CN113624836A - Prediction model for adsorbing/desorbing fruit polyphenol by spherical porous medium and application thereof - Google Patents

Abstract

The invention relates to a polyphenol adsorption/analytical model related technology, in particular to a prediction model for the adsorption/desorption of fruit polyphenols by a spherical porous medium and its application. The present invention takes into account the changes in the properties of porous media, including average pore size, surface area, density and porosity, and numerically studies the mass transfer mechanism of ultrasonic-enhanced porous media adsorption and desorption in combination with a diffusion model, thereby establishing a scientific ultrasonic-enhanced porous media separation The adsorption model and desorption model of purified polyphenols are used to predict the purification efficiency of polyphenols.

Description

Prediction model for adsorbing/desorbing fruit polyphenol by spherical porous medium and application thereof

Technical Field

The invention relates to a polyphenol adsorption/desorption model correlation technique, in particular to a prediction model for adsorbing/desorbing fruit polyphenol by a spherical porous medium and application thereof.

Background

Since polyphenols have various biological activities such as anti-inflammation and anti-oxidation, processing plant polyphenol extracts into commercial products is an important way to utilize plant materials, and both academia and industry have made many efforts to recover polyphenols from plant resources. In order to obtain high purity phenols from plant materials, it is generally necessary to perform solvent extraction, purification, concentration, and drying procedures. Purification is a crucial step in this series of processes, which directly determines the economic value of the phenolic extract.

Adsorption and desorption using porous media as an adsorbent is a simple and effective purification method. However, the conventional adsorption and desorption processes take a long time and have low recovery rate. Therefore, there is a need to improve the purification process of phenolic compounds by continuously improving the adsorption and desorption processes.

The frequency range of ultrasonic waves is 20 to 100kHz, and is widely applied to various processing fields including food processing. In recent years, ultrasound has been increasingly used for adsorption and desorption processes, the mechanical and cavitation properties of which can enhance the adsorption and desorption processes of porous media for polyphenols, pigments, metal ions and various organic contaminants. Currently, much of the research on ultrasound assisted adsorption and desorption focuses on the effect of ultrasound on adsorption/desorption kinetics, modeling kinetic data using simple models to analyze adsorbent characteristics. And few researches are made on the mass transfer mechanism of the ultrasonic enhanced phenolic compound in the adsorption and desorption processes.

And a series of mechanism problems involved in the adsorption and desorption processes of polyphenol on the porous material can be described by a mathematical expression and the influence of ultrasonic on the adsorption and desorption mechanisms can be evaluated. The adsorption/desorption process based on the diffusion phenomenon is simulated by combining the diffusion theory with numerical simulation. In the prior art, research and prediction models about mass transfer mechanisms of ultrasonic enhanced adsorption/desorption are rarely reported.

On the other hand, the cavitation effect of ultrasound to alter the properties of the adsorbent has been widely recognized, particularly as an effect on the particle size of the adsorbent. Thus, both the mass transfer distance and the mass transfer related surface area may change during sonication, and current diffusion models do not account for variations in the particle size and surface area of the adsorbent in simulating an ultrasonically enhanced adsorption/desorption process.

Disclosure of Invention

The invention aims to provide a prediction model for adsorbing/desorbing fruit polyphenol by a spherical porous medium and application thereof, develops a model capable of realizing rapid prediction by deeply researching a mass transfer mechanism and the change of the characteristics of an adsorbent, has small model error and has guiding significance for the research and application of adsorbing polyphenol by an ultrasonic reinforced porous medium.

The invention can research the mass transfer mechanism of the ultrasonic reinforced porous medium adsorption and desorption process through the numerical value of the diffusion model. Changes in resin properties, including average pore size, surface area, density and porosity during sonication were monitored and combined with a surface diffusion model to simulate an ultrasonically enhanced adsorption process. In addition, the desorption process can be simulated by utilizing a universal diffusion model with resin characteristic change, so that the results of adsorbing and desorbing polyphenol by using the ultrasonic enhanced porous medium can be predicted.

In order to achieve the purpose, the specific method of the invention is as follows:

a prediction model for adsorbing/desorbing fruit polyphenol by using a spherical porous medium comprises the following adsorption models:

wherein:

ε_p: porosity of the porous media;

q_m: maximum adsorption capacity (mg/g) of the porous medium as determined by the Langmuir model;

b: langmuir constant (L/mg);

q_A: the real-time adsorption amount (mg/g) of polyphenol per gram of porous medium;

ρ_p: apparent density of porous media (g/mL);

t: a time(s);

x: radial distance (cm), which refers to the length of a point of the porous medium to be measured from the center of the sphere;

D_ep: effective pore volume diffusion coefficient (cm) upon adsorption²/s)；

D_s: suction deviceSurface diffusion coefficient (cm) at time of attachment²/s)；

Initial conditions: t is 0, q _A0 formula II

Boundary conditions:

r: an average radius (cm) of the porous medium;

k_L: liquid external mass transfer coefficient (cm/s);

C_A，L: the real-time total phenol concentration (mg/L) in the solution during the adsorption process; that is, in the adsorption process, the mass mg of polyphenol contained in the solution/the volume L of the adsorption solution;

C_A，S: the concentration of total phenol (mg/L) in the porous media in real time during adsorption. That is, in the adsorption process, the mass mg of polyphenol contained in the porous medium/the volume L of the adsorption solution;

preferably, the parameter q in the adsorption model_mAnd b is obtained by the following method:

measuring isothermal adsorption data of polyphenol adsorption amount per gram of porous medium at different ultrasonic intensities and temperatures along with solution concentration change at equilibrium, and substituting the obtained data into a model shown in formula 10 to obtain q_mAnd b:

q_A,e: the mass (mg/g) of polyphenol adsorbed per gram of porous medium in equilibrium;

q_m: maximum adsorption capacity (mg/g) of the porous medium as determined by the Langmuir model;

b: langmuir constant (L/mg);

C_A，L，e: in solution at equilibriumTotal phenol concentration (mg/L).

C in formula IV after obtaining the isothermal adsorption curve_A,SCan use q_AIs shown, i.e.

At the same time, C is mixed_A,LFitting linearly or non-linearly with time (t) to fit C in formula IV_A,LExpressed in time.

Preferably, said C_A,LThe fitting model with time t is C_A,L＝K₁×exp(K₂*t)+K₃exp(K₄T), wherein K₁、K₂、K₃、K₄Is a constant obtained by fitting according to the actual measurement result.

Preferably, the parameter K in the boundary condition in the adsorption model_LObtained by the following method:

C_A，L: the real-time total phenol concentration (mg/L) in the solution during the adsorption process;

C_A，L，0: initial concentration of total phenol in solution during adsorption (mg/L);

t: a time(s);

m: porous medium mass (g);

s: external surface area per unit mass (cm) of porous medium²/g)；

k_L: liquid external mass transfer coefficient (cm/s);

v: volume of solution (mL);

the calculation mode of S is as follows:

s: external surface area per unit mass (cm) of porous medium²/g)；

R: an average radius (cm) of the porous medium;

ρ_p: apparent density of porous media (g/mL);

said D_epThe calculation method of (c) is as follows:

preferably, the parameter D in the boundary condition in the adsorption model_epObtained by the following method:

D_ep: effective pore volume diffusion coefficient (cm) upon adsorption²/s)；

ε_p: porosity of the porous media;

τ: the tortuosity factor of the porous media;

D_AB: total phenol molecular diffusion coefficient (cm)²/s)；

D_ABThe values are calculated as follows:

D_AB: total phenol molecular diffusion coefficient (cm)²/s)；

T: solution temperature (K);

: solvent hydration coefficient; the hydration coefficient herein refers to the ratio of the number of water molecules to the number of gas molecules in the natural gas hydrate crystal.

M_B: molecular weight of water (g/mol);

η_B: viscosity of water (cP) at a target temperature;

V_A: molecular volume (cm) of polyphenol³Mol). This value is a value summarized by looking up a lot of data. There are many polyphenols including chlorogenic acid, gallic acid, anthocyanins, etc., and we cannot measure the volume of each polyphenol molecule and therefore can only look for experienceThe value is obtained. We believe that 7.345 x 10 is present in the mixed polyphenol system of Sorbus commixta and Vitis vinifera^-18This value is universal. Of course, if the polyphenol is replaced by other polyphenol materials and only one or more polyphenols with large difference from the grapes and the black chokeberries are contained in the other polyphenol materials, the corresponding molecular volume value or empirical value of the polyphenol can be inquired to replace 7.345 x 10^-18。

Preferably, the porous medium has a porosity ε_pThe calculation method of (2) is as follows:

ε_p: porosity of the porous media;

ρ_p: apparent density of porous media (g/mL);

ρ_s: and the tap density (g/mL) of the porous medium.

More preferably, the analytical model of the prediction model is as follows:

C_D，S: real-time total phenol concentration (mg/L) in the porous medium during desorption; namely the ratio of the mass mg of the real-time contained polyphenol in the porous medium to the volume L of the analytic solution;

t is time(s);

x is the radial distance (cm) which refers to the length of a point of the porous medium to be measured from the center of the sphere;

D_e: molecular diffusion coefficient (cm) upon desorption²/s)；

Initial conditions:

t＝0，C_D,S＝C_D,S,0，C _D,L0 formula VI

C_D,S,0: initial concentration of total phenol (mg/L) in porous media during desorption

C_D，L: the real-time total phenol concentration (mg/L) in the solution during desorption, when tWhen 0, since the analysis has not yet started, C_D，LThe value of (D) is also 0.

Boundary conditions:

D_e: molecular diffusion coefficient (cm) upon desorption²/s)；

A: total surface area (cm) of porous medium²)；

C_D，L: the real-time total phenol concentration (mg/L) in the solution during desorption;

C_D，S: real-time total phenol concentration (mg/L) in the porous medium during desorption;

V_L: volume of solution on desorption (L);

t: a time(s);

x: radial distance (cm), which refers to the length of a point of the porous medium to be measured from the center of the sphere;

r: the porous medium has an average radius (cm).

At the same time, C is mixed_D,LFitting linearly or non-linearly with time (t) to fit C in formula VIII_D,LExpressed in time.

Preferably, said C_D,LThe fitting model with time t is C_D,L＝K₅*t/(K₆+ t), wherein K₅、K₆Is a constant obtained by fitting according to the actual measurement result.

The prediction model for adsorbing/desorbing the fruit polyphenol by using the spherical porous medium is applied to adsorbing/desorbing the aronia melanocarpa polyphenol.

The prediction model for adsorbing/desorbing the fruit polyphenol by using the spherical porous medium is applied to adsorbing/desorbing the grape polyphenol.

Advantageous effects

(1) The invention considers the change of the performance of the porous medium, including average aperture, surface area, density and porosity, and combines the numerical value of a diffusion model to research the mass transfer mechanism of the adsorption and desorption of the ultrasonic reinforced porous medium, thereby establishing a scientific adsorption model and desorption model of the porous medium for adsorbing polyphenol based on ultrasonic reinforcement;

(2) the model of the invention has small error and more accurate prediction, and has guiding significance for the research and application of the ultrasonic reinforced porous medium for adsorbing polyphenol.

Drawings

Figure 120 ℃ adsorption isotherm of sorbose on macroporous resin.

Figure 220 deg.C experiment value and prediction value of sorbose adsorption on macroporous resin.

Figure 320℃ under the desorption of the black chokeberry polyphenol from the macroporous resin experimental value and prediction value comparison chart.

Graph comparing the experimental value and the predicted value of grape polyphenol adsorbed on macroporous resin at 440 ℃.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

The present invention will be described in detail below with reference to the attached drawings to facilitate understanding of the present invention by those skilled in the art.

EXAMPLE 1 raw Material preparation

Extracting polyphenol from fresh Sorbus commixta with 50% ethanol solution to obtain crude polyphenol extract. Then removing ethanol by rotary evaporation to obtain polyphenol extractive solution. Macroporous resin XAD-7HP (60-80 mesh, Solarbio technologies, Inc.) is sequentially subjected to 95% ethanol elution, deionized water elution, 4% hydrochloric acid elution, deionized water elution, 5% sodium hydroxide elution and deionized water elution for activation.

Example 2 ultrasound-assisted adsorption and desorption kinetics

In a constant temperature water bath device equipped with a turbine, adsorption and desorption experiments are carried out under the action of ultrasonic waves with certain intensity.

For adsorption experiments, 0.5g of the activated resin of example 1 and 50mL of the polyphenol extract (i.e., the aqueous polyphenol solution obtained in example 1) were first mixed together in a 100mL flask. The flask was then moved to a water bath system and an ultrasonic probe (frequency 20kHz, 1cm diameter) was inserted into the vessel to periodically measure the total phenol concentration in the solution.

When the desorption treatment is performed, the macroporous resin activated in example 1 is soaked in a 20 ℃ sorbus nigra polyphenol extract (i.e., a polyphenol aqueous solution), and is shaken in a water bath for 24 hours, and finally, the polyphenol content on the macroporous resin after the adsorption is finished is measured to be 2.758mg/g (the mass mg of polyphenol in the resin/the mass g of resin). Then, 0.5g of the whole macroporous resin having sorbosol adsorbed thereto was mixed with 50mL of 80% ethanol solution in a 100mL flask. The flask was placed in a water bath system and the same ultrasonic probe was extended into the vessel (frequency 20kHz, diameter 1 cm). The total phenol concentration in the solution was measured periodically.

The adsorption and desorption processes were performed at sonic energy densities of 106W/L and 279W/L, respectively, and shaking (i.e., no sonication) was used as a control.

The adsorption and desorption amounts of polyphenols were calculated as follows

q_A: the real-time adsorption amount (mg/g) of polyphenol per gram of porous medium;

C_A，L，0: initial concentration of total phenol in solution during adsorption (mg/L);

C_A，L，t: the concentration of total phenols in the solution after adsorption for t time (mg/L);

q_D: the amount of polyphenol desorbed by the porous medium (mg/g);

C_D，L，t: the total phenol concentration (mg/L) in the solution after desorption t time;

C_D，L，0: initial total phenol concentration (mg/L) in solution during desorption;

m: the total mass (g) of the porous medium, in this example 0.5 g;

v: volume of solution (mL); in this example 50 ml.

According to the above equations 8 and 9 and the actually measured C_A，L，0、C_A，L，t、C_D，L，t、C_D，L，0And (3) calculating the adsorption and desorption capacity of the macroporous resin on the aronia melanocarpa polyphenol.

TABLE 1 Experimental adsorption of polyphenols on Sorbus commixta by macroporous resin under different conditions

The table above shows the adsorption amount q per gram of porous medium at different adsorption times under various conditions calculated according to the formula shown in formula 8_AThe unit of the adsorption amount of the porous medium is mg/g, namely, how many mg of polyphenol is adsorbed per 1g of the porous medium.

TABLE 2 Experimental desorption of Sorbus commixta polyphenols from macroporous resins under different conditions

Table 2 shows the analytical amounts q of the porous media at different adsorption times under various conditions calculated according to the formula shown in formula 9_DThe desorption amount of the porous medium is expressed in mg/g, that is, how many mg of polyphenol is desorbed per 1g of the porous medium.

Example 3 establishment of isothermal adsorption Curve

Preparing aqueous solution of aronia melanocarpa polyphenol extract with concentration of 50mg/L, 100mg/L, 150mg/L, 200mg/L and 250mg/L respectively by dilution and concentration. Then, 0.5g of macroporous resin and 50mL of polyphenol extract at different concentrations were mixed at 20 ℃ and under ultrasonic intensity of 106 and 279W/L, respectively.

Sonication was carried out for 5h to reach adsorption equilibrium. The total phenol concentration in the solution at equilibrium is then determined and the amount of adsorbed polyphenol per gram of porous media at equilibrium is calculated. At the same time, an adsorption isotherm was established under 100rpm water bath shaking. The resulting isothermal adsorption curves under various conditions at 20 ℃ are shown in FIG. 1. FIG. 1 is a graph with the abscissa representing the concentration C of sorbosone in the solution at equilibrium_A，L，e(mg/L), and the adsorption capacity q of the macroporous resin to the sorbosone when the ordinate is in an equilibrium state_A,e(mg/g), i.e., the mass mg of sorbus nigromaculata polyphenol adsorbed on the macroporous resin per gram, wherein

Representing balance value points under the condition of 279W/L ultrasonic intensity from left to right

Under the condition, the concentration of the sorbus pohuashanensis polyphenol in the solution and the adsorption capacity of the macroporous resin correspond to the concentration when the sorbus pohuashanensis polyphenol extract aqueous solution with the initial concentration of 50mg/L, 100mg/L, 150mg/L, 200mg/L and 250mg/L reaches the equilibrium. The other symbols are analogized in turn.

Fitting the obtained experimental data to a Langmuir isothermal model shown in formula 10 to obtain q under different ultrasonic conditions_mAnd b, the fitting results and the fitting accuracy are shown in Table 3.

q_A,e: the mass (mg/g) of polyphenol adsorbed by the porous medium during the balance;

q_m: maximum adsorption capacity (mg/g) of the porous medium as determined by the Langmuir model;

b: langmuir constant (L/mg);

C_A，L，e: total phenol concentration in solution (mg/L) at equilibrium.

Wherein q is_A,e＝(C₀-C_A,L,e)×V/m，C₀The concentration of the aronia melanocarpa polyphenol extract aqueous solution is 50mg/L, 100mg/L, 150mg/L, 200mg/L and 250mg/L, V is 50mL, and m is 0.5 g.

TABLE 3 Langmuir isothermal model constants and fitting accuracy for macroporous resin adsorption of sorbosol polyphenol

The continuous solid line or broken line curve in FIG. 1 represents C obtained by substituting the constant under the above-mentioned different conditions into formula 10_A，L，eAnd q is_A,e(mg/g) in the graph.

As can be seen from fig. 1, the adsorption isotherm of the ultrasonic-assisted adsorption is always above the adsorption isotherm of the oscillatory adsorption, indicating that the ultrasonic wave can promote the attachment of polyphenols on the macroporous resin. The experimental data were fitted to a Langmuir isotherm model. Under 279W/L sound wave, the adsorption amount of polyphenol approaches a limited value along with the increase of polyphenol in the balance, and under 106W/L sound wave and oscillation conditions, the adsorption amount of macroporous resin is continuously increased.

Example 4 analysis of macroporous resin Properties under sonication

And measuring the particle size distribution of the macroporous resin sample in the ultrasonic-assisted adsorption process by using a laser diffraction particle size analyzer so as to obtain the average particle size of the resin particles.

Measuring apparent density (rho) of macroporous resin particles by adopting a volume displacement method_p) And tap density (ρ)_s) The measurement is made in terms of apparent density and pore volume. Porosity (. epsilon.) of macroporous resin_p) The estimation is performed using equation 5.

ε_p: porosity of the porous media;

ρ_p: apparent density of porous media (g/mL);

ρ_s: and the tap density (g/mL) of the porous medium.

Rho of the porous Medium used in this example_p＝0.4849g/mL，ρ_s＝0.7339g/mL。

Example 5 Mass transfer modeling

The mass transfer model takes into account penetration of the polyphenol through the liquid film around the macroporous resin, intraparticle diffusion and adsorption on the active sites on the surface of the pores to simulate the adsorption process. For intraparticle diffusion, both diffusion in the pore volume and surface diffusion are considered. Thus, the diffusion model is commonly referred to as pore volume and surface diffusion model. Furthermore, it is assumed that the macroporous resin is spherical and isotropic and that the ultrasound induced vibrations cause the suspension to mix homogeneously. The main equation for the adsorption process can be written as equation I, with initial and boundary conditions of II, III, IV. Wherein k is_LDep is obtained according to formula 1 and formula 3.

Wherein:

ε_p: porous media porosity, which has been calculated for the foregoing example 4;

q_m: maximum adsorption capacity (mg/g) of porous media determined by the langmuir model, which value has been calculated for different conditions in the foregoing example 3;

b: langmuir constant (L/mg), which has been calculated for different conditions in the foregoing example 3;

q_A: the mass (mg/g) of polyphenol adsorbed by the porous medium in real time; i.e. the value to be predicted by the present invention;

ρ_p: the apparent density (g/mL) of the porous medium, which has been calculated in example 4 above;

t: a time(s);

x: a radial distance (cm);

D_ep: effective pore volume diffusion coefficient (cm) upon adsorption²(s) calculated by using the formula shown in the following formula 1;

D_s: surface diffusion coefficient (cm) at the time of adsorption²/s)；

Initial conditions: t is 0, q _A0 formula II

Boundary conditions:

r: average radius (cm) of the porous medium, and R of the porous medium in this example was 0.01cm as measured by a particle size analyzer;

k_L: a liquid external mass transfer coefficient (cm/s) determined by the formula shown in the following formula 1;

C_A，L: the real-time total phenol concentration (mg/L) in the solution during the adsorption process;

C_A，S: the concentration (mg/L) of total phenol in the porous medium in real time during the adsorption process; namely, in the adsorption process, the mass mg of the total phenol adsorbed in the porous medium in real time/the volume L of the adsorption solution;

C_A，L: the real-time total phenol concentration (mg/L) in the solution during the adsorption process;

C_A，L，0: initial concentration of total phenol in solution during adsorption (mg/L);

t: a time(s);

m: porous media mass (g), 0.5g in this example;

s: external surface area per unit mass (cm) of porous medium²The calculation mode is shown as formula 2;

k_L: liquid external mass transfer coefficient (cm/s);

v: volume of solution (mL), 50 mL;

the calculation mode of S is as follows:

s: external surface area per unit mass (cm) of porous medium²/g)；

R: an average radius (cm) of the porous medium;

ρ_p: apparent density of porous media (g/mL);

wherein R in the invention is 0.01cm

Said D_epThe calculation method of (c) is as follows:

D_ep: effective pore volume diffusion coefficient (cm) upon adsorption²/s)；

ε_p: porosity of the porous media;

τ: the tortuosity factor of the porous media;

D_AB: total phenol molecular diffusion coefficient (cm)²/s)；

Where τ of the porous medium used in this example is 1.4, the tortuosity factor of the porous medium of the different media is known and can be referred to.

D_ABThe values are calculated as follows:

D_AB: total phenol molecular diffusion coefficient (cm)²/s)；

T: temperature of solution (K)

: solvent hydration coefficient (in this example, the solvent is water when adsorbing, so this value is 2.6)

M_B: the molecular weight (g/mol) of water was 18.02.

η_B: viscosity of Water (cP) at target temperature, 1.0050cP

V_A: molecular volume (cm) of polyphenol³/mol)，7.345*10^-18. The volume of the polyphenol molecule is a value generally suitable for the polyphenol of sorbus nigra and the polyphenol of grape, and is not the molecular volume of a single polyphenol.

After obtaining the isothermal adsorption curve, C can be obtained_A,SWith q_AIs shown, i.e.

Wherein q is_mAnd b values are given in Table 3 above.

Then C is mixed_A,LFitting non-linearly with time (t) to fit C in the boundary condition_A,LExpressed in time. The equation chosen in this example is t ═ K₁×exp(K₂C_A,L)+K₃exp(K₄C_A,L) In which K is₁、K₂、K₃、K₄The values are given in the following table.

TABLE 4 constant values in the adsorption model nonlinear fitting equation

The desorption process is the transfer of the polyphenols from the macroporous resin into the eluting solvent, and the transport of the polyphenols within the resin particles can also be considered as a diffusion phenomenon. Macroporous resins are considered as intact particles and the factor for porosity is temporarily ignored. And some assumptions were made, including the spherical geometry of the resin particles, that the polyphenols were uniformly distributed in the macroporous resin before desorption and that the suspension was uniformly mixed during desorption. The desorption process was then simulated using a spherical diffusion model, with the principal equation as formula V and the initial and boundary conditions as formulas VI, VII, VIII.

C_D，S: real-time total phenol concentration (mg/L) in the porous medium during desorption; the value to be predicted by the model of the invention is the real-time total phenol mass mg in the porous medium/the volume L of the analytic solution during the analytic period;

t is time (min);

x is the radial distance (cm);

D_e: molecular diffusion coefficient (cm) upon desorption²/s)；

Initial conditions:

t＝0，C_D,S＝C_D,S,0，C _D,L0 formula VI

C_D,S,0: initial concentration of total phenol (mg/L) in the porous medium during desorption;

C_D，L: the real-time total phenol concentration (mg/L) in the solution during desorption;

boundary conditions:

D_e: molecular diffusion coefficient (cm) upon desorption²/s)；

A: total surface area (cm) of porous medium²) The total surface area is calculated as the external surface area (cm) of the porous medium per unit mass²/g) total mass of porous medium, i.e. S0.5.

C_D，L: the real-time total phenol concentration (mg/L) in the solution during desorption; namely, the ratio of the mass mg of polyphenol contained in the solution in real time to the volume L of the analysis solution during the analysis;

C_D，S: real-time total phenol concentration (mg/L) in the porous medium during desorption; namely the ratio of the mass mg of the real-time contained polyphenol in the porous medium to the volume L of the analytic solution;

V_L: the volume of solution (L) upon desorption, in this example 0.05L;

t: time (min);

x: a radial distance (cm);

r: the porous medium has an average radius (cm).

C is to be_D,LFitting with the measured value of time t to obtain a fitting equation, and predicting C in the boundary condition in the model_D,LExpressed in time. C selected in this example_D,LFitting equation with time t is C_A,L＝K₅*t/(K₆+ t), wherein K₅、K₆See table below.

TABLE 5 Desorption model C_D,LFitting constant values in an equation non-linearly to time t

In this example, it was experimentally determined that the initial concentration of polyphenol in the resin prior to resolution was 2.758mg/g (mass mg of polyphenol in resin `)Resin mass g), 0.5g of resin initially contained 1.379mg of polyphenol, then the predicted q_D＝(1.379-C_D,S0.05)/0.5, 0.05 in this formula refers to a volume of 0.05L of solution.

Example 6 model analysis

The model was solved using the pdepe function in Matlab. Iteratively modifying Ds values in adsorption model and D in desorption model_eAnd (4) until the predicted value is close to the experimental data, thus obtaining an optimal model, and the error judgment is shown in a formula:

q_A,avg: the average value (mg/g) of the polyphenol adsorption (or desorption) mass of the obtained porous medium is determined by experiments

q_A,e,i: testing the quality (mg/g) of polyphenol adsorbed (or desorbed) by porous medium

q_A,p,i: predicting the mass (mg/g) of polyphenol adsorbed (or desorbed) by porous medium

R²: determining coefficients

RMSE: root mean square error (mg/g)

E: mean relative deviation modulus (%)

Molecular diffusion coefficient (D) of adsorption and desorption experiments in examples_sAnd D_e) Is generally at 10^-5-10^-11Within the range, therefore, the Ds value and D are selected in consideration of the range_eThe value is determined by firstly determining the negative power of ten, then determining the value of one digit (1-9), and determining the first, second and third digits after the decimal point by analogy, thus obtaining the appropriate Ds value and D value quickly_eThe value is obtained.

TABLE 6 Sorbus commixta polyphenol adsorption mass transfer parameters on macroporous resin and model accuracy

As can be seen from the table above, the polyphenol adsorption model disclosed by the invention has good prediction capability.

TABLE 7 Desorption Mass transfer parameters of Sorbus commixta Polyphenol on macroporous resin and accuracy of model

As can be seen from the table above, the polyphenol analysis model disclosed by the invention has good prediction capability.

The values in the table are substituted into the adsorption and desorption amounts at different times predicted by the polyphenol adsorption model and the desorption model of the present invention, as shown in tables 8 and 9. R was calculated from the predicted values in tables 8 and 9 and the measured values in tables 1 and 2²RMSE (mg/g), E (%).

TABLE 8 Matlab Using the model of the present invention to predict the adsorption of sorbosone by macroporous resin under different conditions

TABLE 9 Matlab Using the model of the present invention to predict the amount of sorbose from macroporous resin under different conditions

FIG. 2 shows the relationship between the experimental amount (point) and the predicted amount (line) of sorbose on macroporous resin at 20 ℃. Wherein the abscissa of FIG. 2 is time min and the ordinate is real-time adsorption amount mg/g.

FIG. 3 shows the relationship between the experimental amount (point) and the predicted amount (line) of desorption of sorbosol polyphenol from macroporous resin at 20 ℃. Wherein the abscissa of fig. 3 is time min and the ordinate is real-time analysis amount mg/g.

It can be seen from the figure that with the increase of the adsorption and desorption time, the adsorption amount and the desorption amount both increase and then tend to balance, and the difference between the experimental value and the predicted value is small, which indicates that the predicted model has high precision.

The adsorption model of the present invention uses pdepe function running code in Matlab as follows:

function pdex1

m＝2；

x＝linspace(0,0.01,40)；

t＝linspace(0,300,61)；

sol＝pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t)；

u＝sol(:,:,1)

disp(u)；

a＝u

b_10＝mean(a(3,:))

b_20＝mean(a(5,:))

b_30＝mean(a(7,:))

b_45＝mean(a(10,:))

b_60＝mean(a(13,:))

b_90＝mean(a(19,:))

b_120＝mean(a(25,:))

b_150＝mean(a(31,:))

b_180＝mean(a(37,:))

b_210＝mean(a(43,:))

b_240＝mean(a(49,:))

b_270＝mean(a(55,:))

b_300＝mean(a(61,:))

surf(x,t,u)

title('Numerical solution computed with 20mesh points.')

xlabel('Distance x')

ylabel('Time t')

figure

plot(x,u(end,:))

title('Solution at t＝2')

xlabel('Distance x')

ylabel('u(x,2)')

％--------------------------------------------------------------

function[c,f,s]＝pdex1pde(x,t,u,DuDx)

c＝0.339*102500/(102500-1367*u)^2+0.734；

% c ═ porosity a/(a-b ^ q) ^2+ density

f＝(0.682*60*10^(-6)*102500/(102500-1367*u)^2+0.734*50*10^(-9))*DuDx；

% f [ Dep a/(a-b q) ^2+ Ds density ] dq/dx

s＝0；

％--------------------------------------------------------------

function u0＝pdex1ic(x)

u0 ═ 0; % initial adsorption

％--------------------------------------------------------------

function[pl,ql,pr,qr]＝pdex1bc(xl,ul,xr,ur,t)

pl＝0；

ql＝102500/(102500-1366*ul)^2；％ql＝a/(a-b*q)^2

pr＝-7.433*60*10^(-2)*(1.269*10^(-5)*exp(-0.01477*t)+4.413*10^(-5)*exp(-0.001041*t)-ur/(102500-1367*ur))；

% pr ═ k (concentration of polyphenol in concentrate-q/(a-b ×) and

qr＝0.682*60*10^(-6)*102500/(102500-1367*ul)^2+0.734*50*10^(-9)；

% qr ═ Dep ^ a/(a-b ^ q) ^2+ Ds ^ density Ds ^ 50 ^ 10 (-9) cm2/min

Example 7 prediction model of macroporous resin adsorption of grape polyphenols

50% ethanol as solvent, 30:1(mL: g) solvent: and (3) extracting polyphenol in the grape skin residue after juicing according to the grape skin residue ratio, thereby obtaining a grape polyphenol crude extract. Then removing ethanol by rotary evaporation to obtain grape polyphenol extract.

The ultrasonic intensity during adsorption was 281.3W/L, the adsorption temperature was 40 deg.C, and the control group was shaken in a water bath. The other conditions were the same as those in the above example (the viscosity of water at 40 ℃ C. was 0.6560 cP).

TABLE 10 Experimental adsorption capacity of macroporous resin for adsorbing grape polyphenols

TABLE 11 Langmuir isothermal model constants for macroporous resin adsorption of grape polyphenols

Conditions of treatment	qm(mg/g)	b×103(L/mg)	R2	RMSE
					Oscillation	387.4	0.632	0.980	2.610
281W/L ultrasonic	136.7	3.969	0.972	3.291

TABLE 12 adsorption mass transfer parameters of grape polyphenols on macroporous resins and accuracy of model

TABLE 13 prediction of adsorption capacity of macroporous resin for adsorption of grape polyphenols

The relationship between the experimental value and the predicted value of the macroporous resin for adsorbing the grape polyphenol is shown in figure 4. The point values in fig. 4 are actually measured values, the curves are the predicted values of the model of the invention, the abscissa in fig. 4 is time min, and the ordinate is the adsorption amount mg/g.

From the above experiments, the model still has high prediction accuracy for the grape polyphenol extraction process.

Claims (10)

1. A prediction model for adsorbing/desorbing fruit polyphenol by using a spherical porous medium is characterized in that the adsorption model of the prediction model is as follows:

wherein:

ε_p: porosity of the porous media;

q_m: maximum adsorption capacity (mg/g) of the porous medium as determined by the Langmuir model;

b: langmuir constant (L/mg);

q_A: the real-time adsorption amount (mg/g) of polyphenol per gram of porous medium;

ρ_p: apparent density of porous media (g/mL);

t: a time(s);

x: radial distance (cm), which refers to the length of a point of the porous medium to be measured from the center of the sphere;

D_ep: effective pore volume diffusion coefficient (cm) upon adsorption²/s)；

D_s: surface diffusion coefficient (cm) at the time of adsorption²/s)；

Initial conditions: t is 0, q_A0 formula II

Boundary conditions:

r: an average radius (cm) of the porous medium;

k_L: liquid external mass transfer coefficient (cm/s);

C_A，L: the real-time total phenol concentration (mg/L) in the solution during the adsorption process;

C_A，S: the concentration of total phenol (mg/L) in the porous media in real time during adsorption.

2. Prediction of adsorption/desorption of fruit polyphenols by spherical porous media according to claim 1Model, characterized by a parameter q in the adsorption model_mAnd b is obtained by the following method:

measuring isothermal adsorption data of polyphenol adsorption amount per gram of porous medium changing with solution concentration during equilibrium at certain temperature under different ultrasonic intensity equilibrium, and substituting the obtained data into a model shown as formula 10 to obtain q_mAnd b:

q_A,e: the mass (mg/g) of polyphenol adsorbed per gram of porous medium in equilibrium;

q_m: maximum adsorption capacity (mg/g) of the porous medium as determined by the Langmuir model;

b: langmuir constant (L/mg);

C_A，L，e: total phenol concentration in solution at equilibrium (mg/L);

obtaining an isothermal adsorption curve and q_mAnd b is the value of C in formula IV_A,SRepresented by equation 14 and substituted into the model:

at the same time, C is added_A,LLinear or non-linear fit to time t to model C in formula IV_A,LExpressed in time.

3. The predictive model for the adsorption/desorption of fruit polyphenols by spherical porous media according to claim 2, wherein C is the amount of C_A,LThe fitting model with time t is t ═ K₁×exp(K₂C_A,L)+K₃exp(K₄C_A,L) In which K is₁、K₂、K₃、K₄Are constants obtained by fitting.

4. The spherical porous media adsorption/desorption of claim 1Prediction model of fruit-attached polyphenols, characterized in that parameter K in boundary conditions in the adsorption model_LObtained by the following method:

C_A，L: the real-time total phenol concentration (mg/L) in the solution during the adsorption process;

C_A，L，0: initial concentration of total phenol in solution during adsorption (mg/L);

t: a time(s);

m: porous medium mass (g);

s: external surface area per unit mass (cm) of porous medium²/g)；

k_L: liquid external mass transfer coefficient (cm/s);

v: volume of solution (mL);

the calculation mode of S is as follows:

s: external surface area per unit mass (cm) of porous medium²/g)；

R: an average radius (cm) of the porous medium;

ρ_p: apparent density (g/mL) of the porous medium.

5. The predictive model of spherical porous media for adsorbing/desorbing fruit polyphenols according to claim 1, wherein the parameter D in the boundary condition in the adsorption model is_epObtained by the following method:

D_ep: effective pore volume diffusion coefficient (cm) upon adsorption²/s)；

ε_p: porosity of the porous media;

τ: the tortuosity factor of the porous media;

D_AB: total phenol molecular diffusion coefficient (cm)²/s)；

D_ABThe values are calculated as follows:

D_AB: total phenol molecular diffusion coefficient (cm)²/s)；

T: solution temperature (K);

solvent hydration coefficient;

M_B: molecular weight of water (g/mol);

η_B: viscosity of water (cP) at a target temperature;

V_A: molecular volume (cm) of polyphenol³/mol)。

6. The predictive model for the adsorption/desorption of fruit polyphenols according to claim 1, wherein the porosity of the porous medium is ε_pThe calculation method of (2) is as follows:

ε_p: porosity of the porous media;

ρ_p: apparent density of porous media (g/mL);

ρ_s: and the tap density (g/mL) of the porous medium.

7. A prediction model for adsorbing/desorbing fruit polyphenol by using a spherical porous medium is characterized in that an analytical model of the prediction model is as follows:

C_D，S: real-time total phenol concentration (mg/L) in the porous medium during desorption;

t is time(s);

x is the radial distance (cm) which refers to the length of a point of the porous medium to be measured from the center of the sphere;

D_e: molecular diffusion coefficient (cm) upon desorption²/s)；

Initial conditions:

t＝0，C_D,S＝C_D,S,0，C_D,L0 formula VI

C_D,S,0: initial concentration of total phenol (mg/L) in the porous medium during desorption;

C_D，L: the real-time total phenol concentration (mg/L) in the solution during desorption;

boundary conditions:

D_e: molecular diffusion coefficient (cm) upon desorption²/s)；

A: total surface area (cm) of porous medium²)；

C_D，L: the real-time total phenol concentration (mg/L) in the solution during desorption;

C_D，S: real-time total phenol concentration (mg/L) in the porous medium during desorption;

V_L: volume of solution on desorption (L);

t: a time(s);

x: radial distance (cm), which refers to the length of a point of the porous medium to be measured from the center of the sphere;

r: the porous medium has an average radius (cm).

8. The predictive model for the adsorption/desorption of fruit polyphenols by spherical porous media according to claim 7, wherein C is the amount of C_D,LThe fitting model with time t is C_D,L＝K₅*t/(K₆+ t), wherein K₅、K₆Is a constant obtained by fitting according to the actual measurement result.

9. Use of the predictive model for adsorption/desorption of fruit polyphenols on spherical porous media according to any one of claims 1 to 8 for adsorption/desorption of polyphenols from Sorbus nigra.

10. Use of the spherical porous medium predictive model for adsorption/desorption of fruit polyphenols according to any one of claims 1-8 for adsorption/desorption of grape polyphenols.

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