health. Efficient extraction methods are required to extract the most bioactive compounds from plant material. Modern techniques are replacing conventional methods of flavonoids extraction in order to reduce energy and solvent consumption, increase extraction efficiency, and satisfy growing market demand as well as environmental legislation. The extraction of bioactive molecules compounds is affected by a number of variables. To determine the conditions that ensure the highest extraction yield, it is advisable to analyze the interactions between the above in parallel. In this work, an overview of the advantages and performance of modern methods (microwave-assisted extraction, ultrasound-assisted extraction, pressurized liquids-assisted extraction, and supercritical fluids extraction) for the extraction of flavonoids is presented. This work also presents the application of extraction process optimization and extraction kinetics for flavonoid extraction, using different types of experimental designs for different flavonoid sources and different extraction methods. The general conclusion of all the studies listed is that an experimental design combined with RSM modeling reduces the number of experiments that should be performed to achieve maximum extraction yield.

1. Introduction

Plants produce a wide range of different specialized metabolites, traditionally referred to as ‘secondary metabolites’. These are chemical compounds involved in numerous biological functions within plants, including plant responses to abiotic and biotic stresses [1]. The best-studied group of specialized plant metabolites to date are the flavonoids, which include over 6000 molecules with diverse structures [2]. Mouradov and Spangenberg [3] summarize that flavonoids in plants function, among other things, as protection against insect feeding and defense against microbes, as sunscreens to absorb UV radiation and strong light, to attract insect pollinators, as antioxidants, for pollen germination, for biological communication in the rhizosphere, and as developmental regulators involved in auxin transport and catabolism. They have been the focus of scientific attention for the past 30 years, mainly due to numerous scientific findings on their beneficial effects on human health due to their antioxidant, antimicrobial, anticancer, neuroprotective, cardioprotective, and anti-inflammatory properties [4,5,6]. They are used in the food industry as natural antioxidants or colorants. Flavonoids have a 15-carbon flavone backbone, C6-C3-C6 (Figure 1), with two benzene rings (A and B) connected by a trinuclear pyran ring (C). The position of the B catechol ring on the C pyran ring, as well as the number and position of the hydroxyl groups on the catechol group of the B ring, have a major influence on the chemical properties and biological activity of flavonoids [7].

Due to their important role in plants and their numerous health benefits, much attention has been paid for years to the development of the most effective methods for their extraction and characterization [8]. The most commonly used methods for characterization and quantification of known flavonoids are high performance liquid chromatography (HPLC) coupled with DAD/PDA detectors or mass spectrometry (MS). For the elucidation of unknown structures, multistep MS or NMR can be used. Gas chromatography (GC) is rarely used because it requires derivatization before analysis and derivatization is a time-consuming process involving hazardous reagents/solvents, sometimes under extreme temperature and pressure conditions [9]. Recently, the MALDI imaging method has also enabled the identification of flavonoids in situ in the tissue under study without extraction [10], but this method is not widely used due to its high cost. For the correct identification and further use of flavonoids, the crucial step is the extraction of flavonoids. Effective extraction techniques are necessary to extract the largest amount of bioactive chemicals from plant material [11,12]. To minimize energy and solvent consumption, increase extraction efficiency, and meet increasing market demand and environmental regulations, modern techniques (such as microwaves, ultrasound, pressurized fluids, and supercritical fluids) are replacing traditional flavonoid extraction methods [13,14]. Numerous factors such as solvent selection, temperature, contact time, liquid-to-solid ratio, particle size, and pH affect the extraction of bioactive molecular compounds [15]. In order to define the process conditions that ensure maximum extraction yield, it is recommended to simultaneously analyze the interaction between the listed factors. Therefore, mathematical and statistical tools such as response surface methodology (RSM) and artificial neural networks (ANN) are often used to study the effects of different factors and their interactions on extraction efficiency [16,17,18]. Although reaction surface models are commonly used to explain how process variables affect extraction efficiency, these models do not always provide data that support mass transfer and the dynamics of the extraction process, so the use of kinetic models is required to understand the extraction process [19,20,21]. Mathematical modeling is required to evaluate extraction kinetics and ensure the maximum product reproducibility [11,15].

Based on the above, this paper reviews the advantages and performance of modern methods (microwave-assisted extraction, ultrasound-assisted extraction, pressurized liquid-assisted extraction, and supercritical fluid extraction) for flavonoid extraction with the emphasis on the use of new approaches such as the use of deep eutectic solvents as environmentally friendly solvents. In addition, the application of extraction process optimization and extraction kinetics to improve the efficiency of the extraction process was also reviewed.

2. Flavonoids Classification and Sources

Flavonoids are a diverse group of specialized metabolites derived from the general structure of a 15-carbon skeleton (Figure 1). Based on their structure, which can be distinguished by the pattern of the central heterocyclic pyran ring of the flavan core structure, flavonoids can be divided into six groups: Flavones, flavonols, flavan-3-ols, flavanonols, flavanones, isoflavones, and anthocyanins (

Table 1. The structure and examples of flavonoids from different groups.

Flavones	Flavonols	Flavan-3-ols
apigenin luteolin acacetin	kaempferol myricetin quercetin fisetin	cathechin epicatechin epigallocatechin
Flavanone	Isoflavones	Anthocyanins
hesperetine naringenin	genistein daidzein glycitein	cyanidin, delphinidin, malvidin, pelargonidin, peonidin, and petunidin

).

Flavonoids can occur in free form in plants, but are more commonly glycosylated, methylated, acetylated, prenylated, or polymerized [22]. Most commonly, flavonoid glycosides, O-glycosides, and, less commonly, C-glycosides are identified with a single oligosaccharide or, in some cases, a polysaccharide unit [23]. Glycosidation improves solubility, biodistribution, and metabolism by increasing transport across cell membranes [24]. Methylated flavonoids are rarer than free forms or flavonoid glycosides, and common types of methylation include C-methylation and O-methylation, which enhance flavonoid entry into cells and prevent degradation [22]. Some plants accumulate biflavonoids, flavonoid dimers consisting of two monoflavonoids through a direct link or a linear linker [25,26], or even flavonoid trimers or tetramers [27].

Flavonoids are distributed throughout the plant body, but the quality and quantity of specific flavonoids vary widely among different plants, plant organs, and even the same plants grown under different environmental conditions [28]. In general, the occurrence and amount of flavonoids in some plant samples are influenced by genetic and environmental factors, and some flavonoids may be specific to a particular plant genus, species, or even cultivar. Some examples of flavonoids detected in various plant samples are presented in

Table 2. Examples of flavonoids molecules characterized in plant material extracts.

Source	Flavonoids Group	Characterized Molecules	Extraction Method
cocoa shell [29]	flavanols	(+)-catechin, (−)-epicatechin, procyanidine	pressurized liquid extraction
wine grape [30]	flavanols	(+)-catechin, (−)-epicatechin, (−)-epigallocatechin	ultrasound-assisted extraction
tea leaves [31]	flavanols	19 molecules including epigallocatechin gallate, epigallocatechin, epicatechin gallate, epicatechin, and their corresponding stereoisomers	conventional extraction
	flavonols	19 molecules with kaempferol, quercetin, and myricetin aglycones
peach fruit [32]	anthocyanins	cyanidin-3-O-glucoside cyanidin-3-O-rutinoside	ultrasound-assisted extraction
	flavanols	catechin, epicatechin procyanidin B1
	flavonols	rutin, quercetin–3–O–galactoside, quercetin–3–O–glucoside
Astragalus membranaceus plant [33]	flavonols	isoquercitrin, astragalin	ultrasound-assisted extraction
orange peel [34]	flavanones	hesperidin, nariruti	supercritical water extraction
citrus pomace [35]	flavanones	naringin, hesperidin	enzyme-assisted extraction
dried flowers of Trollius chinensis Bunge [36]	flavones	orientin, vitexin and 2″-O-galactopyranosylorientin	natural deep eutectic solvents extraction
Trichosanthes kirilowii Maxim [37]	flavones	isoquercitrin, rutin, quercetin, luteoloside, luteolin, tangeretin, apigenin, apigenin-7-O-glucuronide, kaempferol, kaempferide	ultrasound-assisted extraction
Aronia melanocarpa [38]	anthocyanins	delphinidin, cyanidin, petunidin, pelargonidin, peonidin, and malvidin	ultrasonic-microwave-assisted natural deep eutectic solvent extraction
Polypodium vulgare L. [39]	flavanols	(+)-catechin-7-O-α-L-arabinoside, (+)-catechin-7-O-β-D -apioside	conventional extraction
apple samples [40]	flavanols	(+)-catechin, (−)-epicatechin, procyanidin B1, procyanidin B2, procyanidin C1	ultrasound-assisted extraction

.

In recent years, modern analytical techniques have become available and some flavonoids that occur at lower concentrations can now be more easily detected. In addition, new extraction methods have also been optimized to achieve the most efficient extraction.

3. Sample Preparation and Hydrolysis

Generally, flavonoids are isolated from plant tissues, from the food matrix, or from liquid samples (biological fluids or beverages). For some liquid samples, it is sufficient to centrifuge and filter them before analysis, but for some matrices the whole process is much more complex. Flavonoids can be isolated from fresh plant material, but in this case the samples should be kept at low temperature and the extraction should start soon after harvest to prevent enzymatic or chemical degradation and to modify the particles of the plant material to contribute to the release of bioactive compounds loosely bound to the cell wall polymers [41].

Many different methods can be employed in sample preparation (Figure 2) but nowadays, plant material is most commonly dried by freeze-drying, convection drying, or microwave vacuum drying (

Table 3. Literature reports on the influence of drying methods on flavonoid content.

Sources	Drying Methods	Results
green tea (Camellia sinensis) leaves [42]	sun, shade, oven 60 °C, 80 °C and 100 °C, microwave and freeze-drying	the highest total flavonoid content was obtained in oven drying at 60 °C and 100 °C
lemons (Citrus limon)	freeze-drying and air-drying [43]	freeze-drying provides extracts with higher amounts of flavonoids
	freeze-drying and air-drying [44]	freeze-drying is more suitable for extraction of flavanones or flavones; while air-drying was the best for flavanols
Dryopteris erythrosora leaves [45]	shade one day then oven-dried at 75 °C for 48 h, dried in the sun, then oven-dried at 75 °C for 48 h, oven-dried at 75 °C for 48 h	the highest flavonoids yield was from first drying the plant material in the shade and then completing the drying process in an oven at 75 °C
birch leaves [46]	air-drying at ambient temperature, oven-drying at 40 °C and 80 °C, freeze-drying–prefreezing with liquid N2, freeze-drying–prefreezing at −18 °C, freeze-drying without prefreezing, storing frozen for 12 days without drying, and immediate extraction of fresh samples	freeze-drying of leaves frozen at −18 °C is preferred as a drying method
orange peel [47]	fresh, oven-dried and freeze-dried peel	freeze-drying preserves the concentration of the flavonoids, while oven-dried peel presented a decrease of glycosylated flavonoids and an increase of aglycone forms
Helicteres hirsuta Lour. Leaves [48]	hot-air drying, low-temperature-air drying, infrared drying and vacuum drying	the leaves dried under either hot-air drying at 80 °C, or vacuum drying at 50 °C yielded the highest amount of total flavonoid content
blueberry, cherry, cranberry and strawberry [49]	hot-air drying, freeze-drying and refractance window-drying	higher levels of flavonoids were found in all the freeze-dried samples except strawberry
Sage (Salvia officinalis L.) [50]	air-drying at shade and ambient 22 °C, drying in a hot air oven with natural convection at 45 °C and 65 °C, drying in a microwave oven at 600 W/30 g and 800 W/30 g of fresh plant; drying in an infrared moisture analyzer at 45 °C and 65 °C.	the highest total flavonoid content was determinate in the air-dried plants
Cosmos caudatus [51]	air-, oven- and freeze-drying	the freeze-drying and air drying were the best methods for flavonoids
Allium cepa red cv. and A. sativum [52]	microwave, air-drying, or freeze-drying	microwave and freeze-dried samples show similar profile
Stevia rebaudiana leaves [53]	hot air-drying, freeze-drying and shade-drying	the majority of the compounds analyzed reached their maximum values with the freeze-drying method

). As is evident from Table 3, most studies reported that freeze-drying is the preferred method for pretreatment of samples to obtain most of the flavonoids.

After drying, the samples are usually ground to a fine powder. This can be done manually with a mortar and pestle or by grinding over a long period of time. For example, Rajha et al. [54] studied the effect of particle size on the extraction of flavonoids from grape by-products and reported that the highest amount was obtained with a grinding time of 6.8 min and a solid–liquid ratio of 3 mL/g. The solid–liquid ratio is also an important parameter and depends on the plant tissue and the content of specific flavonoids we want to detect. Sometimes, the use of an excessive amount of the samples can lead to the extraction of other compounds present in the samples, which can lead to a “matrix effect” during the analysis, caused by the change in ionization efficiency of the target analyses in the presence of co-eluting compounds in the same matrix. In this case, the flavonoids of interest are difficult to detect. On the other hand, the flavonoids of interest are below the detection limit if we use too small a sample amount. Therefore, this parameter also needs to be optimized. For example, for the determination of total flavonoid content in shoots of Brassicaceae, 30 mg of dehydrated samples per 1 mL of 80% methanol was used [55], while for fresh strawberries, using the same extraction solvent, 1 g per 10 mL of solvent was used [56]. Today, often deep eutectic solvents have been used for flavonoid extraction. For the extraction of flavonoids from wolfberries, 20:1 mg/mL [57] and for buckwheat sprouts, 100:1 mg/mL [58] of the ratio of extracted samples to solvent was used.

Flavonoids are present in complex forms in matrices, and hydrolysis has often been used to remove sugar units from glycosides. Hydrolysis can be acidic, basic, or enzymatic [59]. For example, Nuutila et al. [60] obtained the best results by refluxing at 80 °C for 2 h with 1.2 M HCl in 50% aqueous methanol with the addition of 2 mg ascorbic acid as an antioxidant. Balli et al. [61] compared basic (1 g defatted flour was suspended in 25 mL MeOH:H₂O 7:3 v/v (0.1 M NaOH); the solution was sonicated at 60 °C for 1 h, then CH₃COOH was added until the pH was 6.5–7.0) and acid hydrolysis (1 g defatted flour was extracted with 25 mL MeOH:H2SO4 9:1 v/v; the solution was sonicated at 60° C for 2 h) were used for the extraction of total flavonoids from millet and reported that acid hydrolysis was able to extract the highest amount of total phenolic compounds, while basic hydrolysis underestimated the phenolic concentration. Sometimes enzymatic processes and fermentation are also used [41] before extraction to improve the extraction efficiency. Enzymatic hydrolysis prior to extraction can boost extraction efficiency by improving solvent dispersion, mass transfer, particle size reduction, and contact area [62]. Krakowska et al. [63] and Krakowska-Sieprawska, et al. [41] studied the potential of enzyme-assisted supercritical extraction of phenolic from Medicago sativa leaves. The degradation of the plant material was enhanced using commercially available multi enzyme preparation containing five different enzymes: xylanase, beta-glucanase, cellulase, amylase and protease. The results showed that the extraction yield was about twice as high when enzymatic hydrolysis was performed before extraction. Of course, the choice of the right hydrolysis technique depends on the experimental design and the desire to detect the flavonoids we are interested in.

After the sample has been prepared and stored appropriately, various liquid–liquid or solid–liquid extractions can be used to extract flavonoids. The most commonly used method is extraction by solvents (methanol, ethanol, acetone, water, etc.). Unfortunately, this method consumes large amounts of solvents, is time consuming, and can result in low extraction efficiency. For this reason, new technologies, new solvents, and new approaches are constantly being sought to eliminate some of the aforementioned drawbacks of the so-called traditional methods. Some of the new approaches are the application of so-called green technologies such as:

• ultrasound-assisted extraction (UAE)
• enzyme-assisted extraction (EAE)
• microwave-assisted extraction (MAE)
• pulsed electric field-assisted extraction (PEFAE)
• supercritical fluid extraction (SFE)
• liquid extraction under pressure (PLE)
• ohmic heater-assisted extraction (OHAE)

Each type of method has a specific scope depending on the target molecules to be extracted or on the plant material. The most commonly used methods for flavonoid extraction are UAE, MAE, SFE and PLE. Although these methods are described as safe, efficient, suitable for extraction of sensitive compounds, short, etc., they must be carefully selected based on the sample and target compounds, as mentioned earlier. The selection of a suitable method still does not guarantee maximum extraction efficiency, so the selected methods usually need to be optimized. In general, all extraction techniques require optimization of variables such as particle size, solvent for extraction, temperature, time and sample-to-solvent ratio (Figure 3), and these variables should be the starting point for optimization of the extraction protocol.

The selection of the other variables that should be optimized depends strongly on the extraction technique. Some of them are discussed in this article depending on the chosen extraction technique.

4. Selection of Variables for the Optimization of Modern Techniques for Flavonoids Extraction

4.1. Ultrasound Assisted Extraction

As described by Yusoff et al. [64] ultrasound-assisted extraction (UAE) is considered an environmentally friendly extraction technique due to its high productivity with minimal solvent and time consumption and its suitability for molecules with high thermal sensitivity (Figure 4a). The frequency of ultrasound ranges from 20 kHz to 100 kHz, and high powers (10–1000 W/cm) can be generated, sufficient to break intermolecular bonds. When the energy is higher than 10 W/cm, a cavitation effect (growth and collapse of bubbles) occurs. When the bubble collapses near the cell wall, it generates high temperature (up to 5000 K) and high pressure (up to 100 ATM), allowing the solvent to penetrate the cell, resulting in enhanced mass transfer. In addition to mass transfer, high pressure and temperature can rupture the cell wall and cell membranes and reduce the particle size, releasing the intracellular material and promoting the extraction process [62,63,64]. Optimization of UAE extraction should include selection of the proper solvent, particle size, temperature, time and solvent-to-solid ratio, as in traditional methods, but also optimization of ultrasound parameters (power and frequency) [65,66] (Figure 4b).

Liao et al. [67] analyzed the effect of the ethanol concentration, particle size, solvent-to-solid ratio, temperature, ultrasonic power and ultrasonic frequency on the extraction of flavonoids from peanut shells and showed that usage of ultrasound reduces the extraction process from 280 to 80 min in the case of Soxhlet extraction. Similarly, Zimare et al. [68] studied the effect of methanol ratio, temperature and extraction time on the total flavonoid content of Lobelia nicatianifolia leaves and showed that plant tissues were extensively ruptured during ultrasonication and that UAE significantly increased the antioxidant capacity of the extracts. Garcia-Castello et al. [69] compared the efficiency of conventional solid–liquid extraction and UAE for flavonoids extraction from grapefruit peels and showed that UAE was more than 50% more efficient regarding the bioactives extraction yield, while Meregalli et al. [70] compared conventional extraction and UAE for the extraction of bioactive red Araçá fruit (Psidium cattleainum Sabine) and presented approximately 6% higher flavonoids extraction yield when using UAE. Irakli et al. [71] explored how to increase the yield of oleuropein, hydroxytyrosol, flavonoids and phenolic acids extracted from olive leaves in order to reduce operational expenses with the potential for using reduced solvent amount, shorter extraction periods, and reduced extraction temperatures. They showed that UAE with acetone as the extraction solvent can be efficiently used to produce olive leaves extracts that are rich in bioactive compounds. Moreover, Wang et al. [72] proposed a negative pressure cavitation-based ultrasound-assisted extraction (NPC-UAE) for the efficient extraction of six flavonoids from the flower buds of Sophora japonica L. using ethanol as the extraction solvent and showed that the combination of the two extraction methods resulted in better extraction yields compared to the UAE method, while Saeed et al. [73] coupled enzyme-assisted extraction with the UAE method to improve the extraction efficiency of bioactive compounds from Gymnema sylvestre. The proposed extraction method was found to be three times more efficient than the conventional maceration performed as a control. During ultrasound-assisted solvent enzymatic extraction (UAE-EAE) ultrasonic waves promote enzymatic extraction by cracking cell walls to allow for enzyme-aided reactions and the subsequent release of desired components [74,75]. Wani et al. [76] compared the extraction efficiency of hot water extraction and the pulsed ultrasound-assisted extraction (PUSAE). Based on the extraction yield of total flavonoids, total phenols, antioxidant activity, and vitamin C from papaya pulp and peel they showed higher performance of PUSAE.

4.2. Microwave-Assisted Extraction

In microwave-assisted extraction (MAE) (Figure 5a), microwaves are used to heat the matrix [77]. Their frequency ranges from 300 MHz to 300 GHz. Magnetic and electric fields in microwaves are perpendicular to one another. The electric field causes heating by ionic conduction and dipole rotation [78]. Depending on their dielectric characteristics, the components absorb microwave radiation. The radiation promotes cell rupture, allowing liquid to penetrate through the plant matrix. On the other hand, plant material enters the solution from outside the cells [79]. According to Bagade et al. [80], the efficiency of microwave-assisted extraction is affected by: (i) solvent nature and volume, (ii) extraction time, (iii) microwave power, (iv) operating temperature and (v) properties of the matrix, and all listed factors must be taken into account during process optimization (Figure 5b).

Abbas et al. [81] compared the efficiency of microwave-assisted extraction, ultrasound-assisted extraction and Soxhlet extraction using ethyl acetate as solvent for the extraction of bioactive compounds from Lagenaria siceraria and showed that MAE was the most efficient method for the extraction of flavonoids (24.28 mg/g), while Plazzotta et al. [82] showed that MEA was more efficient than UAE for flavonoids from peach waste. Similarly, Ling et al. [64] compared maceration, ultrasonic- and microwave-assisted extraction for total phenolic content and total flavonoid content of Cassia alata. Their results showed that microwave MAE has the highest TPC and TFC yield (37.92 mg/g DW, 135.18 mg/g DW), followed by ultrasonic-assisted extraction and maceration extraction. Moreover, Elakremi et al. [83] compared the conventional maceration and MAE extraction yield of polyphenols and flavonides from Pistacia vera L. leaves (male and female), Alara et al. [84] compared the conventional maceration and MAE extraction yield for extraction of flavonoids from the Vernonia amygdalina leaf, and Dahmoune et al. [85] studied UAE and MAE for extraction of flavonoids from Myrtus communis L. In all the experiments described, MAE was the preferred method for obtaining the highest extraction yield of flavonoids. Similarly, Darvishzadeh and Orsat [86] presented MAE as the best method for the extraction of three flavonoids with therapeutic properties including isorhamnetin, luteolin and rutin from the leaves and flowers of the Russian olive. Akbari et al. [87] analyzed the most important factor affecting flavonoids extraction yields from fenugreek seeds and showed that ethanol concentration was the most significant and contributing factor for the MAE process. Pinela et al. [88] analyzed the effects of processing time, extraction temperature, ethanol concentration and solid-to-liquid ratio on the flavonoids recovery from tomato using MAE and their results showed that water was preferable as a solvent.

Furthermore, Xie et al. [89] coupled MAE and aqueous two-phase systems (ATPS) for the simultaneous extraction and determination of vitexin, isovitexin, orientin and isoorientin from Crotalaria sessiliflora L. They described that MAE with ethanol/ammonium sulfate ATPS ensures from two to five fold higher extraction yield of specific flavonoid when compared to a mono-phase solvent such as water and ethanol. On the other hand, Gu et al. [90] evaluated the applicability of the ten ionic liquids for MAE of flavonoids hesperidin, hyperoside and rutin from the leaves of Sorbus tianschanica and selected 1-hexyl-3-methylimidazolium tetrafluoborate as the extracting solvent, while Liu et al. [91] enhanced flavonoids extraction from Helichrysum arenarium by using 1.0 M [C 8mim]Bras as the solvent.

4.3. Pressurized Liquid Extraction

Since the dissolution rate, speed of mass transport, and extraction rate of bioactive molecules, as well as specimen wettability and permeability, enhance with temperature, accelerated solvent extraction (ASE), also known as pressurized liquid extraction (PLE) (Figure 6a), is undertaken statically by utilizing heat and pressure to the solvent system and specimens [92]. According to Soria et al. [93] PLE is based on conventional heating at high temperatures and up to 200 bar of pressure, where high pressure is applied to ensure the solvent is in a liquid condition while high temperature is used to make the analytes more soluble and enhance their extraction from the material (Figure 6b).

PLE technology is considered “green” extraction technology because of the decreased solvent usage (approximately 100–200 mL of solvent) and speeding up (extraction time approximately 20 min) of the extraction process [94,95] compared to traditional solid–liquid extraction techniques such as Soxhlet extraction [96]. Another practical advantage over the classic extraction method is that the extract does not need to be filtered after processing because the starting material remains in the extraction cell [97].

Quantitative extraction of various samples of environmental organic chemicals from soils and lipids, as well as the examination of food and biological samples, have all been conducted using PLE technology [98,99,100,101,102]. Regarding the flavonoids extraction, Kamali et al. [103] compared the extraction efficiency of percolation extraction PLE from Dracocephalum kotschy, Golmakami et al. [104] compared the extraction efficiency of percolation extraction PLE from the roots of Scutellaria pinnatifida, while Lama-Muñoz et al. [105] and Alves et al. [106] compared extraction with Soxhlet method and PLE for analysis of olive leaves bioactive molecules and extraction of bioactive compounds from Monteverdia aquifolia leaves, respectively. All the described studies showed extraction yield improvement when using PLE over classic extraction methods. Moreover, Corazza et al. [107] evaluated PLE extraction conditions (pressure 100–200 bar, flow rate 1–3 mL/min and time 0–60 min) using goldenberry as the extraction matrix and ethanol as the extraction solvent. They showed that the highest yield of bioactive compounds was obtained for 10 min of extraction and that the compounds were extracted at 100 bar and 200 bar regardless of the flow rate. On the other hand, Oliveira et al. [108] compared PLE and UAE for the extraction of bioactive compounds from industrial Tahiti limes (Citrus latifólia Tan.). While UAE was conducted with variable ultrasonic power (160–792 W), time (2–10 min), and solvent-to-feed mass ratio (20–40 kg solvent/kg dry pomace), PLE was carried out at various temperatures (60–110 °C) and time periods (5–40 min). In the case of PLE, the highest temperature (110 °C) produced the best results for the overall yield and total phenolic, with the exception of flavonoids (hesperidin and narirutin), which were not significantly affected by temperature. Both methods used ethanol and water (3:1, wt.) as the solvent. Recently, researchers have focused on combining the UAE and PLE into ultrasound-assisted pressurized liquid extraction (UAPLE) to improve the mass transfer rate and thus increase the extraction yield [100,109,110].

As described by da Silva et al. [97], PLE is unable to discriminate between compounds from related phenolic classes. The resulting extracts consist of a variety of compounds and therefore it is necessary to couple extraction and separation methods to obtain the target molecule. For this reason, Qian et al. [111] developed rapid pressurized liquid extraction and high-performance liquid chromatography coupled with diode array detection and mass spectrometry (HPLC-DAD–MS) for the simultaneous determination of a flavonoid (panasenoside), nine saponins (ginsenoside Rg1, Re, Rf, Rg2, Rb1, Rc, Rb2, Rb3 and Rd) and two polyacetylenes (panaxydol and panaxynol) in Folium Ginseng and Radix Ginseng. Similarly, Chaves et al. [112], Souza et al. [113] and da Silva et al. [97] combined PLE and in-line solid phase extraction to extract and concentrate phenolic molecules from lemon peel, mate (Ilex paraguariensis) leaves and apples, respectively. Their results showed that the new approach not only allowed fractionation of the compounds, but also gave equivalent or higher yields of all chemical classes compared to previous methods such as pressured liquid extraction alone, stirring, maceration, and ultrasound-assisted extraction.

4.4. Supercritical Fluids Extraction

Supercritical fluids extraction (SFE, Figure 7a) is categorized as a new extraction process that is a more ecologically friendly way to create native compounds that have uses in many different sectors, from sustainable sources including herbs, spices, aromatic, and medicinal plants [114,115]. This method uses supercritical fluids to isolate and remove certain bioactive molecules [116,117,118].

Chemical solvents known as supercritical fluids may be pressed exceeding their critical point, are often regarded as ecologically safe, and are frequently utilized in the extraction procedure because of their great performance and distinctive properties [119]. Many substances, including ammonia, ethane, ethane, fluoroform, nitrous oxide, propane, water, xenon and carbon dioxide can be used as supercritical fluids (SCF) [120]. Unquestionably, carbon dioxide is the one that is used the most frequently, because it is inexpensive, eco-friendly, and GRAS (generally acknowledged as safe) [121]. Furthermore, CO₂ is gaseous at normal temperature and pressure, making extract recovery relatively straightforward and enabling the production of extracts without the need of solvents [122]. The ability of SFE employing CO₂ to be operated at low temperatures using a non-oxidant medium, which permits the extraction of thermally labile or readily oxidized chemicals, is also crucial for the extraction of food and natural products [123]. The limiting of the target compound and the inability to extract polar molecules is a SC-drawback, so in order to improve and aid in the polarity of SC-CO₂, ethanol must be added to the extraction system [124]. The limiting of the target compound and inability to extract polar molecules is SC-drawback. Ethanol can enhance SC-CO₂ mass-transfer and diffusivity [125].

Temperature, pressure, supercritical CO₂ flow, the presence of a modifier, and extraction time are the main variables that influence the SC-CO₂ extraction technique’s effectiveness expressed as selectivity, yield, and/or extraction rate [126,127] (Figure 7b). So, the impact of the important SC-CO₂ extraction parameters must be studied in order to enhance extraction yield [128]. According to Melloul et al. [129], with the introduction of supercritical carbon dioxide extraction, a wide variety of plant sources now serve as a significant source of bioactive chemicals with intriguing uses in complex sectors including food, pharmaceutical, and cosmetics. For example, Martínez-Ávila et al. [130] applied supercritical CO₂ for the selective extraction of bioactive phytochemicals from black beans (Phaseolus vulgaris L.), Melloul et al. [129] for extraction of bioactive compounds from Peganum harmala plant seeds, while De Aguiar et al. [131] used pure supercritical CO₂ and supercritical CO₂ with modifiers for bioactive compounds extraction from Capsicium peppers.

Song et al. [132] and Yang et al. [133] showed that the SFE-CO₂ extraction ensured a considerable increase in flavonoid production, antioxidant activity, and antiproliferative activity of the extracts compared with conventional Soxhlet extraction and ultrasound-assisted extraction when Xinjiang jujube leaves and Puerariae lobatae root, Pinus massoniana needle, Citrus reticulata peel and their mixture were used. Similar results were in the study by Milovanovic et al. [134] where flavonoids-rich extract (TF = 208.6–564.5 µg/g) of dandelion seeds was prepared by SFE-CO₂ extraction at temperatures of 40 and 60 °C and pressures of 100 to 450 bar and in the study by de Souza Correa et al. [135], in which a rutin-rich extract from blackberry seeds was prepared at 70 °C and 25 MPa using ethanol as co-solvent. In the extract prepped by Song et al. [132], the authors detected eight flavonoids in the prepared extracts, namely quercetin 3-O-robinobioside, rutin, hyperoside (quercetin-3-O-D-galactoside), quercetin-3-O-D-glucoside, kaempferol-3-O-robinobioside, kaempferol-3-O-glucoside, quercetin-3-O-β-L-arabi-nosyl-(1→2)-α-L-rhamnoside and quercetin-3-O-β-D-xylosyl-(1→2)-α-L-rhamnoside. On the other hand, Yang et al. [136] detected six representative flavonoids (apigenin, baicalin, baicalein, luteolin, naringenin and wogonin) when performing SFE-CO₂ extraction of Scutellaria barbata with different percentages of ethanol as co-solvent (0–14.5%), dynamic extraction times (5–240 min), temperatures (33–62 °C) and pressures (10.5–31.5 MPa). Furthermore, Végh et al. [137] efficiently developed SFE-CO₂ method to co-extract the sesquiterpene lactones and the twelve lipophilic flavonoids simultaneously from the leaves of Tanacetum parthenium L. The described extraction was performed using 7% ethanol as co-solvent at a temperature of 64 °C and a pressure of 22 MPa. Uquiche et al. [138] also showed the positive effect of using co-solvent application in the SFE-CO₂ on the extraction yield of flavonoids, namely quercetin, kaempferol and resveratrol from Leptocarpha rivularis. In the presented study, temperature had no significant effect on the extraction yield but a positive effect of pressure on the increase of extraction yield was noticed, which was explained by the rise in CO₂’s solubility due to the pressure-induced growth in its density. With growing interest in using fruit and vegetable residues at the rich source of the bioactive molecules, there is also an increasing trend in using SFE-CO₂ extraction as an effective green extraction technology for exploring the bioactive potential of food and vegetable residues. For example, Fornereto Soldan et al. [139] used SFE-CO₂ for extracting phenolics, flavonoids, fatty acids, and carotenoids from Capsicum annuum industrial waste, Argun et al. [140] for phenolics and flavonoids extraction from orange processing waste, Goyeneche et al. [141] for bioactives recovery from beetroot leaves, Restrepo-Serna and Cardona Alzate [142] for bioactive compounds extraction from five fruit wastes including mango peels, yellow passion fruit seeds, raspberry seeds, mandarin peels, and açaí berry exhausted pulp, and Jha and Sit [143] for the extraction of phytochemical from Terminalia chebula pulp.

4.5. Application of Environmentally Friendly Extraction Solvents

Although intensive work is being performed to develop new approaches to the extraction process, work continues to improve conventional methods in which extraction is based on solvent extraction. The development of new solvents for extraction has taken a step forward. To make the extraction process environmentally friendly, there is a specific focus on the selection of green solvents. Aqueous two-phase systems (ATPS, Figure 8) are recognized as an efficient alternative to the traditionally used organic solvents [144] due to their moderate process conditions, environmentally friendly qualities, capacity for continuous operation, easy scaling-up, rapid phase separation, low cost, and great throughput [58,145,146]. They can be formed by mixing of different components in water. The most common combination is two polymers and a polymer–salt (i.e., phosphate salt).

Zhu et al. [147] efficiently coupled UAE and ATPS for the extraction of flavonoids from jujube peels, Xu et al. [148] used ammonium sulfate-ethanol ATPS for the extraction of bioactive compounds from Aronia melanocarpa berries, Zhou et al. [149] selected a dipotassium hydrogen phosphate–ethanol system for extracting four flavonoids (lysioside C, nevadensin-7-sambubioside, ikarisoside B, and nevadensin) from Lysionotus pauciflorus, Liang et al. [150] used polyethylene glycol–ammonium sulfate ATPS as the extraction medium for extraction of flavonoids from hawthorn leaves, and Li et al. [151] applied ethanol–ammonium sulfate for flavonoids extraction from Tibetan sea-buckthorn (Hippophae thibetana) fruit.

Deep eutectic solvents (DESs) are becoming increasingly popular as an alternative to the traditionally used organic solvents for the extraction process [57,152,153,154,155,156,157]. DESs are often produced using safe, nontoxic, and affordable and biodegradable components [158,159,160,161,162]. A quaternary ammonium salt serves as both a hydrogen bond acceptor (HBA) and a hydrogen bond donor (HBD), which associate with one another through hydrogen bonding, in a DES, which is a combination of two or more compounds having a melting point lower than the individual components [160]. There are numerous examples of the use of DESs as efficient media for the extraction of bioactive molecules from various sources [163].

Today, DESs are often used in combination with modern extraction techniques. There are also examples of the use of DESs coupled with UAE for the extraction of flavonoids. For example: (i) Shang et al. [164] examined the effectiveness of nine various choline chloride-based DES systems with various compositions (contained glucose, citric acid, glycerol, urea, citric acid, glycerol, 1,4-butanediol, lactic acid, malonic acid, malic acid, or xylosic alcohol as hydrogen bond donor) for the extraction of flavonoids from C. paliurus leaves and the choline chloride/1,4-butanediol system (1:5 molar ratio) was selected as the optimal system for maximizing the flavonoid extraction yield; (ii) Zhang et al. [45] analyzed the efficiency of eight DESs (hydrogen bond acceptors (HBA) were choline chloride, levulinic acid, lactic acid, malic acid, and citric acid; hydrogen bond donors (HBD) were ethylene glycol, L-proline-levulinic acid, 1,4-butanediol, and glycerol) for flavonoids extraction from Acanthopanax senticosus and DES composed of glycerol and levulinic acid (1:1) was chosen as the most appropriate extraction solvent; (iii) Mansur et al. [58] evaluated 18 different choline chloride-based DESs as solvent for the flavonoids extraction from common buckwheat (Fagopyrum esculentum) sprouts and selected choline chloride–triethylene glycol DES with 20% water as the most efficient; (iv) Meng et al. [165] analyzed the efficiency of eight DESs (HBA: choline and L-proline; HBD: 1,4-butanediol, glucose, glycerol, lactic acid, ethylene glycol and 1,2-propanediol) for the extraction of flavonoids including quercetin, kaempferol, isorhamnetin and naringenin from the traditional Chinese herbal medicine Pollen Typhae and DES composed of choline chloride and 1,2-propanediol (ChPri) at 1:4 M ratio was selected as the most efficient; (v) Ali et al. [57] screened potential of 11 DESs (HBA: choline and L-proline; HBD: 1,2-propanediol, glycerol, ethylene glycol, malic acid, malonic acid, p-toluenesulfonic acid, levulinic acid, oxalic acod, resorcinol, xylitol and urea) for flavonoids extraction from Lycium barbarum L. fruit and the 1:2 M mixture of choline chloride and p-toluene sulfonic acid was more efficient to get high extraction yields of flavonoids including myricetin (57.2 mg/g), morin (12.7 mg/g), and rutin (9.1 mg/g); (vi) Rashid et al. [166] explored seven different natural deep eutectic solvents (NADESs) for the extraction of bioactive compounds from apple pomace and used choline chloride: glycerol (1:2), choline chloride: lactic acid (1:3) and choline chloride: citric acid (1:1) for further process optimization; (vii) Lei et al. [167] prepared 30 NADES and selected choline chlorice–lactatic acid as the optimal medium for the extraction of 16 flavonoids from Selaginella moellendorffii. DES were also used in MAE processes: (i) Liu et al. [168] selected DES, ChCl/1,4-Butanediol (1/2, mol/mol) with 20% water as the best solvent based on the highest extraction efficiency for the extraction of flavonoids from Hibiscus manihot; (ii) Yu et al. [169] used choline chloride–glycolic acid DES for extraction of four flavonoids (liquiritin, isoliquiritin, liquiritigenin, and isoliquiritigenin) from Glycyrrhiza residues and showed that maximal total extraction yield achieved with DES was 83.03% higher than that of 60% ethanol; (iii) Zhang et al. [170] studied ten different NADEs (HBA: choline chloride; HBD: lactic acid, malic acid, glacial acetic acid, glucose, fructose, sucrose, glycerol, ethylene glycol, 1,4-butanediol and urea) for the extraction of flavonoid molecules from spent sweet potato and NADES, synthesized by choline chloride and malic acid (molar ratio 1:2), exhibited the highest extraction yield.

5. Statistical and Mathematical Modeling Techniques for Optimization Flavonoid Extraction Parameters

Numerous variables, such as solvent concentration and type, extraction time, extraction temperature, solvent pH, solid-to-liquid phase ratio, etc., affect the extraction efficiency in terms of the quantity of extracted chemicals and their biological activity [171]. Therefore, all these variables and their interactions must be taken into account to obtain the highest extraction efficiency. In order to determine the best extraction settings, statistical and mathematical modeling techniques are utilized. More literature data have recently emerged that highlight the significance of using mathematical modeling tools to optimize the extraction process [12,15,172,173]. As a result, multivariate analysis approaches (such as response surface methodology) are rapidly replacing and/or being compared to one-at-a-time methodologies. In the one-factor-at-a-time method, the value of one factor is changed while the values of the other factors remain unchanged. Regardless of which optimization method is chosen, the optimization process follows the same steps as shown in Figure 9.

Experimental design-based response surface methodology (RSM) consists of mathematical and statistical methods that can be used to model and explore processes where a significant number of factors affect the final outcome [174]. To find the output–input interactions, it is essential to understand how the variables interact during the process [175]. The RSM approach ensures the selection of the appropriate process conditions by mathematically modeling the relationships between variables based on observable data [176]. According to Tirado-Kulieva et al. [17] RMS application include four stages: (i) variables selection, (ii) experimental design, (iii) development of the model for description of the data and (iv) determination of the optimal process conditions (Figure 10.).

In order to establish the best settings for these variables that produce the greatest response, it is crucial to fit a mathematical model equation. This will allow a rough prediction of the link between the response and the independent variables [177]. The most important step presents statistical validation of the developed RSM model and if the model is not adequate, the irrelevant variables must be removed and the experimental runs must be redone [178]. After carefully choosing the variables that have a significant impact on the replies, RSM should be conducted [179]. Screening studies such as factorial designs can be used for this. The linear effects of the variables on the output are estimated using these first order designs [180]. These designs do not estimate curvature. The curvature-interaction of the variables is estimated via second-order designs such central composite and its variations (the rotatable CCD, the spherical CCD, the small composite design, and the face-centered cube), Box–Behnken, and Doelhert designs, and is then presented as a quadratic equation [181]. The application of RMS modeling for optimization of the flavonoids extraction process is given in

Table 4. Optimization of the flavonoids extraction process.

Extraction Method	Flavonoids Source	Design of Experiment and Modeling Method	Optimal Process Conditions	Flavonoids Extraction Yield
UAE	peanut (Arachis hypogaea L.) [67]	Single-factor experiment and RSM	particle size of 0.285 mm, solvent to solid ratio of 40 mL/g, extraction temperature of 55 °C, ultrasonic power of 120 W and ultrasonic frequency of 45 kHz and 70% ethanol as the solvent	9.263 mg/g
UAE	leaves of Lobelia nicotianifolia [68]	Full factorial design and RSM	75.25% of methanol, extraction temperature 62.72 °C, and 9.44 min of extraction process.	23.78 mg/g dry weight
UAE	jujube peels [147]		K2HPO4 35% (w/w), ethanol 20% (w/w), solid–liquid ratio 1:30 g/mL (w/v), ultrasonic power 200 W, and extraction time 50 min
NPC-UAE	flower buds of Sophora japonica L. [72]	Box–Behnken design and RSM	ethanol concentration 72%, time 16 min, liquid to solid ratio 25:1 mL/g, ultrasonic intensity 0.347 W/cm2, negative pressure −0.07 MPa and temperature 60 °C	extraction yields of rutin, nicotiflorin, narcissin, quercetin, kaempferol and isorhamnetin were 125.17, 15.02, 25.61, 51.89, 4.32 and 6.30 mg/g
UAE	Olea europea L. leaves [71]	Single-factor experiment and RSM	extraction in ultrasonic bath frequency 37 kHz with 50% acetone for 10 min at 60 °C	2.94 mg/g dry weight
UAE	grapefruit peels [69]	Central composite design and RSM	extraction in ultrasonic bath frequency 40 kHz with 40% ethanol for 55 min at 25 °C	Hesperidin (0.74 mg/g dry weight) and narirutin (0.70 mg/g dry weight) were the most abundant flavonoids
UAE	Acanthopanax senticosus [182]	Single-factor experiments and Box–Behnken design of experiments and RSM	extraction in ultrasonic bath frequency 20 kHz. Solid-to-liquid ratio of 1:10 g/mL (ethanol as the solvent), extraction time of 35 min, and power of 200	14.83 mg/g dry weight
UAE	Ficaria kochii [183]	Rotatable central composite design and RSM	ratio of solvent (methanol) to raw material, 10%; extraction time, 50 min and extraction temperature, 60 °C.	11.754 mg/g dry weight
UAE	Crinum asiaticum [184]	Single-factor experiment and RSM	extraction in ultrasonic bath maximum power of 180 W, 60% ethanol concentration, 64 °C for extraction temperature, 1:28 (v/w) solid-to-liquid ratio with extraction time for 47 min	1.64%
UAE	guava (Psidium guajava L.) [185]	Face-centered design and RSM	extraction in ultrasonic bath maximum power of 250 W. Ultrasonic temperature of 62.19 °C, extraction time of 14.94 min, and loading ratio of 0.19 g/mL (water as the extraction solvent)	288.13 mg/g
UAE	Cyclocarya paliurus leaves [164]	Single-factor experiment and RSM	DES water content (v/v), 30%; extraction time, 30 min; temperature, 60 °C; and solid–liquid ratio, 20 mg/mL.	kaempferol (0.117 mg/g), kaempferol-7-O-α-l-rhamnoside (3.183 mg/g), quercetin (0.034 mg/g), quercetin-3-O-β-d-glucuronide (3.628 mg/g), and kaempferol-3-O-β-d-glucuronide (0.331 mg/g).
UAE	Acanthopanax senticosus [186]	Box–Behnken design of experiments and RSM	ultrasonic power of 500 W, water content of 28%, solid–liquid ratio of 1:18 g/mL, extraction temperature of 55 °C, and extraction time of 73 min.	23.928 mg/g
UAE	common buckwheat (Fagopyrum esculentum) sprouts [147]	Central composite design and RSM	ultrasound power of 700 W, extraction temperature of 56 °C and extraction time of 40 min.	Recovery > 97%
UAE	Pollen typhae [165]	Single-factor experiment and RSM	DES composed of choline chloride and 1,2-propanediol (ChPri) at 1:4 M ratio, 30% of aqueous solution, 50:1 mg/mL for solid–liquid ratio, and 35 min for extraction time	Recovery in the range of 86.87–98.89%
UAE	Melia azedarach [187]	Box–Behnken design of experiments and RSM	temperature (46.4 °C), ultrasound amplitude (100%; 130 W power) and glycerol-choline chloride DES concentration (50%)	21.880 mg/g
UAE-EAE	Gymnema sylvestre [73]	Single-factor experiment and RSM	time, temperature, pH, and amount of enzyme cocktail were 150 min, 64.80 °C, 5.64, and 7.49 mL	54.20 mg/g
UAE	apple samples [40]	Three-level three-factor central composite design and RSM	4.61 °C, an extraction time of 26.90 min, and ultrasonic power 480 W.	6.58 mg/g
UAE	Aronia melanocarpa berries [148]	Box–Behnken design of experiments and RSM	ammonium sulfate concentration of 0.320 g/mL, ethanol-water ratio of 0.71, ultrasonic time of 50 min and ultrasonic power of 200 W	11.67 mg/g
UAE	Lysionotus pauciflorus [149]	Single-factor experiment and RSM	45 g ATPS (made of 30% ethanol/18% K2HPO4) in 43 °C for 30 min	four flavonoids could reach 2.56, 2.06, 3.62, and 6.28 mg/g
UAE	hawthorn leaves [150]	Box–Behnken design of experiments and RSM	ratio of solid to liquid 1:37, ultrasonic time 40 min, ultrasonic power 360 W, ultrasonic temperature 65 °C	2.86%
UAE	Astragalus membranaceus steams and levaes [33]	Box–Behnken design of experiments and RSM	extraction time of 35 min, ethanol concentration of 75 %, liquid–solid ratio of 40 mL/g, and extraction temperature of 58 °C	22.027 mg/g
DES-UAE	Ixora javanica flowers [188]	Single-factor experiment and Box–Behnken design of experiments and RSM	extraction time of 40 min, 25% water content in DES and a solid-to-liquid ratio of 1:25 g/mL	89.732 mg/g
DES-UAE	Scutellaria baicalensis [189]	Box–Behnken design of experiments and RSM	molar ratio of betaine/acetic acid was 1:4, the water content was 40%, the solid/liquid ratio was 1:100 g/mL, the extraction temperature was 52 °C, and the extraction time was 23 min.	scutellarin, baicalin, baicalein, wogonoside, wogonin, and oroxylin A were 0.73 ± 0.04, 11.93 ± 0.36, 2.57 ± 0.12, 1.26 ± 0.08, 0.41 ± 0.2, and 0.17 ± 0.04%, respectively
NADES-UAE	Selaginella moellendorffii [167]	Single-factor experiment and RSM	water content of 24%, extraction power of 260 W, liquid/solid ratio of 24:1 mL/g and extraction time of 43 min	5.72 mg/g
MAE-UAE	Aronia melanocarpa [38]	Box–Behnken design of experiments and RSM	microwave power was 230 W, extraction time was 367 s, extraction temperature were 52 °C. Solvent NADES	4.456 mg/g
MAE	Lagenaria siceraria [81]	Full factorial design of experiment and RSM	optimized power and time for TFC were 480 W and 40 s	24.22 mg/L
MAE	Trigonella-foenum graecum [87]	One-factor at time and RSM	3 min irradiation time, microwave power 600 W, 60% solvent concentration, 1:10 g/mL of feed-to-solvent ratio and 70 °C temperature
MAE	Crotalaria sessiliflora L [89]	Single-factor experiment and RSM	ethanol concentration 32% and (NH4)2SO4 concentration 22% for formation of the ATPS, extraction temperature 80 °C, extraction time 8 min, solvent-to-material ratio 50:1.	extraction yields and recoveries ranged from 162.7 to 240.0 g/g and from 94.14% to 105.5%, respectively.
MAE	Sorbus tianschanica leaves [90]	Factorial design and RSM	1.0 M [C6mim][BF4], –0.08 MPa for vacuum, 19 min and 420 W for microwave irradiation time and power, and 15 mL/g for liquid–solid ratio	recovery yields more than 84.14%, 82.40% and 89.33%
MAE	tomato [88]	5-level full factorial Box–Behnken design and RSM	the global optimum processing conditions (t = 20 min; T = 180 °C; Et = 0%; and S/L = 45 g/L)	quercetin pentosylrutinoside (6.78 mg/g) and quercetin-3-O-rutinoside (11.7 mg/g)
MAE	Pistacia vera L. leaves [83]	Single-factor experiment and RSM	70 °C and 61 °C, and 5.6 and 12 min for male and female leaves	Male leaves: 82.16 mg/g Female leaves: 83.34 mg/g
MAE	leaves of Vernonia amygdalina [84]	Face-centered central composite design and RSM	7 min of irradiation time, 416 W of microwave power level, 100 ºC of temperature, and 0.10 g/mL of feed-to-solvent ratio	TFC = 87.05 mg/g
MAE	Myrtus communis leaves [85]	Single-factor method and RSM	extraction time 1.04 min, ethanol proportion 42%, MW powere 500 W, liquid to solid ration 32 mL/g	5.02 mg/g
MAE	Russian olive leaves and flowers [86]	Two-level fractional factorial designs and RSM	solid to solvent ratio of 7.5 (w/v), citric acid molarity of 2 M, ethanol concentration of 59.8% and 66.4%, and temperature of 97.4 °C and 97.5 °C
MAE	Hibiscus manihot L. flower [168]	Taguchi orthogonal design and RSM	temperature 73 °C, time 20 min and liquid/solid ratio 26 mL/g	16.704 mg/g
MAE	Helichrysum arenarium [91]	Box–Behnken design and RSM	5 mL/g liquid–solid ratio, 20 min microwave irradiation time and 525 W microwave irradiation power. 1.0 M [C8mim]Br was used as the solvent for the extraction	astragalin (0.83 mg/g), quercetin (0.42 mg/g), luteolin (0.62 mg/g), kaempferol (0.99 mg/g) and apigenin (0.19 mg/g)
MAE	fruits of Ficus racemosa [190]	Central composite design and RSM	3.5 pH, 360.55 W microwave power and 30 s time (water as the extraction solvent)	Quercetin 36.96 mg/100 mL
MAE	Peach waste [82]	22-factorial design and RSM	frozen samples: microwave power of 540 W and extraction time of 50 s dried samples: microwave power of 900 W and extraction time of 50 s	TF (frozen samples) = 120.47 mg/100 g TF (dried samples) = 74.75 mg/100 g
MAE	Apium graveolens L. [191]	Box–Behnken design and RSM	microwave power of 500 W at 30 mL/g solid–solvent ratio with 75.6% (v/v) ethanol concentration	0.62 g/100 g
MAE	Alpinia oxyphylla [192]	Orthogonal design and RSM	ethanol concentration of 50%, solid–liquid ratio of 1:20, temperature of 70 C, and cycle index of 3	28.24%
MAE	Salvia plebeian [193]	Box–Behnken design and RSM	ethanol concentration was 56%, the ratio of material to liquid was 1:30 g/mL, the extraction time was 5 min, the extraction power was 560 W	2.38 mg/
MAE	avocado (Persea americana Mill.) seeds [194]	Central composite design and RSM	ethanol concentration of 58.3% (v/v), microwave power of 400 W, and extraction time of 4.8 min.	21.84 mg/g
MAE	sweet potato (Ipomoea batatas L.) leaves [170]	Single-factor experiments and RSM	microwave power of 470 W, extraction temperature of 54 °C, extraction time of 21 min, and solid–liquid ratio of 70 mg/mL.	40.21 mg/g
MAE	grape skin [195]	Box–Behnken design and RSM	solvent 60% ethanol, extraction time 5 min at 40 °C	total anthocyanins 12,545.19 mg/g
PLE	aerial parts of Dracocephalum kotschyi [103]	Circumscribed central composite (CCC) design and RSM	temperature, pressure, static time, dynamic time, and the solvent flow rate were adjusted 74 °C, 34 bar, 11.33 min, 17.45 min, and 0.7 mL/min	6.13 mg/g
PLE	roots of Scutellaria pinnatifida [104]	Circumscribed central composite (CCC) design and RSM	temperature, pressure, static time, dynamic time, and the solvent flow rate were adjusted 65.8 °C, 39.2 bar, 12.9 min, 18.9 min, and 0.76 mL/min	127.78 mg/g
PLE	goji berry fruits [121]	Factorial experimental design and RSM	180 °C and 86% ethanol in water	TF = 3.02 mg/g
UAPLE	Passion fruit [196]	Single-factor experiments and RSM	10 g/min in 68.54 min	7.8%
SFE-CO2	Xinjiang jujube (Ziziphus jujuba Mill.) leaves [132]	Box–Behnken design and RSM	temperature of 52.52 °C, a pressure of 27.12 MPa, a time of 113.42 min, and a cosolvent flow rate of 0.44 mL/mi	29.05 mg/g
SFE-CO2	Odontonema strictum leave [197]	Randomized design full factorial and RSM	extraction time of 270 min and a pressure of 200 bars,	230.48 mg/g
SFE-CO2	Maydis stigma [198]	Box–Behnken design and RSM	a temperature of 50.88 °C, a pressure of 41.80 MPa, a co-solvent amount of 2.488 mL/g and an extraction time of 120 min with 0.4-mm particle sizes and 20% aqueous ethanol as the co-solvent	4.24 mg/g
UAESFE	Iberis amara [199]	Single-factor experiments and RSM	25 MPa pressure, 46 °C temperature, 0.34 W/mL ultrasonic energy density
SFE-CO2	Lippia origanoides K. and Lippia graveolens K. [200]	Fractional factorial screening design and RSM	307 bar, 5% ethanol, 96 min and 43 g CO2/min	55 mg/g
SFE-CO2	Leptocarpha rivularis leaves [138]	Box–Behnken design and RSM	temperature 60 °C, pressure 20 MPa and co-solvent (ethanol) concentration 2 wt.%	176.6 mg/g
SFE-CO2	Terminalia chebula pulp [143]	Central composite rotatable design using RSM coupled with desirability function (DF) and genetic algorithm (GA) and ANN with GA	RSM-DF were 3.34 mL/min, 166.94 bar, 51.97 °C, 67.47 min, for RSM-GA were 3.23 mL/min, 172.79 bar, 52.37 °C, 68.53 min, while that for ANN-GA were 3.30 mL/min, 174.07 bar, 51.18 °C, 65.23 min.	RSM-DF 137 mg/mL RSM-GA 136.58 mg/mL ANN-GA 135.55 mg/mL
EA-SFE	Medicago sativa leaves [63]	The response surface methodology (RSM) based on Box–Behnken design	the temperature of 68 °C, the pressure of 205 bar and 15.5% of the co-solvent addition	3250 mg/g

. It is observed that different types of experiment designs and different extraction methods were used for different flavonoids sources but the general conclusion of all listed researches is that the design of the experiment coupled with RSM modeling reduces the number of experiments performed to achieve the maximum extraction yield.

Response surface models are frequently applied to describe how process variables affect extraction effectiveness, but these models do not always provide data supporting mass transfer and the dynamics of the extraction process, requiring the application of kinetic models to gain understanding of the extraction procedure [201]. To assess the extraction kinetics and guarantee the maximum level of product repeatability, a mathematical model is necessary [67,202,203,204]. As stated by Piwowarska and González-Alvarez [205], in order to decrease the consumption of energy, time, and chemical reagents, mathematical modeling of solid–liquid extraction processes is a key engineering technique in the design process. Furthermore, understanding complicated mass transfer, diffusion, and thermodynamic characteristics impacting the extraction requires the use of kinetic modeling [11].

The literature shows that the solid–liquid extraction procedures for the extraction of bioactive compounds from plant materials can be described using various mathematical models. The models used include Peleg, Page, Elovich, the second-order model, diffusion model, logarithmic model and Ponomaryov’s empirical equation [11] (

Table 5. Kinetic models mostly used for the description of the solid–liquid extraction process of bioactive molecules.

Kinetic Model	Equation	Parameters
Equilibrium-dependent model [206]	$\frac{dc\left(t\right)}{dt}=k·\left(c_e-c\left(t\right)\right)$	c is the concentration of the dissolved substance in the liquid phase, k is the transport coefficient and ce is the dissolved substance concentration at the equilibrium
Second-order model [207]	$\frac{dc\left(t\right)}{dt}=k·{\left(c_e-c\left(t\right)\right)}^2$	c is the concentration of the dissolved substance in the liquid phase, k is the transport coefficient and ce is the dissolved substance concentration at the equilibrium
Peleg’s model [208]	$c\left(t\right)=c_0+\frac{t}{K_1+K_2·t}$	c(t) presents the concentration of the dissolved substance at the time t, K1 is Peleg’s rate constant (relates to extraction rate at the very beginning of the extraction process), K2 is Peleg’s capacity constant (relates to maximum dissolved substance concentration and c0 is the concentration of dissolved substance at time t = 0.
Page’s model [209]	$c\left(t\right)=e^{-k·t^n}$	k and n are Page’s model constants and c(t) represents the concentration of dissolved substance at time t
Logarithmic model [209]	$c\left(t\right)=a·\log \left(t\right)+b$	a and b are Logarithmic model constants and c(t) represents the concentration of dissolved substance at time t
Ponomaryov’s model [210]	$1-\frac{c\left(t\right)}{c_e}=b+k·t$	b and k are Ponomaryov’s model constants, c(t) represents the concentration at time t and ce is the equilibrium concentration
Lewis empirical model [211]	$c\left(t\right)=e^{-a·t}$	a is Lewis’s model constants, and c(t) represents the concentration at time t
Henderson and Pabis empirical model [212]	$c\left(t\right)=a·e^{-b·t}$	a and b are Henderson and Pabis model constants and c(t) represent the concentration at time t
Power-law model [213]	$y=B·t^n$	y represents extraction yield or final concentration, B extraction solvent constant, n diffusion exponent and t extraction time
Two-site kinetic model [214]	$\frac{c\left(t\right)}{c_{\infty }}=1-F·e^{-k_1·t}-\left(1-F\right)·e^{-k_2·t}$	c∞ represents the maximum extracted concentration, F denotes the number of biocompounds discharged quickly, (1 − F) denoted the amount of biocompound components released gradually, k1 and k2 are first-order rate constants of rapid and slow phases
Mass transfer model [215]	$\frac{\partial c}{\partial t}=D\frac{{\partial }^{2}c}{\partial x^2}$	c is concentration, t is time, D is the diffusion coefficients and x is the diffusion distance

).

The literature states that a kinetic model describing solid–liquid extraction can be developed using an empirical and mechanistic method [216]. The mechanistic method involves a hypothetical description of the occurrences, whereas the empirical approach is based on facts from trials. According to Sturzoiu and Stroescu [216], solid–liquid extraction includes two stages; the first stage is the washing stage, during which the solute and solvent are first mixed and the second step uses a diffusion technique for a significantly slower solute transport. As described by Sridhar et al. [217], understanding the kinetics of the extraction depends heavily on the concentration of the substances (Cs), the extraction order (n), the activation energy (Ea), and the rate constant (k). An overview of the models used to describe the flavonoids extraction kinetics is given in

Table 6. Application of kinetic modeling in flavonoids extraction.

Extraction Method	Flavonoids Source	Kinetic Model	Model Performance
UAE [67]	Peanut (Arachis hypogaea L.)	Phenomenological model and Peleg’s model	the mean absolute errors (MPE) for phenomenological model in range 0.158–0.809% and for Peleg’s model in range 0.675 to 1.817%
MEA [219]	Terminalia bellerica	Second-order kinetic model	The average absolute relative deviation (AARD) and the relative standard deviation between the experimental data and those predicted by second-order kinetics are 0.38% and 0.62%, respectively.
MAE [91]	Helichrysum arenarium	First-order kinetic model	R2 > 0.98
UAE [203]	Lentils (Lens culinaris L.)	Parabolic diffusion Power law Peleg’s model Elovich’s model	RMS and SEE diminished and R2 increased in the following order: hyperbolic model → parabolic model → Elovich’s equation → power-law model.
Conventional extraction [204]	Linden (Tilia cordata M.) flowers	Unsteady-state diffusion Film theory Ponomaryov	R2 increased in the following order Film theory -> Empirical equation of Ponomaryov -> Unsteady diffusion through plant material
Conventional extraction (infusion) [202]	Roots of Carlina acaulis	change in the concentration of the target substance in the cell volume over time change in the concentration of the target substance in intercellular space over time material balance equation
PLE [29]	Cocoa shell	Peleg’s model	R2 were high in all experimental data set (0.9335–0.9930)
UAPLE [196]	Passionfruit	Spline model two-site desorption model	Spline model> two-site desorption model
UAE-SC CO2 [136]	Scutellaria barbata	Second-order kinetic model	R2 = 0.98 at all analyzed temperatures (T = 33, 39, 45, 52 °C)
SFE-CO2 [220]	Brazilian orchid tree (Bauhinia forficata)	Empirical model dividing extraction process into three periods	R2 > 0.960○for analyzed extraction conditions
SFE-CO2 [139]	Capsicum annuum pepper	Logistic and spline model	R2 > 0.99 for both models for all analyzed extraction conditions

. The viability of several mathematical models has been investigated for different flavonoids sources; however, understanding the process in the early phase of extraction presents the most challenging problem [117,218].

6. Conclusions

There is a growing interest in the extraction of bioactive molecules, namely flavonoids from plant materials. It is also noted that the mentioned modern extraction methods (microwave-assisted extraction, ultrasound-assisted extraction, pressurized liquids-assisted extraction, and supercritical fluids extraction) ensure higher extraction yields with lower energy and solvent consumption compared to the classic extraction method. However, due to the different sources of bioactive molecules, it is necessary to specifically define the optimal process conditions for the selected plant material. Therefore, it is necessary to use mathematical tools to optimize the extraction process and to analyze the extraction dynamics.