Response surface based method for predicting dispersion of titanium dioxide slurry

Abstract

The present application relates to the material chemical technology field, disclose a kind of titanium white initial product slurry dispersibility prediction methods based on response surface, comprising: S1, key process parameters are selected from candidate process parameters by single factor experiment;S2, with key process parameters as independent variable, slurry dispersibility index as response value, adopt response surface experimental design to construct polynomial fitting model;S3, regression analysis and variance analysis are carried out to the model, verify the significance and fitting degree of the model;S4, based on the verified model, the prediction of slurry dispersibility index or process parameter optimization is carried out.The present application can complete slurry dispersibility prediction within seconds by constructing the quantitative prediction model between process parameters and dispersibility index, change dispersibility evaluation from "post-detection" to "prior prediction", solve the problem that existing rotary viscosity detection is strong, insufficient, single information, suitable for chlorination method and sulfuric acid method titanium white initial product slurry dispersibility fast prediction and process optimization.

Description

Technical Field

[0001] This invention relates to the field of materials and chemical engineering, and more specifically, to a method for predicting the dispersibility of titanium dioxide slurry based on response surface methodology. Background Technology

[0002] In the wet surface treatment process of titanium dioxide, to ensure the consistency and uniformity of the subsequent inorganic coating, the raw titanium dioxide product needs to be pre-processed by pulping, dispersion, and sand milling to obtain a suspension slurry with good deagglomeration and near-monodispersibility. Accurate evaluation and prediction of slurry dispersibility are of great significance for optimizing the surface treatment process.

[0003] Currently, companies generally rely on offline rotational viscometer testing to evaluate the dispersibility of raw titanium dioxide slurries. This method has the following drawbacks:

[0004] First, it has a strong lag, requiring 15 to 30 minutes from sampling to completing the test. By the time the results are fed back, the slurry has already entered the downstream process, making real-time control impossible.

[0005] Secondly, the sensitivity and accuracy are insufficient. Rotational viscosity is affected by many factors such as temperature, shear rate, and rotor selection. It may not be able to respond in time when the dispersion state changes. Viscosity fluctuations may also originate from non-dispersion factors. Especially in high-salt chlorination systems, it is difficult to distinguish between the two essentially different anomalies of "salt-induced thickening" and "insufficient dispersion".

[0006] Third, the indicators are too simplistic. Good macro-level fluidity does not equate to complete particle deagglomeration. A single viscosity index cannot reflect microscopic information such as the degree of agglomeration, particle size distribution, and double-layer state, which can easily lead to inaccurate process control.

[0007] For the performance testing of titanium dioxide, existing technologies have proposed improved solutions. A search revealed Chinese patent application CN122306507A, which discloses an accurate method for determining the relative tinting strength of titanium dioxide. This method introduces a scraper fineness meter into the titanium dioxide tinting strength detection system, establishing a quantitative relationship between the fineness difference and the deviation in tinting strength measurement, and discovering a critical threshold of 10μm. However, this method primarily targets the tinting strength of finished titanium dioxide pigments, a coloring performance indicator. The test object is the finished titanium dioxide product after a complete production process, and the purpose is to evaluate the application performance of the pigment, rather than the real-time evaluation of the dispersion state of the titanium dioxide slurry before the wet surface treatment process. Furthermore, this method still falls under the category of offline testing, requiring multiple steps such as base material homogenization pretreatment, test slurry preparation, coating preparation, and multi-point testing. This also results in a long testing cycle and an inability to meet the online quality control requirements of the pulping process. In addition, this method does not involve modeling the quantitative relationship between process parameters and dispersion indicators, and cannot achieve forward-looking prediction of the slurry dispersion state under different process conditions.

[0008] Furthermore, existing optimization methods rely on extensive offline viscosity data for derivation. The inherent lag in detection, combined with low-dimensional characteristics, results in an excessively long cycle from process optimization to feedback, failing to meet the demands for rapid prediction and proactive control of slurry dispersion. In the pulping and dispersion process, the slurry dispersion is influenced by multiple factors, including TiO2 content, pH value, type and amount of dispersant, and stirring intensity. These factors interact in complex ways, and single-dimensional offline detection methods cannot systematically characterize the coupling effects between variables, making it difficult to accurately match optimal dispersion conditions during process control. Therefore, there is an urgent need to develop an evaluation method that can rapidly predict dispersibility, systematically characterize variable coupling effects, and is applicable to both chloride and sulfuric acid titanium dioxide systems.

[0009] To address these issues, this application proposes a response surface methodology-based method for predicting the dispersibility of titanium dioxide slurry raw materials. Summary of the Invention

[0010] The purpose of this invention is to address the problems of existing rotational viscosity detection methods, such as strong lag (15-30 minutes), insufficient sensitivity, limited information (unable to reflect the degree of agglomeration, particle size distribution, and double-layer state), and low prediction accuracy due to neglecting the interaction between process variables. This invention provides a response surface methodology for predicting the dispersibility of titanium dioxide slurry. The method of this invention, through a systematic “screening-modeling-prediction / optimization” process, fully considers the interaction between variables, significantly improving the prediction accuracy and process optimization efficiency of the dispersion behavior of titanium dioxide slurry system.

[0011] The above-mentioned objective of the present invention is achieved as follows:

[0012] A response surface methodology-based method for predicting the dispersibility of titanium dioxide slurry raw materials includes the following steps:

[0013] S1. Screening of key factors: Based on the powder dispersion theory, several candidate process parameters affecting the dispersibility of slurry were identified. The independent influence of each parameter on dispersibility was analyzed through single-factor experiments, and key process parameters were screened out.

[0014] S2. Response surface model construction: Using the key process parameters as independent variables and the slurry dispersibility index as the response value, a multinomial fitting model reflecting the relationship between the independent variables and the response value is constructed using response surface experimental design.

[0015] S3. Model significance verification: Perform regression analysis and variance analysis on the polynomial fitting model to verify the significance and goodness of fit of the model;

[0016] S4. Dispersion Prediction and Process Optimization: Based on the validated polynomial fitting model, the slurry dispersion index is predicted by inputting given process parameters, or optimization is performed within the process parameter design space to obtain the optimal combination of process parameters that optimizes the dispersion index.

[0017] Furthermore, the titanium dioxide precursor includes titanium dioxide precursor produced by the chloride process and / or titanium dioxide precursor produced by the sulfuric acid process.

[0018] Furthermore, the candidate process parameters in step S1 include at least two of the following: TiO2 content in the slurry, pH value of the slurry, amount of dispersant added, and dispersion stirring intensity.

[0019] Furthermore, the slurry dispersibility index is the slurry rotational viscosity; in the key factor screening stage, at least one of the following indicators is used for comprehensive judgment: absolute value of Zeta potential, average particle size of slurry, and particle size distribution of slurry.

[0020] Furthermore, the response surface experimental design in step S2 adopts either Box-Behnken design or central composite design.

[0021] Furthermore, the polynomial fitting model in step S2 is a polynomial regression model that includes linear terms, quadratic terms, and pairwise interaction terms for each factor.

[0022] Furthermore, the validation of model significance in step S3 includes: calculating the model's coefficient of determination R. 2 With the adjusted coefficient of determination R 2 adj, and perform an F-test on the model.

[0023] Furthermore, the optimization calculation in step S4 uses ridge analysis or gradient descent algorithm to determine the optimal combination of process parameters that makes the dispersion index reach its best in the response surface predicted by the model.

[0024] Furthermore, the relative deviation between the measured dispersion index and the model prediction in step S4 is no greater than 5%.

[0025] Furthermore, the key process parameters selected in step S1 are the TiO2 content of the slurry, the pH value of the slurry, and the amount of dispersant added.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. This invention transforms dispersibility evaluation from "post-event detection" to "pre-event prediction," completely eliminating detection lag. Existing offline rotational viscosity testing takes 15-30 minutes, and by the time the test results are returned, the slurry has already entered the downstream process, making real-time control impossible. This invention, by constructing a quantitative prediction model between process parameters and dispersibility indicators, can predict the dispersibility of slurry under any given process conditions within seconds. It transforms the traditional "lag detection" relying on offline experiments into model-based "instant prediction," fundamentally solving the problem of detection lag and providing technical possibilities for online quality control and forward-looking decision-making in the pulping process.

[0028] 2. This invention achieves multi-dimensional dispersion index characterization, breaking through the information bottleneck of single viscosity; in the key factor screening stage, this invention can be supplemented by indicators such as absolute value of Zeta potential, average particle size of slurry, and particle size distribution of slurry for comprehensive judgment, making the dispersion evaluation more comprehensive and accurate, and effectively avoiding the process control failure caused by "false compliance" of viscosity.

[0029] 3. This invention fully considers the interactive coupling effects between process variables, significantly improving prediction accuracy. It employs response surface methodology to construct a multinomial regression model containing linear, quadratic, and pairwise interaction terms for each factor. Regression analysis and variance analysis verify the model's significance, systematically characterizing the impact of interactions between key process parameters on dispersion. According to the specific implementation plan, the model's coefficient of determination R0 is... 2 The coefficient of determination can reach 0.9911, with an adjusted coefficient of determination R. 2 The adj value reaches 0.9750, indicating that the polynomial model can explain most (>97.5%) of the data variation and has a good fit.

[0030] 4. The optimization results of this invention are reliable and have been fully verified. This invention obtains the optimal combination of process parameters by performing a global optimization search on the model response surface. Through experimental verification, the relative deviation between the measured dispersion index and the model prediction value is no more than 5%, indicating that the model prediction accuracy is good and the optimization results are reliable.

[0031] In summary, this invention effectively overcomes the shortcomings of existing rotational viscosity detection methods, such as strong lag, insufficient sensitivity, and limited information. It significantly improves the prediction accuracy and response efficiency of titanium dioxide primary slurry dispersion, providing reliable technical support for the refined control and online quality regulation of titanium dioxide wet surface treatment processes. Attached Figure Description

[0032] Figure 1The following are the influence diagrams on the rotational viscosity of titanium dioxide slurry in the embodiments of the present invention ((a) is the influence diagram of TiO2 content on the rotational viscosity of the slurry, (b) is the influence diagram of pH on the rotational viscosity of the slurry, (c) is the influence diagram of dispersion and stirring intensity on the rotational viscosity of the slurry, and (d) is the influence diagram of dispersant addition amount on the rotational viscosity of the slurry).

[0033] Figure 2 The following are the analysis diagrams of the influence of factors on the Zeta potential of titanium dioxide slurry in the embodiments of the present invention ((a) is the analysis diagram of the influence of TiO2 content on the Zeta potential of slurry, (b) is the analysis diagram of the influence of slurry pH on Zeta potential, (c) is the analysis diagram of the influence of dispersion and stirring intensity on the Zeta potential of slurry, and (d) is the analysis diagram of the influence of dispersant addition amount on the Zeta potential of slurry). Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the following description is provided in conjunction with the appendix. Figure 1-2 The present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0035] The implementation of the present invention will be described in detail below with reference to specific embodiments.

[0036] Example 1: In a specific example, a single-factor screening experiment was first performed.

[0037] Rutile titanium dioxide precursor from a chloride process titanium dioxide production line was used. Slurries with different solid contents were prepared in a pulping tank using deionized water as the dispersion medium, with the slurry temperature maintained at 25±2℃. Candidate process parameters included: TiO2 content of the slurry, pH value of the slurry, amount of dispersant added, and dispersion stirring intensity. The independent effects of each parameter on the dispersibility of the slurry were investigated through single-factor experiments. The main dispersibility index used was the rotational viscosity of the slurry, and the absolute value of the Zeta potential was monitored as a reference. The single-factor experimental design is shown in Table 1.

[0038] Table 1 Single-factor experimental design table

[0039] The independent effects of each parameter on the dispersibility of the slurry were investigated one by one through single-factor experiments. The dispersibility indexes selected were the rotational viscosity of the slurry (measured using an NDJ-1 type rotational viscometer, a No. 3 rotor, at 12 rpm) and the absolute value of the Zeta potential (measured using a Zetasizer Nano ZS potentiometer).

[0040] according to Figure 1(a) The TiO2 content has a significant impact on the dispersibility of the titanium dioxide slurry. As the TiO2 content decreases, the slurry viscosity decreases significantly, and the dispersion effect improves. However, too low a content will adversely affect the effect of the subsequent sand milling process. Therefore, the TiO2 content was determined to be >450 g / L. Figure 1 (b) The viscosity of the slurry first decreases and then increases with the increase of the pH of the system, and the pH range of the slurry is determined to be 9.0 to 10.0. Based on... Figure 1 (c) The viscosity of the slurry decreases with increasing dispersion stirring speed, and the effect tends to level off above 300 rpm. According to Figure 1 (d) The viscosity of the slurry first increases and then decreases with the increase of the dispersant dosage, and the range of dispersant dosage is determined to be 0.1% to 0.3%. The above experimental results show that the TiO2 content, pH value, and dispersant dosage of the slurry have a significant impact on dispersibility. The effect tends to be gradual when the stirring speed is above 300 rpm. Therefore, TiO2 content, pH value, and dispersant dosage are determined as key process parameters.

[0041] S2, Response Surface Model Construction

[0042] Using the key process parameters screened by S1 as independent variables: TiO2 content X1 (450~650 g / L), pH value X2 (9.4~10.2), and dispersant addition amount X3 (based on SiO2 / TiO2 mass ratio, 0.1%~0.3%), and the rotational viscosity of the slurry as the response value Y, a three-factor, three-level response surface experimental scheme was established using Box-Behnken design (BBD).

[0043] Table 2. Factors and Levels in Response Surface Experiment Design

[0044] The experimental design matrix contained 15 experimental points, which were conducted in a randomized order. The slurry preparation and dispersion conditions for each experimental point were as follows: titanium dioxide concentrate was weighed according to the designed solids content, added to deionized water, adjusted to the target pH value with NaOH or dilute HCl, and the corresponding amount of dispersant was added. The mixture was stirred and dispersed at 300 rpm for 30 min, and then the rotational viscosity of the slurry at each experimental point was measured. The response surface methodology results are shown in Table 3.

[0045] Table 3 Results of Response Surface Experiment

[0046] For the 15 sets of experimental data, a second-order polynomial model was used for fitting, and the model form is as follows:

[0047] Y=1.81727E+05-72.55605X1-32030.97813X2-54476.45000X3+12.03875X1X2-96.99575X1X3+7281.25000X2X3-0.019895X1 2 +1220.28906X2 2 +55700.37500X3 2 (Equation 1);

[0048] S3, Model Significance Validation

[0049] Regression analysis and variance analysis were performed on the above polynomial fitting model, and the results are shown in Table 4.

[0050] Table 4. Analysis of Variance for Response Surface Model

[0051] R 2 Adj = 0.9750, R 2 _Pred = 0.8581, Adeq Precision = 28.2567, CV% =13.22;

[0052] Note: " / " indicates that it is not involved.

[0053] The results show that the model p-value < 0.0001, indicating that the model is highly significant; the p-value for the lack-of-fit term is 0.0113, indicating a certain degree of lack of fit, but its F-value (87.97) mainly stems from the extremely high model significance, and the pure error is relatively small (1294.84). Considering both the model's coefficient of determination R² = 0.9911 and the adjusted coefficient of determination R... 2 The values ​​of _adj=0.9750 are all very high, indicating that the polynomial model can explain most (>97.5%) of the data variation, with a good fit. It has extremely high reference value and application reliability for prediction and optimization in engineering practice.

[0054] S4, Process Parameter Optimization

[0055] Based on the validated polynomial fitting model, optimization calculations are performed within the process parameter design space. Ridge analysis is employed, using the fmincon function in MATLAB software to perform a global optimization search on the model response surface, solving for the combination of process parameters that minimizes the rotational viscosity of the slurry (response value Y).

[0056] The optimization results are as follows: the slurry solid content is 454.4 g / L, the pH value is 9.8, and the dispersant addition is 0.26% (based on the SiO2 / TiO2 mass ratio). Under these optimal conditions, the model predicts a minimum rotational viscosity of 101.4 mPa·s.

[0057] S5. Experimental Verification

[0058] Three parallel verification experiments were conducted according to the optimal process parameter combination obtained in S4: Deionized water was added to the pulping tank, the temperature was maintained at 25℃, titanium dioxide chloride primary product was added until the solid content was 454.4 g / L, dispersant (addition amount 0.26%) was added, the pH was adjusted to 9.8 with NaOH, and the mixture was stirred and dispersed at 300 rpm for 30 min. The rotational viscosity of the slurry was measured. The verification test results are shown in Table 5 below.

[0059] Table 5 Results of the Optimal Process Parameter Verification Test

[0060] The measured values ​​of the three verification experiments were 103.5 mPa·s, 100.9 mPa·s, and 102.0 mPa·s, respectively, with an average value of 102.03 mPa·s. The relative deviation from the model prediction value of 101.4 mPa·s was 1.3%, which is less than the 5% threshold, indicating that the model prediction accuracy is good and the optimization results are reliable.

[0061] Example 2: In this example, deionized water was added to the pulping tank, and the temperature was maintained at 25°C. Titanium dioxide concentrate was added until the TiO2 content reached 450 g / L. A dispersant (0.22% added, based on the SiO2 / TiO2 mass ratio) was added, and the pH was adjusted to 9.6 with NaOH. The mixture was stirred and dispersed at 300 rpm for 30 min, and the rotational viscosity of the slurry was measured. In this example, the measured viscosity was 319 mPa·s.

[0062] According to Equation 1 established in Example 1 above, the predicted viscosity is 328.89 mPa·s under the conditions of TiO2 content of 450 g / L, pH of 9.6, and dispersant addition of 0.22%. The relative deviation between the measured value and the predicted value is 3.10%.

[0063] Example 3: In this example, deionized water was added to the pulping tank, and the temperature was maintained at 25°C. Titanium dioxide concentrate was added until the TiO2 content reached 475 g / L. A dispersant (0.23% added, based on the SiO2 / TiO2 mass ratio) was added, and the pH was adjusted to 10.0 with NaOH. The mixture was stirred and dispersed at 300 rpm for 30 min, and the rotational viscosity of the slurry was measured. In this example, the measured viscosity was 275 mPa·s.

[0064] According to Equation 1 established in Example 1 above, the predicted viscosity is 274.94 mPa·s under the conditions of TiO2 content of 475 g / L, pH of 10.0, and dispersant addition of 0.23%. The relative deviation between the measured value and the predicted value is 0.022%.

[0065] Example 4: In this example, deionized water was added to the pulping tank, and the temperature was maintained at 25°C. Titanium dioxide concentrate was added until the TiO2 content reached 525 g / L. A dispersant (0.15% added, based on the SiO2 / TiO2 mass ratio) was added, and the pH was adjusted to 9.9 with NaOH. The mixture was stirred and dispersed at 300 rpm for 30 min, and the rotational viscosity of the slurry was measured. In this example, the measured viscosity was 1938 mPa·s.

[0066] According to Equation 1 established in Example 1 above, the predicted viscosity is 1953.42 mPa·s under the conditions of TiO2 content of 525 g / L, pH of 9.9, and dispersant addition of 0.15%. The relative deviation between the measured value and the predicted value is 0.796%.

[0067] Example 5: In this example, deionized water was added to the pulping tank, and the temperature was maintained at 25°C. Titanium dioxide concentrate was added until the TiO2 content reached 570 g / L. A dispersant (0.26% added, based on the SiO2 / TiO2 mass ratio) was added, and the pH was adjusted to 9.7 with NaOH. The mixture was stirred and dispersed at 300 rpm for 30 min, and the rotational viscosity of the slurry was measured. In this example, the measured viscosity was 1106 mPa·s.

[0068] According to Equation 1 established in Example 1 above, the predicted viscosity is 1099.03 mPa·s under the conditions of TiO2 content of 570 g / L, pH of 9.7, and dispersant addition of 0.26%. The relative deviation between the measured value and the predicted value is 0.630%.

[0069] Example 6: In this example, deionized water was added to the pulping tank, and the temperature was maintained at 25°C. Titanium dioxide concentrate was added until the TiO2 content reached 600 g / L. A dispersant (0.25% added, based on the SiO2 / TiO2 mass ratio) was added, and the pH was adjusted to 10.2 with NaOH. The mixture was stirred and dispersed at 300 rpm for 30 min, and the rotational viscosity of the slurry was measured. In this example, the measured viscosity was 2109 mPa·s.

[0070] According to Equation 1 established in Example 1 above, under the conditions of TiO2 content of 600 g / L, pH of 10.2, and dispersant addition of 0.25%, the predicted viscosity is 2071.20 mPa·s. The relative deviation between the measured value and the predicted value is 1.792%.

[0071] To better understand the prediction and verification effects under different process conditions in Examples 2 to 6 of the present invention, the experimental conditions and results of each example are summarized in Table 6.

[0072] Table 6 Comparison of measured and predicted viscosity values ​​under different process conditions

[0073] In summary, through the above embodiments of the present invention, the independent effects of TiO2 content, pH value, dispersant addition amount, and dispersion stirring intensity on rotational viscosity and Zeta potential were systematically investigated through single-factor experiments (Table 1). From these experiments, three key process parameters—TiO2 content, pH value, and dispersant addition amount—were selected. Based on this, a three-factor, three-level response surface methodology was established using a Box-Behnken design. Regression analysis yielded a second-order polynomial prediction model (Equation 1) containing linear, quadratic, and pairwise interaction terms for each factor. Analysis of variance showed that the model's P-value was <0.0001 (highly significant), and the coefficient of determination R0 was [value missing]. 2 =0.9911, Adjusted coefficient of determination R 2The adj=0.9750 indicates that the model can explain more than 97.5% of the data variation, showing a good fit. Furthermore, ridge analysis was used to optimize the model response surface, obtaining the optimal combination of process parameters (TiO2 content 454.4 g / L, pH=9.8, dispersant dosage 0.26%). The average measured viscosity from three parallel validation experiments was 102.03 mPa·s, with a relative deviation of only 1.3% (<5%) from the model prediction of 101.4 mPa·s. Moreover, validation results under different process conditions (TiO2 content 450~600 g / L, pH 9.6~10.2, dispersant dosage 0.15%~0.26%) showed that the maximum relative deviation between the measured and predicted viscosity values ​​was only 3.10%, and the minimum was 0.022%, all below the 5% threshold. The aforementioned progressive experiments fully demonstrate that the response surface prediction model constructed in this invention has good prediction accuracy and engineering reliability within a wide range of process parameter windows. It transforms the evaluation of dispersibility from "post-event detection" relying on offline rotational viscometers (requiring 15-30 minutes) to "instant prediction" based on the model (completed within seconds), breaking through the information bottleneck of a single viscosity index. It can effectively distinguish between two fundamentally different types of dispersion anomalies: "salt-induced thickening" and "insufficient dispersion." Furthermore, it can systematically quantify the impact of the interactive coupling effect between key process variables such as TiO2 content and dispersant dosage (P=0.0007) and TiO2 content and pH (P=0.0144) on dispersibility. This is something that existing offline rotational viscosity detection methods and isochromic force correction methods cannot achieve.

[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the dispersibility of titanium dioxide primary slurry based on response surface methodology, characterized in that, Includes the following steps: S1. Screening of key factors: Based on the powder dispersion theory, several candidate process parameters affecting the dispersibility of slurry were identified. The independent influence of each parameter on dispersibility was analyzed through single-factor experiments, and key process parameters were screened out. S2. Response surface model construction: Using the key process parameters as independent variables and the slurry dispersibility index as the response value, a multinomial fitting model reflecting the relationship between the independent variables and the response value is constructed using response surface experimental design. S3. Model significance verification: Perform regression analysis and variance analysis on the polynomial fitting model to verify the significance and goodness of fit of the model; S4. Dispersion Prediction and Process Optimization: Based on the validated polynomial fitting model, the slurry dispersion index is predicted by inputting given process parameters, or optimization is performed within the process parameter design space to obtain the optimal combination of process parameters that optimizes the dispersion index.

2. The method according to claim 1, characterized in that, The titanium dioxide precursors include titanium dioxide precursors produced by the chloride process and / or titanium dioxide precursors produced by the sulfuric acid process.

3. The method according to claim 1, characterized in that, The candidate process parameters in step S1 include at least two of the following: TiO2 content of slurry, pH value of slurry, amount of dispersant added, and dispersion and stirring intensity.

4. The method according to claim 1, characterized in that, The slurry dispersibility index is the slurry rotational viscosity; During the key factor screening stage, at least one of the following indicators is used for comprehensive judgment: absolute value of Zeta potential, average particle size of slurry, and particle size distribution of slurry.

5. The method according to claim 1, characterized in that, The response surface experimental design in step S2 adopts either Box-Behnken design or central composite design.

6. The method according to claim 1, characterized in that, The polynomial fitting model in step S2 is a polynomial regression model that includes linear terms, quadratic terms, and pairwise interaction terms for each factor.

7. The method according to claim 1, characterized in that, Step S3, verifying the significance of the model, includes calculating the model's coefficient of determination R. 2 With the adjusted coefficient of determination R 2 adj, and perform an F-test on the model.

8. The method according to claim 1, characterized in that, The optimization calculation in step S4 uses ridge analysis or gradient descent algorithm to determine the optimal combination of process parameters that makes the dispersion index reach the optimal value in the response surface predicted by the model.

9. The method according to claim 1, characterized in that, The relative deviation between the measured dispersion index and the model prediction in step S4 is no greater than 5%.

10. The method according to claim 1, characterized in that, The key process parameters selected in step S1 are the TiO2 content of the slurry, the pH value of the slurry, and the amount of dispersant added.

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