### Kinetics of impregnation extraction

The impregnation kinetic curves of *Salvia miltiorrhiza* with 4 particle sizes of 5–10, 10–24, 24–50, and 50–65 mesh in three batches of D1, D2, and D3 have been measured. The impregnation kinetic curves have been proven in Fig. 4. It may be seen from Fig. 4c and (d) that when the particle dimension of the *Salvia miltiorrhiza* medicinal items was small, equilibrium of impregnation was reached inside 5 min. This can be as a result of following two causes. Firstly, when the medicinal materials powders have been smaller, extra cell partitions have been destroyed within the pulverization course of, which decreased the mass switch resistance. Secondly, the smaller particle dimension of the medicinal materials elevated its floor space for mass switch. On the identical time, the precise floor space of the medicinal materials elevated, which was additionally conducive to the diffusion of the lively ingredient. It may be seen from Fig. 4a,b that the focus of SAB elevated at first when the particle dimension of the salvia medicinal items was bigger, then step by step tended to succeed in equilibrium after a sure time period. The content material of lively substances in medicinal supplies from completely different sources was fairly completely different, and due to this fact the focus of the extract was additionally completely different after they have been in equilibrium. On the entire, the impregnation equilibrium will be achieved in a comparatively brief time period, and even 5–10 mesh medicinal supplies can mainly attain the impregnation equilibrium inside 5 h.

Because the 24–50 mesh and 50–65 mesh medicinal supplies stability rapidly, solely the 5–10 mesh and 10–24 mesh medicinal supplies have been used for kinetic mannequin becoming. The kinetic mannequin becoming outcomes of the three batches of medicinal supplies have been proven in Desk 3. It may be seen from Desk 3 that for the impregnation curves of *Salvia miltiorrhiza* with completely different batches and completely different particle sizes, the becoming impact of every kinetic mannequin was comparatively good, and the R^{2} obtained by most fittings was higher than 0.90, amongst which the Diffusion mannequin had the most effective becoming impact. In truth, we are able to discover that the typical R^{2} of Peleg’s mannequin and the Diffusion mannequin is comparatively shut, indicating that each fashions can match kinetic curves properly. Nevertheless, contemplating that the bodily which means of the Diffusion mannequin parameters is extra express (the place ({D}_{eff}) is the obvious diffusion coefficient), the Diffusion mannequin was lastly chosen. The curve obtained from the becoming was proven in Fig. 4, and the parameter values obtained from the becoming have been proven in Desk 4. It may be seen that the becoming parameters of the identical batch of medicinal supplies of various particle sizes have been comparatively shut, which indicated that the batch of medicinal supplies is a crucial issue affecting the maceration course of.

### Percolation curve

Based on Desk 2, the obtained single-factor percolation experiment outcomes have been proven in Fig. 5. It may be seen from Fig. 5 that when the particle dimension was bigger, the diffusion resistance of the elements within the medicinal particles was comparatively giant. Due to this fact, the diffusion fee of SAB was sluggish, the focus of the percolation curve decreased extra slowly, and the time required to realize the identical goal yield was longer. When the percolation stream fee was bigger, the focus of percolation curve decreases quicker, and the extraction pace was larger. The mass of the medicinal materials primarily affected the ultimate SAB yield however had no apparent impact on the reducing pace of the percolation curve. For various batches of *Salvia miltiorrhiza*, the upper the SAB content material per unit mass, the upper the ultimate yield. This confirmed that the percolation technique of *Salvia miltiorrhiza* was affected by a number of elements.

### Willpower of SAB content material in medicinal supplies

On this work, the content material of SAB in *Salvia miltiorrhiza* was decided by ultrasonic extraction and a number of impregnation strategies. The content material of SAB in some batches of medicinal supplies measured by ultrasonic extraction technique and a number of dipping technique was proven in Desk 5. The outcomes of ultrasonic extraction technique and a number of impregnation technique had little distinction. In contrast with the a number of impregnation technique, the ultrasonic extraction technique was easier and fewer time-consuming. Due to this fact, the content material of SAB in *Salvia miltiorrhiza* was decided by ultrasonic extraction technique. From the measurement outcomes, the content material of SAB in numerous batches of medicinal supplies varies drastically, however the particle dimension had little impact on the utmost extraction quantity of SAB. This implies that if the extraction time is longer, we are able to nonetheless obtain a passable extraction impact with out utilizing smaller particle sizes.

### Willpower of *D*

_{is} of medicinal supplies

*D*

Based on Components (3), the* D*_{is} of various batches of *Salvia miltiorrhiza* with completely different particle sizes have been calculated as proven in Desk 6. It may be seen from Desk 6 that the *D*_{is} of SAB in numerous batches and completely different particle sizes of *Salvia miltiorrhiza* within the immersion stage have been related, mainly between 1.1 and 1.35. There was a sure hole within the *D*_{is} of medicinal supplies between completely different batches, however the common worth is between 1.15 and 1.30. Amongst completely different particle sizes in the identical batch, the *D*_{is} elevated barely with the lower of particle dimension. Below the identical particle dimension in the identical batch, the general distinction of the *D*_{is} of medicinal supplies measured by completely different strong–liquid ratios was small. As a result of small change of the *D*_{is}, with a view to simplify the mannequin parameters, the typical worth of the *D*_{is} of every batch of 10–24 mesh medicinal supplies was 1.21 to foretell the *D*_{is} worth of the next percolation course of.

### Willpower of SAB focus on the preliminary time of percolation

Based on the impregnation kinetic knowledge in 3.1, the time to succeed in equilibrium was comparatively brief in the course of the impregnation of *Salvia miltiorrhiza*, and the preliminary time of dynamic percolation will be thought to be the impregnation equilibrium time. Due to this fact, Components (15) will be derived and calculated in accordance with Formulation (4) and (5). The expected worth ({C}_{w}^{0}) on the preliminary second of the single-factor experiment of percolation was obtained. On the identical time, the relative error *RE* of its prediction was calculated in accordance with Components (16).

$${C}_{w}^{0}=frac{{M}_{0}m}{{D}_{is}{V}_{s}+{V}_{w}}$$

(15)

$$RE=frac{left|widehat{{y}_{i}}-{y}_{i}proper|}{{y}_{i}}instances 100mathrm{%}$$

(16)

The experimental worth and predicted worth on the preliminary time of the single-factor percolation experiment predicted by Components (15) have been proven in Fig. 6, and *RE* worth was 5.8%. General, the anticipated worth of the SAB focus on the preliminary time of percolation was not a lot completely different from the precise worth, and the relative error was lower than 10%, indicating that the prediction technique was possible. Though the medicinal supplies have been immersed within the percolation column and couldn’t be shaken just like the immersion kinetics check, the strong–liquid equilibrium was mainly achieved as a result of lengthy immersion time.

### Figuring out the particle dimension of the medicinal materials, the mattress layer voidage , and the enlargement coefficient of the medicinal materials

On this examine, various kinds of sieves have been used to differentiate the particle dimension of the Chinese language medicinal powder. Due to this fact, in accordance with the scale of the mesh, the typical worth of the mesh diameter of the mesh was taken because the particle dimension of the medicinal materials, which have been 0.3 cm (5–10 mesh), 0.1425 cm (10–24 mesh), 0.0603 cm (24–50 mesh). After the percolation, the water in percolation column was obtained by filtration, the quantity was measured, and the ratio of the water to the full quantity of the percolation column was thought to be the mattress layer voidage. When predicting the percolation curve, the full top* H* of the percolation column must be identified. Due to this fact, in accordance with the 9 teams of single issue experiments in Desk 2, the enlargement coefficient *α* of the medicinal materials (the quantity of the medicinal materials per unit weight after the medicinal materials was absolutely swelled) was calculated. The amount within the percolation cylinder after swelling, after which roughly predicts the full top *H* of the percolation column throughout percolation. Amongst them, the enlargement coefficient of medicinal supplies is calculated by Components (17).

$$alpha =frac{pi {d}^{2}hvarepsilon }{4m}$$

(17)

the place, *d* represents diameter of seepage tube. *H* was calculated by Components (18).

$$H=frac{4malpha }{(1-varepsilon )pi {d}^{2}}$$

(18)

The *ε* and α of the medicinal supplies measured within the single-factor percolation experiment obtained in accordance with Desk 2 have been proven in Desk 7. It may be seen from Desk 7 that beneath completely different batches and experimental circumstances, the *ε* was not a lot completely different, which was round 0.3–0.4, and the *α* is usually between 3.5 and 4.5. To be able to simplify the calculation, each the voidage and the enlargement ratio coefficient of medicinal supplies have been taken as common values, which have been 0.37 and three.81, respectively, and have been set as mounted values within the subsequent prediction calculation.

### Willpower of the calculation formulation of mass switch coefficient and axial diffusion coefficient

From the evaluation in Fig. 2, it may be seen that the leaching of elements in *Salvia miltiorrhiza* primarily consists of two steps, one was the mass switch from the within of the medicinal materials to the floor of the medicinal materials, and the opposite was diffusion from the medicinal materials floor to the answer. Due to this fact, when calculating, the mass switch coefficient (*Okay*_{x}) will be divided into inner mass switch coefficient (*okay*_{int}) and exterior mass switch coefficient (*okay*_{ext}*)*. The calculation components was listed as Components (19)^{16}.

$${Okay}_{x}={ left[frac{1}{{k}_{int}}+frac{1}{{k}_{ext}}right]}^{-1}$$

(19)

The components for calculating the inner mass switch coefficient was proven in Components (20)^{16}. The worth of *D*_{eff} will be calculated in accordance with the (frac{{D}_{eff}}{{r}^{2}}) worth of *Salvia miltiorrhiza* dipping by becoming. The typical worth of *D*_{eff} in 5–10 mesh was 1.073 × 10^{–8} m^{2}/min, and the typical worth of *D*_{eff} in 10–24 mesh was 1.104 × 10^{–8} m^{2}/min. The 2 values have been related, and due to the simplicity of the calculation, the typical will be taken 1.089 × 10^{–8} m^{2}/min.

$${okay}_{int}=frac{5{D}_{eff}}{r}$$

(20)

There have been many experiences in regards to the exterior mass switch coefficient. A number of extensively used mass switch coefficient formulation proven in Desk 8 have been chosen for trial becoming, and the extra appropriate exterior mass switch coefficient components was chosen from them.

Within the desk, *Sh* was the Sherwood quantity, which was calculated by Components (21). *Sc* was the Schmidt quantity, which was calculated by Components (22). *Re* was the Reynolds quantity, which was calculated by Components (23).

$$Sh=frac{2{okay}_{ext}r}{{D}_{m}}$$

(21)

$$Sc=frac{mu }{rho {D}_{m}}$$

(22)

right here, *ρ* was answer density, *μ* was viscosity coefficient.

$${R}_{e}=frac{2rho {u}_{0}r}{mu }$$

(23)

*D*_{m} was molecular diffusion coefficient of solute, the calculation technique of which will be seen in supplementary materials. The calculation consequence was 5.83 × 10^{–10} m^{2}/s.

The Matlab was used for calculation, and the calculation outcomes of 9 teams of single-factor percolation experiments utilizing completely different calculation formulation for *Okay*_{ext} have been proven in Desk 9.

As proven in Desk 9, the mass switch coefficient values calculated by completely different formulation have been fairly completely different, and the order of magnitude spans from 10^{–3} to 10^{–5} m/min. Amongst them, the Wilson and Geankoplis components calculated the biggest worth, and the Wakao and Funazkri components calculated the smallest worth. When the 9 teams of single issue experiments have been calculated with the identical components, there was no vital distinction within the experimental values of the 5 teams E1–E3, E8, and E9, which proved that the batch of medicinal supplies and the standard of medicinal supplies had no nice affect on the *Okay*_{ext}. The experimental outcomes of E1, E4 and E5 teams confirmed that the worth of *Okay*_{ext} will increase with the rise of percolation stream fee. The experimental outcomes of E1, E6 and E7 confirmed that the *Okay*_{ext} elevated with the lower of particle dimension. It was proved that the percolation flowrate and the particle dimension of the medicinal items have been the principle elements affecting the *Okay*_{ext}. The calculation of the *D*_{ax} was fitted with the components in Desk 10.

The place, the calculations components of Peclet quantity (*Pe*) was proven in Components (24).

The calculation outcomes of 9 teams of single-factor percolation experiments utilizing completely different axial diffusion coefficient calculation formulation have been proven in Desk 11.

It may be seen from Desk 11 that the *D*_{ax} calculated by the Athayle components was bigger, and the calculation outcomes of the opposite 4 formulation have been related, all inside the order of magnitude of 10^{–5}–10^{–6}. From the calculation outcomes obtained by 9 teams of single issue experiments utilizing the identical components, the *D*_{ax} values of the 5 teams of E1, E2, E3, E8, and E9 have been related, indicating that the standard of the medicinal materials and the batch of medicinal supplies had completely different *D*_{ax}, whose impact was comparatively small. Nevertheless, the *D*_{ax} values of the three teams of experiments E1, E4, and E5 have been completely different. With the rise of percolation stream fee, the *D*_{ax} elevated. The *D*_{ax} values of the three teams of experiments E1, E6 and E7 elevated with the rise of the particle dimension of the medicinal items. To sum up, it confirmed that the percolation flowrate and the particle dimension of the medicinal items had a comparatively giant affect on the *D*_{ax}.

To be able to additional display the suitable *okay*_{ext} and *D*_{ax}, the formulation of various* Okay*_{ext} and *D*_{ax} have been mixed in pairs and substituted into 9 teams of single-factor percolation experiments for prediction. The typical R^{2} obtained in 9 teams of experiments for various components mixtures was proven in Desk 12.

As proven in Desk 12, the fitted consequence R^{2} obtained within the desk was the typical worth of the fitted R^{2} of 9 teams of single-factor percolation experiments. The mix of Wilson and Geankoplis and Koch and Brady components have been extra appropriate for the *okay*_{int} within the *Salvia miltiorrhiza* percolation experiment and calculation of the* D*_{ax}.

The calculation outcomes of the above varied parameters have been substituted into 9 teams of *Salvia miltiorrhiza* single-factor percolation experiments. The outcomes have been proven in Fig. 5. The expected curves have been just like the precise curves, and R^{2} was higher than 0.94, which proved that the established mechanism mannequin had a great prediction impact and was extra dependable.

### Sensitivity evaluation of seepage parameters

To be able to measure the affect of measurement errors of various parameters on the ultimate prediction impact, the sensitivity evaluation of percolation parameters was carried out on this examine, together with *r*, *ε*, *D*_{is}, *okay*_{int}, *okay*_{ext}, *D*_{ax}. Taking the parameter values obtained from the E1 percolation experiment for instance, the measured values of various parameters and the set error ranges have been proven in Desk 13. Sensitivity evaluation was carried out with Matlab, and 10,000 simulations have been carried out on the percolation technique of *Salvia miltiorrhiza*. Throughout the simulation, the measurement or calculation errors inside the vary proven in Desk 13 have been randomly generated, and the percolation technique of *Salvia miltiorrhiza* was predicted in accordance with these random experimental errors.

The scatter diagram between every course of parameter and R^{2} have been proven in Fig. 7, and the correlation coefficient values have been proven in Desk 14. In Fig. 7a–f, the distribution legislation of the scatter factors in Fig. 7f was the obvious. The higher fringe of the scatter diagram was easy, indicating that the *D*_{is} had the best affect on R^{2}. When the *D*_{is} was between 1.0 and 1.2, R^{2} was the very best and the variation vary was small. When the *D*_{is} was between 1.2 and 1.3, R^{2} decreased with the rise of the *D*_{is}.

It may be seen from Desk 14 that the correlation coefficients between the 5 parameters of *r*, *ε*, *D*_{is}, *okay*_{int}, *okay*_{ext}, *D*_{ax} and R^{2} of the fitted outcomes have been all vital (*P* worth < 0.01). The correlation coefficients between the three parameters of *ε*, *okay*_{ext}, *D*_{is} and R^{2} have been all unfavorable numbers, indicating that when the measured values of *ε*, *okay*_{ext}, *D*_{is} have been smaller, R^{2} was bigger. The correlation coefficient between the three parameters of *r*, *D*_{ax}, *okay*_{int} and R^{2} was a constructive worth, indicating that when the measured values of *r*, *D*_{ax}, *okay*_{int} have been bigger, R^{2} was bigger. Among the many six parameters, absolutely the values of the relative coefficients of *r*, *ε*, *okay*_{int}, *okay*_{ext}, *D*_{ax} have been all between 0.1 and 0.2, whereas absolutely the worth of the relative coefficient of the *D*_{is} reached 0.8, indicating that the *D*_{is} had an excellent affect on R^{2}.

### Calculation of design area

The design area was calculated. The analysis index was set as the ultimate focus of percolation was lower than 0.1 mg/g, and the yield of SAB was higher than 1700 mg. Based on the earlier experimental outcomes, some experimental parameters have been mounted within the design area calculation, the enlargement coefficient of medicinal supplies was mounted at 3.81, the mattress layer voidage was mounted at 0.37, and the quantity partition coefficient was mounted at 1.21. The properties of the medicinal supplies, the vary of parameters, and the vary of parameter disturbance in the course of the calculation are proven in Desk 15. Every experimental level was repeatedly calculated 100 instances to calculate the likelihood of reaching the usual. When the likelihood of reaching the usual exceeds 0.9, the mixture of properties and parameters of the medicinal materials is taken into account to be inside the design area. The design area was calculated in accordance with the properties of medicinal supplies (particle dimension of medicinal items and content material of SAB) and course of parameters (percolation stream fee, dosage of medicinal supplies), as proven in Fig. 8.

To be able to confirm the reliability of the design area, factors have been chosen inside and outdoors the design area for verification, and the brand new batch A5 was chosen for the experiment. The precise verification experimental circumstances are proven in Desk 16 and Fig. 8g–h, and the outcomes have been proven in Desk 17. The outcomes confirmed that the measured values obtained by the three units of verification experiments have been near the anticipated values, indicating that the mannequin had good predictability and the constructed design area was extra dependable.