Influence of particle size in supercritical carbon dioxide extraction of roselle (Hibiscus sabdariffa) on bioactive compound recovery, extraction rate, diffusivity, and solubility

The purpose of this work was to establish the best particle size for recovering high yields of total phenolic compounds (TPC), total anthocyanin compounds(TAC) and total flavonoid compounds (TFC) from roselle (Hibiscus sabdariffa) by applying supercritical carbon dioxide (ScCO2). The extraction rate, diffusivity and solubility of yield in ScCO2 were also studied and calculated utilizing models. Pressure (10 and 30 MPa), temperature (40 and 60 °C), and particle size (250 µm < dp < 355 µm, 355 µm < dp < 425 µm and 425 µm < dp < 500 µm) were employed as variables in this experiment. The greatest recovery was 11.96% yield, 7.16 mg/100 g TAC, 42.93 mg/100 g TPC and 239.36 mg/100 g TFC under the conditions of 30 MPA, 40 °C and 250 µm < dp < 355 µm, respectively. The extraction rate of supercritical carbon dioxide in roselle extraction ranged from 5.19 E−03 to 1.35 E−03 mg/s fitted using the Esquivel model. The diffusivity coefficient of ScCO2 ranged from 2.17E−12 to 3.72E−11 mg/s2, as fitted by a single sphere model. The greatest solubility of global yield, TAC, TPC and TFC in ScCO2 was 1.50 g/L, 0.3 mg/L, 1.69 mg/L and 9.97 mg/L, respectively, with a particle size of 250 µm < dp < 355 µm. The smaller particle size of roselle provides the maximum bioactive compound recovery and solubility. Furthermore, the diffusivity and extraction of ScCO2 are increased by decreasing the particle size. Therefore, a smaller particle size is appropriate for roselle extraction by ScCO2 based on the experimental and modelling data.

Supercritical carbon dioxide (ScCO 2 ). The equipment consisted of a 50 mL extraction vessel (internal diameter: 1.4 cm; length: 33 cm), a CO 2 pump (Lab Alliance's Supercritical 24), a back pressure regulator (Jasco BP 2080 Plus Automated BPR, Japan), and an oven (Memmert, Japan). Roselle powder (3 ± 0.005 g) was added to an extraction vessel, and the CO 2 temperature chiller was adjusted to 6 °C. To find the optimal particle size, particle sizes of 250 µm < dp < 355 µm, 355 µm < dp < 425 µm and 425 µm < dp < 500 µm were used. The backpressure regulator's heater was set to 50 °C. After slowly adding liquid CO 2 , 0.24 mL/min ethanol was introduced as an entrainer (V Etoh /V CO2 ). The extraction time was set to 60 min. The extract contained the ethanol as a cosolvent was dried using vacuum evaporator at temperature of 40 °C to prevent the degradation process. Table 1 summarizes the extraction parameters and responses. The schematic design of ScCO 2 extraction utilizing ethanol as a cosolvent is shown in Fig. 1.

Analysis of total anthocyanin content (TAC).
A pH differential technique was used to assess the anthocyanin content of roselle calyces extract 18 . Two dilutions of the same material were prepared using potassium chloride (0.025 M) and sodium acetate trihydrate solutions (0.4 M), respectively. Both were adjusted to pH Table 1. The particle size parameters and responses of yield (%), TAC (mg/100 g), TPC (mg/100 g) and TFC (mg/100 g).
The TAC was calculated as mg cyanidin-3-glucoside (cya 3-glu)/100 g of dry roselle as in Eq. (1); A is absorbance, MW is the molecular weight of cyanidin 3-glucoside (449.2 g/mol), DF is the dilution factor, Ɛ is the cyanidin 3-glucoside extinction coefficient (26,900 L/cm mol), and L is the cell path length (1 cm). TAC (mg/L) was transformed to mg of roselle extract per 100 g of dried roselle.
Analysis of total phenolic compounds (TPC). According to Rizkiyah et al. 3 , the total phenolic compounds in each sample were determined. 5 mL of Folin-Ciocalteu reagent was sonicated for 5 min in 50 mL of distilled water and 40 mL of distilled water containing 3 g of Na 2 CO 3 . The concentration of extract was set 1 mg/ mL. Furthermore, 1 mL of diluted extract was added 5 mL of Folin-Ciocalteu solution. The addition of 4 mL of Na 2 CO 3 solution was followed by a 30 min rest at room temperature. Using a UV-Vis spectrophotometer, the absorbance at 760 nm was measured (Jasco, Japan). The limit of detection (LOD) and limit of quantification (LOQ) were 23.31 and 70.63, respectively. The total phenolic compounds were analyzed using a gallic acid standard curve, and the results are reported in milligrams of gallic acid equivalents per 100 g of dried roselle (mg/100 g).
(1) Absorbance : (A 520 − A7 00 )pH 1.0 − (A 520 − A 700 ) pH 4.5 .  www.nature.com/scientificreports/ Analysis of total flavonoid compounds (TFC). The analysis of total flavonoid compounds was conducted using Putra et al. 19 . The concentration of extract was set 1 mg/mL. 1 mL of sample was mixed with 0.2 mL of 10% Al 2 NO 3 and 0.2 mL of 1.0 M CH 3 COOK at room temperature for 40 min. At 415 nm, the absorbance of each sample was measured using a UV-Vis spectrophotometer (Jasco, Japan). The limit of detection (LOD) and limit of quantification (LOQ) were 21.34 and 64.67, respectively Using quercetin as a standard, a standard curve was constructed, and the results were reported as mg quercetin equivalents per 100 g of dried roselle (mg/100 g).
Calculation of global yield recovery. The global yield recovery was calculated using Eq.
where m a is the mass of the extract (g) and m ab is the mass of the sample (g). where y is the predicted global yield (mg), k are the adjustable parameters (s), and t is the extraction time (s). The extraction rate of the global yield can be obtained by y/k (mg/s). Brunner's model also has two adjustable parameters ( Y 2 andk 2 ) that represent a specific solution of Fick's law, as shown in Eq. (5) 15 : where GY is the global yield (mg), y is the predicted total phenolic or flavonoid content (mg/g), 1/k is the adjustable parameter and t is the extraction time (s). The extraction rate of global yield can be obtained by y/k (mg/s).
Single sphere model. A single sphere model was proposed by Reverchon 17 with the following assumptions: 1. Intra particle of mass transfer is the main factor in the extraction process. 2. Resistance of mass transfer is zero between the extract and the solvent. 3. The roselle as a raw material is an inert porous sphere. 4. Particle size of roselle is homogenous. 5. Global yield is extracted move through the particles by process 'similar to diffusion.
The diffusion equation for a constant diffusion coefficient takes the form of Eq. (6).
where Mt is the total amount of diffusing substance at a specific time, M∞ is the corresponding quantity after infinite time, D e is the diffusivity coefficient (m 2 /s), R is the radius of the particle (m) and t is time (s). In this investigation, the solver in Microsoft Excel 2021 was used to determine the diffusivity coefficient. where GY(g) is the global yield (g) and �V co2 (L) is the total CO 2 consumption. The total CO 2 consumption is measured based on the flowmeter of the CO 2 pump.  www.nature.com/scientificreports/ Average absolute relative deviation (AARD). The AARD value is used to identify the optimal model between the model and the experimental data and is shown in Eq. (8).
where n is the number of data points, E model is the model data, and E exp is the experimental data.
Coefficient of determination (R 2 ). The R 2 value is used to establish the optimal model between the model and experimental data, as shown by Eq. (9) Based on Eq. (9), i (EM i − ED i ) 2 is the residual data (i.e. an error between the model and the experimental data). Meanwhile, i (x i − x) 2 is the variance of the data.

Results and discussion
The dried roselle was grounded and sieved to various particle sizes of 250 µm < dp < 355 µm, 355 µm < dp < 425 µm and 425 µm < dp < 500 µm. The exclusion of particle size dp < 250 was due to the clogging of the apparatus. Fine particle of dried roselle will be compact in high pressure condition. Therefore, the extraction efficiency of the process will be reduced 20 . The moisture content of dried roselle was maintained below than 8%. This prevented the production of ice particles in the extraction tube 4 . Additionally, this development will block the ScCO 2 extraction tube. In this research, the effect of particle size was examined and discussed with the responses of bioactive compound's recovery, diffusivity, extraction rate and solubility.
Effect of particle size on global yield, TAC, TPC and TFC. The particle size of the sample matrix is crucial for obtaining the maximum yield of supercritical carbon dioxide extraction using ethanol as an entrainer/ cosolvent. Reducing the solute particle size will increase the extraction process yield 14 . Although reducing the particle size will increase the extract yield, previous researchers have reported that reducing the particle size does not always increase the yield extract. Therefore, preliminary studies are required to determine the optimal particle size to obtain the highest extract yield with various particle sizes 6 . In this investigation, roselle was produced via milling, where the milling process may enhance the specific area of the particle solute and damage the cell walls of roselle by decreasing the particle size 21 .  Table 1 also shows the particle size parameters and responses of yield (%), TAC (mg/100 g), TPC (mg/100 g) and TFC (mg/100 g). The results show that decreasing the particle size from 425 µm < dp < 500 µm to 250 µm < dp < 355 µm at constant parameters (a) 10 MPa, 40 °C, (b) 10 MPa, 60 °C, (c) 30 MPa, 40 °C, and (d) 30 MPa, 60 °C increases the global yield, total anthocyanin content (TAC), total phenolic compounds (TPC) and total flavonoid compounds (TFC), as shown in Figs. 2, 3, 4 and 5. Reducing the particle size improves the sample contact area with extraction solvents. Grinding produced coarser and smaller samples, but powdering produced more homogeneous and smaller particles, resulting in improved surface contact with extraction solvents. The solvent must make contact with the solute, and a particle size less than 0.5 mm is optimal for efficient extraction. Reverchon et al. 22 also mentioned that larger particles may result in lengthy diffusion-controlled solvent extraction and that slow diffusion can significantly impact the extraction kinetics.
Sodeifian et al. 23 discovered that particle size may have two contradictory impacts on extraction yield. In contrast, the grinding procedure increases the contact area between the supercritical fluid and the samples, hence increasing the extraction yield. In fact, from a mass transfer stand point, additional particle size reduction may inhibit the extraction process, since the volatile oil may be simply reabsorbed on matrix surfaces, resulting in a decrease in solute transport.
In addition, the small size of particles may contribute to bed caking formation (particles sticking together, channelling) along the bed through which ScCO 2 can flow more efficiently, resulting in insufficient contact between the sample and ScCO 2 and, ultimately, insufficient extraction yield. Furthermore, Putra et al. 6 also found that the fine particle of peanut skin (dp < 250 µm) give low extraction efficiency of catechin as polar compounds. The polarity of catechin is similar to the anthocyanin, thus the process can be compared. This phenomenon is due to the small size of particles may contribute to bed caking formation during the extraction. It reduced the extraction efficiency of ScCO 2 . It is also reducing the diffusivity of CO 2 to break the cell wall of materials.
Additionally, Darbandi et al. 24 discovered that grinding the material prior to the extraction procedure enhances the interfacial area. In addition, crushing the particles facilitates the release of oil from the cells. During the grinding process, certain cells are damaged, and the contained oil is released from the shattered cells. ScCO 2 makes this quantity of released extract containing bioactive compounds more accessible, and it dissolves rapidly in the solvent. Milling the particles reduces the intraparticle barrier to mass transfer in addition to these benefits. Consequently, the route of diffusion in solids becomes shorter. Thus, the solute will be easier to move, www.nature.com/scientificreports/ and the extraction yield will increase. The aforementioned causes may explain why the extraction yield increases as the particle size decreases. Sabio et al. 25 also studied the impact of particle size on the extraction yield of a combination of tomato skin and seeds. Contrary to this research, greater particle size increases yield more than smaller particle size at constant pressure of 300 bar, temperature of 60 °C, and flow rate of 0.792 kg/h for two distinct particle sizes. Larger particles in this instance give a unique diffusion-controlled extraction but need a lengthy processing time. The extraction yield increased as the particle size decreased. This is the result of the increased interfacial area.

Influence of the particle size of roselle on the extraction rate of global yield. Brunner's and
Esquivel's models were used for the investigation of the extraction rate because they require fewer adjustable www.nature.com/scientificreports/ parameters and are simply fitted to experimental data 9 . Table 2 demonstrates that the findings of Brunner and Esquivel's model fit the global yield recovery from roselle using ScCO 2 . Meanwhile, Fig. 6 shows that the experimental data are fitted by Esquivel's model at pressures of 10 and 30 MPa, temperatures of 40 and 60 °C, and particle sizes (250 µm < dp < 355 µm, 355 µm < dp < 425 µm and 425 µm < dp < 500 µm).
On the basis of the average coefficients of determination (R 2 ) and the average absolute relative deviation (AARD), the most appropriate model was identified and is displayed in Table 2. The mathematical model with the greatest average coefficients of determination (i.e., R 2 > 1) and the lowest average absolute relative deviation (AARD < 10%) was the most suitable. Table 2 demonstrates that Esquivel's model provided a better fitting for global yield recovery than Brunner's model, indicating that it might give more accurate data on the extraction rate of global yield.
The average extraction rate of the global yield was 0.01 mg/s, as shown in Table 2. On the other hand, a pressure of 10 MPa, temperature of 60 °C and particle size of 250 µm < dp < 355 µm gave the maximum extraction rate (1.35 E−02 mg/s) and at pressure 30 MPa, tempereature 40 °C and particle size 425 µm < dp < 500 µm gives www.nature.com/scientificreports/ the minimum extraction rate (5.15E−03 mg/s). Overall, the particle size of 250 µm < dp < 355 µm gives a higher extraction rate of global yield compared to 355 µm < dp < 425 µm and 425 µm < dp < 500 µm, as shown in Fig. 7. It is often assumed that cavitation effects, heat impacts, and mechanical effects have a substantial impact on the ScCO 2 extraction method 12 . These actions result in cell wall disintegration, particle size reduction, and an increase in reaction rate by mass transfer of the cell wall, without altering the extracts' structure or function 26,27 . Therefore, a smaller particle size might improve the particle cell wall damage, hence increasing the extraction rate and global yield.

Influence of the particle size of roselle on diffusivity of global yield.
To determine the diffusivity coefficient and mass transfer between solvent and solute on supercritical carbon dioxide, the single sphere model is typically employed as the kinetic model. The single sphere model is easier to use than other kinetic models because it has a single adjustable parameter compared to other models 28 . Table 3 demonstrates that the findings      www.nature.com/scientificreports/ of the single sphere model fit the global yield recovery from roselle using ScCO 2 . Meanwhile, Fig. 8 shows that the experimental data are fitted by a single sphere model at pressures of 10 and 30 MPa, temperatures of 40 and 60 °C, and particle sizes (250 µm < dp < 355 µm, 355 µm < dp < 425 µm and 425 µm < dp < 500 µm). On this variable, the single sphere model is slightly successful in fitting the experimental data with a higher percentage of error. This is because the single sphere model is suitable for high pressure conditions; hence, this pressure is not enough to obtain a high diffusivity of solvent 29 . Table 3 shows that the design of the experiment for this study based on all single sphere model experiments has an error higher than 5%. Table 3 shows that the average diffusivity coefficient was 7.83E−12 m 2 /s. on the other hand, the pressure 10 MPa, tempereature 60 °C and particle size 250 µm < dp < 355 µm gives the maximum diffusivity coefficient (3.72E−11 m 2 /s) and at pressure 30 MPa, tempereature 40 °C and particle size 425 µm < dp < 500 µm gives the minimum diffusivity coefficient (2.17E−12 m 2 /s). Moreover, the results show that a particle size of 250 µm < dp < 355 µm at different lowest and highest constant pressures and temperatures gives the maximum oil yield and diffusivity coefficient. This confirms that 250 µm < dp < 355 µm is the optimum particle size due to the high diffusivity coefficient of the extraction process, as shown in Fig. 9.
The high diffusivity coefficient indicates the high mass transfer process between supercritical carbon dioxide and extract as a solute. Therefore, increasing the diffusivity of the extraction will enhance the kinetic transfer of the extract to dissolve into the solvent 30 . Decreasing De indicates the difficulty of supercritical solvent diffusion into the pores of particles to dissolve the solute and implies that the mass transfer resistance is mainly located in the solid phase 31 .
Influence of the particle size of roselle on the solubility of global yield, TAC, TPC and TFC. Solubility data are a valuable measure, especially in ScCO 2 extraction, to encourage the extraction process. Therefore, the extraction conditions can be determined appropriately by using this information. The solubility of roselle extracts in ScCO 2 under various operating conditions is shown in Table 4, where the average solubility of global yield, TAC, TPC and TFC were 1.05 g/L, 0.17 mg/L, 1.19 mg/L and 6.69 mg/L, respectively. The solubility was evaluated at pressures of 10 and 30 MPa, temperatures of 40 and 60 °C and particle sizes of 250 µm < dp < 355 µm, 355 µm < dp < 425 µm and 425 µm < dp < 500 µm. The value of ScCO2 density was obtained from Engineering toolbox (https:// www. engin eerin gtool box. com/ carbon-dioxi de-densi ty-speci fic-weight-tempe rature-press ure-d_ 2018. html). www.nature.com/scientificreports/ Figure 10 shows that the higher pressures and lowest particle size increased the solubility of the extract because the increase in pressure enhances the density of solvents. In addition, the increase in pressure increases the solvation power of the ScCO 2 mixture to roselle 32 . Table 4 also shows that the lowest particle size of 250 µm < dp < 355 µm gives the highest solubility TAC, TPC and TFC. Fine particles are simpler to extract because they have a large surface area per unit volume, contain a high proportion of "free oil" and need less distance for the "tied oil" to reach the surface, which minimizes the internal mass transfer resistance 33,34 . Reverchon 17 found that the influence of particle size on cumulative solubility may be described in terms of mass transfer resistances. The extraction of solute from the solid matrix presents two forms of mass transfer resistances, namely, internal mass transfer resistance and exterior mass transfer resistance 35 . If the internal mass transfer mechanisms comprise the governing phase of the extraction process, the particle size of the roselle matter may greatly impact the cumulative extraction yield. In this condition, extraction from various particle sizes will mostly depend on the length of the diffusion path 20 . If internal mass transfer or equilibrium is the controlling stage of the process, the particle size could significantly impact the extraction rate/solubility 36 .

Conclusion
Roselle (Hibiscus sabdariffa) provides anthocyanin, phenolic, flavonoid, and antioxidant components, among other things. The essential compounds in roselle are extracted using ScCO 2 as a green solvent. Mechanical parameters, such as the particle size of materials, have been slightly studied by researchers to enhance the efficiency of ScCO 2 extraction. The particle size of roselle was studied to obtain the best particle size with high global yield and anthocyanin, phenolic and flavonoid compounds. The greatest recovery was 11.96% yield, 7.16 mg/100 g TAC, 42.93 mg/100 g TPC and 239.36 mg/100 g TFC under the conditions of 30 MPA, 40 °C and 250 µm < dp < 355 µm, respectively. The extraction rate of ScCO 2 in roselle extraction was ranged from 5.19 E−03 to 1.35 E−03 mg/s fitted using the Esquivel model. The diffusivity coefficient of ScCO 2 ranged from 2.17E−12 to 3.72E−11 mg/s 2 , as fitted by a single sphere model. The maximum solubility of global yield, TAC, TPC and TFC in ScCO 2 was 1.50 g/L, 0.3 mg/L, 1.69 mg/L and 9.97 mg/L, respectively, with a particle size of 250 µm < dp < 355 µm. In conclusion, a reduced particle size enhances the solubility, diffusivity, extraction rate and recovery of the extract.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.