A method and system for characterizing the thixotropic properties of semi-solid foods
By establishing a structural parameter evolution model for semi-solid foods and deriving analytical solutions, combined with a thixotropic constitutive model, the problem of accurately characterizing the thixotropy of semi-solid foods in existing technologies is solved, achieving high-precision simulation and quantification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HOHAI UNIV
- Filing Date
- 2026-04-07
- Publication Date
- 2026-06-30
AI Technical Summary
Existing mathematical models cannot accurately characterize the thixotropic process of semi-solid foods, especially since the thixotropic curve changes with temperature, making it impossible to effectively predict their behavior.
A thixotropic constitutive model was adopted, and a structural parameter evolution model for semi-solid foods was established using fractional derivatives defined by Caputo. Analytical solutions were derived, and the model parameters were fitted with experimental data to simulate the variation of viscosity and shear stress.
It achieves precise quantification of the thixotropy of semi-solid foods, and the simulation results are in high agreement with the experimental data, providing a high-precision theoretical tool for food processing and quality control.
Smart Images
Figure CN122306619A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to processing and quality testing technology for semi-solid foods, and in particular to a method and system for characterizing the thixotropic properties of semi-solid foods. Background Technology
[0002] Semi-solid foods often exhibit complex rheological behaviors during processing and consumption. Thixotropy, as one of their key rheological properties, refers to the behavior of a material whose apparent viscosity decreases over time under constant shear, but which partially or completely recovers its original structure after the shear is removed. This property directly affects the perceived texture, spreadability, pumpability, and shelf-life stability of the food. From a sensory perspective, thixotropy determines the melting sensation in the mouth, the smoothness during swallowing, and the experience during use (such as the softening and recovery of jam or butter during spreading). From an engineering perspective, it profoundly impacts pipeline energy consumption, filling accuracy, and packaging design. Therefore, in-depth exploration of the thixotropy of semi-solid foods not only helps to reveal the constitutive relationship between their microstructure and macroscopic properties but also provides important theoretical basis and technical support for quality control, process optimization, and new product development in the food industry.
[0003] However, the intrinsic mechanism of thixotropy is highly complex, involving the dynamics of colloidal network structure disruption and reconstruction, interparticle interactions, and the microscopic phase behavior of multiphase systems. To accurately characterize the thixotropic process in semi-solid foods, researchers have developed a mathematical model. However, existing experimental results indicate that this mathematical model is inaccurate in characterizing the thixotropic process of semi-solid foods. External factors such as temperature can alter the thixotropic curve.
[0004] Currently, the thixotropic process of semi-solid foods has become a key concern in food processing and transportation. While devices for measuring the thixotropy of semi-solid foods have been developed, they cannot effectively characterize the thixotropic process or predict it based on existing data. Summary of the Invention
[0005] Purpose of the invention: One objective of this invention is to provide a method for characterizing the thixotropy of semi-solid foods, using a thixotropic constitutive model to characterize the process of viscosity or shear stress of semi-solid foods changing over time.
[0006] Technical solution: The method described in this invention includes the following steps:
[0007] S1. Select the thixotropic process of semi-solid food as the research object, and conduct experiments to obtain experimental data on the change of viscosity or shear stress of semi-solid food over time within the observation period.
[0008] S2. Establish a structural parameter evolution model to characterize semi-solid foods and derive the analytical solution of the model;
[0009] S3. Substitute the analytical solution of the model obtained in step S2 into the thixotropic constitutive model of the semi-solid food to obtain the viscosity or shear stress expression of the semi-solid food.
[0010] S4. Combine the experimental data in step S1 to obtain the parameters of the thixotropic constitutive model of semi-solid food in step S3, and use the model to quantify the experimental data in step S1.
[0011] S5. Based on the model parameters obtained from the fitting, simulate the variation curve of viscosity or shear stress of semi-solid food.
[0012] Furthermore, the experimental data in step S1 are the characteristics of the decrease in viscosity or shear stress of semi-solid food over time during the observation period.
[0013] Furthermore, a structural parameter evolution model characterizing semi-solid foods is established, and the analytical solution of the model is derived; including:
[0014] The structural parameter evolution model for semi-solid foods is as follows:
[0015] ;
[0016] in, Define the fractional derivative for Caputo. The order of the fractional derivative. For the structural parameters of semi-solid foods, when Time represents the structural parameters of a semi-solid food when its structure is not destroyed. The structure parameter t represents the time when the structure of the semi-solid food is completely destroyed, a represents the structural recovery rate of the semi-solid food, and b represents the structural destruction rate of the semi-solid food. Let m be the applied shear rate, and m be the shear rate exponent of the failure term; the analytical solution of the structural parameter evolution model for semi-solid food is derived as follows:
[0017] ;
[0018] in, The structural parameters of semi-solid food under equilibrium conditions. The structural parameters of the semi-solid food in its initial state. It is the Mittag-Leffler function.
[0019] Furthermore, the derivation process of the analytical solution for the structural parameter evolution model of semi-solid foods is as follows:
[0020] Applying a Laplace transform to both sides of the structural parameter evolution model for semi-solid foods and rearranging the results, we obtain:
[0021] ;
[0022] Where s is the complex variable after the Laplace transform of time t. for The image function is used to perform an inverse Laplace transform on the obtained result:
[0023] ;
[0024] make Substitute The formula yields the analytical solution for the evolution model of the structural parameters of semi-solid foods.
[0025] Furthermore, by substituting the analytical solution of the model into the thixotropic constitutive model of the semi-solid food, the viscosity or shear stress expression of the semi-solid food is obtained; including:
[0026] The thixotropic constitutive model of semi-solid foods is expressed as follows:
[0027] ;
[0028] in, For the shear stress of semi-solid foods, For the applied shear rate, The viscosity of semi-solid foods The viscosity of a semi-solid food under infinite time conditions. The viscosity of a semi-solid food in its initial state. Structural parameters for semi-solid foods;
[0029] The viscosity expression for semi-solid foods is:
[0030] ;
[0031] in, It is the viscosity of semi-solid foods under equilibrium conditions. The structural parameters of semi-solid food under equilibrium conditions. Let be the structural parameters of the semi-solid food in its initial state, where 'a' is the structural recovery rate of the semi-solid food and 'b' is the structural destruction rate of the semi-solid food. Let m be the applied shear rate, m be the shear rate exponent of the failure term, and t be time. The order of the fractional derivative. It is a Mittag-Leffler function;
[0032] The expression for the shear stress of semi-solid foods is:
[0033] ;
[0034] in, It is the shear stress of a semi-solid food under equilibrium conditions. It is the shear stress of a semi-solid food in its initial state.
[0035] Furthermore, the parameters of the thixotropic constitutive model of the semi-solid food were fitted using the nonlinear least squares method. These parameters included the viscosity of the semi-solid food at equilibrium. Viscosity of semi-solid food in its initial state The order of fractional derivatives The structural recovery rate (a) of semi-solid foods, the structural destruction rate (b) of semi-solid foods, and the shear rate exponent (m) of the destruction term.
[0036] The system corresponding to the method described in this invention includes:
[0037] The data acquisition unit is used to select the thixotropic process of semi-solid food as the research object, conduct experiments to obtain experimental data on the change of viscosity or shear stress of semi-solid food over time within the observation period;
[0038] The model building unit is used to establish a structural parameter evolution model characterizing semi-solid food and derive the analytical solution of the model; the viscosity or shear stress expression of semi-solid food is obtained by substituting the analytical solution of the model into the thixotropic constitutive model of semi-solid food.
[0039] The parameter fitting unit is used to fit the parameters of the constitutive model of thixotropy of semi-solid food by combining experimental data, and the experimental data is quantified by the model.
[0040] The variation curve acquisition unit is used to simulate the variation curve of viscosity or shear stress of semi-solid food based on the model parameters obtained from the fitting.
[0041] An electronic device for storing and executing the method includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of the method for characterizing the thixotropy of semi-solid foods.
[0042] A computer-readable storage medium for storing and executing the method, the computer-readable storage medium storing computer instructions, which, when invoked, are used to execute the steps of the method for characterizing the thixotropy of semi-solid foods.
[0043] A computer program product for performing the method includes a computer program / instructions that, when executed by a processor, implement the steps of the method for characterizing the thixotropy of semi-solid foods.
[0044] Beneficial Effects: Compared with existing technologies, the significant technical effects of this invention are as follows: Based on a thixotropic process characterizing semi-solid foods as the research object, experimental data on the changes in viscosity or shear stress of semi-solid foods over time at different times are obtained. Then, a structural parameter evolution model of semi-solid foods is established, analytical solutions are derived, and these solutions are substituted into a thixotropic constitutive model to obtain expressions for the viscosity or shear stress of semi-solid foods. Combined with experimental data, the parameters of the thixotropic constitutive model are determined. Compared with traditional constitutive models, the thixotropic constitutive model of this invention can accurately quantify the thixotropic curve of semi-solid foods and accurately simulate the changes in viscosity or shear stress of semi-solid foods over time. In the method of this invention, Caputo's definition of fractional derivatives is used to obtain power-law time-dependent results. The analytical solutions are clear, the calculations are simple, and the simulation accuracy is high. It has a wide range of practical applications and can provide an effective theoretical tool for controlling the processing and quality control of semi-solid foods. Attached Figure Description
[0045] Figure 1 This is a flowchart of the method of the present invention;
[0046] Figure 2 This is a comparison chart of the viscosity data of acai berry pulp fitted by the method model of this invention and the traditional constitutive model;
[0047] Figure 3 This is a comparison chart of the beef mincing stress data fitted by the method model of this invention and the traditional constitutive model. Detailed Implementation
[0048] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited to the embodiments described.
[0049] This invention aims to provide a novel method for characterizing the thixotropy of semi-solid foods, which can obtain the general laws governing the change of viscosity or shear stress over time, thereby providing an important theoretical basis for applications.
[0050] like Figure 1 As shown, the method of the present invention includes the following steps:
[0051] S1. Select the thixotropic process of a specific semi-solid food as the research object, and conduct experiments to obtain experimental data on the change of viscosity or shear stress of the semi-solid food over time within the observation period.
[0052] The experimental data show the characteristics of the decrease in viscosity or shear stress of semi-solid foods over time.
[0053] S2. Establish a structural parameter evolution model characterizing the thixotropic process of semi-solid foods, and derive the analytical solution of the model;
[0054] The structural parameter evolution model for semi-solid foods is as follows:
[0055] (1)
[0056] in, Define the fractional derivative for Caputo. The order of the fractional derivative. For the structural parameters of semi-solid foods, when Time represents the structural parameters of a semi-solid food when its structure is intact, that is, the structural parameters of a semi-solid food in its initial state. The structural parameters of a semi-solid food when its structure is completely destroyed are denoted by t, where t is time, a is the structural recovery rate of the semi-solid food, b is the structural destruction rate of the semi-solid food, and m is the shear rate exponent of the destruction term. Given the applied shear rate, the process of deriving the analytical solution of the structural parameter evolution model for semi-solid foods is as follows:
[0057] The Laplace transform was applied to both sides of the structural parameter evolution model for semi-solid foods, and the results were simplified to obtain the following:
[0058] (2)
[0059] Where s is the complex variable after the Laplace transform of time t. for The image function. Perform an inverse Laplace transform on the obtained result:
[0060] (3)
[0061] in, The structural parameters of the semi-solid food in its initial state are 1. For Mittag-Leffler functions, The structural parameters of a semi-solid food under equilibrium conditions are when The solution is obtained from the structural parameter evolution model of semi-solid foods. Substituting these values into the model yields the analytical solution for the structural parameter evolution model of semi-solid foods:
[0062] (4)
[0063] S3. Substitute the analytical solution of the model obtained in step S2 into the thixotropic constitutive model of the semi-solid food to obtain the viscosity or shear stress expression of the semi-solid food.
[0064] The thixotropic constitutive model of semi-solid foods is expressed as follows:
[0065] (5)
[0066] in, For the shear stress of semi-solid foods, For the applied shear rate, The viscosity of semi-solid foods The viscosity of a semi-solid food under infinite time conditions. The viscosity of a semi-solid food in its initial state.
[0067] The viscosity expression for semi-solid foods is:
[0068] (6)
[0069] in, It is the viscosity of semi-solid food in equilibrium state;
[0070] The expression for the shear stress of semi-solid foods is:
[0071] (7)
[0072] in, It is the shear stress of a semi-solid food in equilibrium. It is the shear stress of a semi-solid food in its initial state.
[0073] S4. By combining the experimental data on the change of viscosity or shear stress of semi-solid food over time, the parameters of the thixotropic constitutive model of semi-solid food in step S3 are obtained by fitting.
[0074] Specifically: Based on experimental data, the parameters of the thixotropic constitutive model of the semi-solid food in step S3 were fitted using the nonlinear least squares method: the viscosity of the semi-solid food under equilibrium conditions. The viscosity of semi-solid food in its initial state The order of the fractional derivative , the structural recovery rate a of semi-solid food, the structural destruction rate b of semi-solid food, and the shear rate exponent m of the destruction term.
[0075] S5. Based on the parameters of the fitted constitutive model of the thixotropic properties of semi-solid foods, simulate the change curve of the thixotropic properties of semi-solid foods, that is, simulate the process of the viscosity or shear stress of semi-solid foods changing with time, to guide practical applications.
[0076] In another embodiment, the system corresponding to the method of the present invention includes:
[0077] The data acquisition unit is used to select the thixotropic process of semi-solid food as the research object, conduct experiments to obtain experimental data on the change of viscosity or shear stress of semi-solid food over time within the observation period;
[0078] The model building unit is used to establish a structural parameter evolution model characterizing semi-solid food and derive the analytical solution of the model; the viscosity or shear stress expression of semi-solid food is obtained by substituting the analytical solution of the model into the thixotropic constitutive model of semi-solid food.
[0079] The parameter fitting unit is used to fit the parameters of the constitutive model of thixotropy of semi-solid food by combining experimental data, and the experimental data is quantified by the model.
[0080] The variation curve acquisition unit is used to simulate the variation curve of viscosity or shear stress of semi-solid food based on the model parameters obtained from the fitting.
[0081] In another embodiment, an electronic device includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of the method for characterizing the thixotropy of semi-solid foods.
[0082] In another embodiment, a computer-readable storage medium stores computer instructions that, when invoked, are used to perform the steps of the method for characterizing the thixotropy of semi-solid foods.
[0083] In another embodiment, a computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the method for characterizing the thixotropy of semi-solid foods.
[0084] Example verification:
[0085] Please see Figure 1 , Figure 2 , Figure 3 As shown, the method for characterizing the thixotropic properties of semi-solid foods according to the present invention is specifically operated as follows:
[0086] (1) The specific experiment was conducted by using two sets of experiments from the literature, one using acai berry pulp and the other using beef puree as semi-solid foods, and extracting experimental data on the viscosity and shear stress of the semi-solid foods as a function of time. (For details, see the literature HC Costa, FO Arouca, DO Silva, LGM Vieira, Study ofrheological properties of açai berry pulp: an analysis of its time-dependent behavior and the effect of temperature, J. Biol. Phys. 44(4) (2018) 557-577. and the literature MD Alvarez, W. Canet, Time-independent and time-dependent rheological characterization of vegetable-based infant purees, J. Food Eng. 114(4) (2013) 449-464.)
[0087] (2) The experimental data from step (1) were fitted using the viscosity and shear stress expressions derived from the thixotropic constitutive model. Simultaneously, to verify the feasibility of the thixotropic constitutive model of this invention, the characterization results of the traditional constitutive model were compared with those of the thixotropic constitutive model of this invention. (See attached figure) Figure 2 and Figure 3 The results show that traditional constitutive models cannot effectively characterize the changes in viscosity or shear stress in semi-solid foods, while the thixotropic constitutive model of this invention has a high degree of agreement with the experimental data and a significant fitting advantage. The parameters and goodness of fit of the thixotropic constitutive model of this invention, calculated using the nonlinear least squares method, are shown in Tables 1 and 2. Tables 1 and 2 demonstrate the feasibility of this characterization method.
[0088] Table 1. Parameters and goodness of fit of the thixotropic constitutive model for the thixotropic process of acai berry pulp.
[0089]
[0090] Table 2. Parameters and goodness of fit of the thixotropic constitutive model for the thixotropic process of beef puree.
[0091]
[0092] This invention focuses on the thixotropic process of semi-solid foods. It obtains experimental data on the changes in viscosity or shear stress over time at different moments, then establishes a structural parameter evolution model for the semi-solid foods, derives analytical solutions, and substitutes these solutions into a thixotropic constitutive model to obtain expressions for the viscosity or shear stress of the semi-solid foods. Combining this with experimental data, the parameters of the thixotropic constitutive model are determined, the thixotropic curve of the semi-solid foods is quantified, and the variation law of the thixotropic process is simulated. The method of this invention employs Caputo's definition of fractional derivatives, which provides clear analytical solutions, is computationally simple, and has high simulation accuracy. It has a wide range of practical applications and can provide an effective theoretical tool for characterizing the thixotropic process of semi-solid foods.
Claims
1. A method for characterizing the thixotropic properties of semi-solid foods, characterized in that, Includes the following steps: S1. Select the thixotropic process of semi-solid food as the research object, and conduct experiments to obtain experimental data on the change of viscosity or shear stress of semi-solid food over time within the observation period. S2. Establish a structural parameter evolution model to characterize semi-solid foods and derive the analytical solution of the model; S3. Substitute the analytical solution of the model obtained in step S2 into the thixotropic constitutive model of the semi-solid food to obtain the viscosity or shear stress expression of the semi-solid food. S4. Combine the experimental data in step S1 to obtain the parameters of the thixotropic constitutive model of semi-solid food in step S3, and use the model to quantify the experimental data in step S1. S5. Based on the model parameters obtained from the fitting, simulate the variation curve of viscosity or shear stress of semi-solid food.
2. The method according to claim 1, characterized in that, The experimental data in step S1 are the characteristics of the decrease in viscosity or shear stress of semi-solid food over time during the observation period.
3. The method according to claim 1, characterized in that, Establish a structural parameter evolution model characterizing semi-solid foods and derive the analytical solution of the model; including: The structural parameter evolution model for semi-solid foods is as follows: ； in, Define the fractional derivative for Caputo. The order of the fractional derivative. For the structural parameters of semi-solid foods, when Time represents the structural parameters of a semi-solid food when its structure is not destroyed. The structure parameter t represents the time when the structure of the semi-solid food is completely destroyed, a represents the structural recovery rate of the semi-solid food, and b represents the structural destruction rate of the semi-solid food. Let m be the applied shear rate, and m be the shear rate exponent of the failure term; the analytical solution of the structural parameter evolution model for semi-solid food is derived as follows: ； in, The structural parameters of semi-solid food under equilibrium conditions. The structural parameters of the semi-solid food in its initial state. It is the Mittag-Leffler function.
4. The method according to claim 3, characterized in that, The derivation process of the analytical solution of the structural parameter evolution model for semi-solid foods is as follows: Applying a Laplace transform to both sides of the structural parameter evolution model for semi-solid foods and rearranging the results, we obtain: ； Where s is the complex variable after the Laplace transform of time t. for The image function is used to perform an inverse Laplace transform on the obtained result: ； make Substitute The formula yields the analytical solution for the evolution model of the structural parameters of semi-solid foods.
5. The method according to claim 1, characterized in that, Substituting the analytical solution of the model into the thixotropic constitutive model of semi-solid foods, we obtain the viscosity or shear stress expressions for the semi-solid foods; including: The thixotropic constitutive model of semi-solid foods is expressed as follows: ； in, For the shear stress of semi-solid foods, For the applied shear rate, The viscosity of semi-solid foods The viscosity of a semi-solid food under infinite time conditions. The viscosity of a semi-solid food in its initial state. Structural parameters for semi-solid foods; The viscosity expression for semi-solid foods is: ； in, It is the viscosity of semi-solid foods under equilibrium conditions. The structural parameters of semi-solid food under equilibrium conditions. Let be the structural parameters of the semi-solid food in its initial state, where 'a' is the structural recovery rate of the semi-solid food and 'b' is the structural destruction rate of the semi-solid food. Let m be the applied shear rate, m be the shear rate exponent of the failure term, and t be time. The order of the fractional derivative. It is a Mittag-Leffler function; The expression for the shear stress of semi-solid foods is: ； in, It is the shear stress of a semi-solid food under equilibrium conditions. It is the shear stress of a semi-solid food in its initial state.
6. The method according to claim 1, characterized in that, The parameters of the thixotropic constitutive model of semi-solid food were fitted using the nonlinear least squares method. These parameters included the viscosity of the semi-solid food at equilibrium. Viscosity of semi-solid food in its initial state The order of fractional derivatives The structural recovery rate (a) of semi-solid foods, the structural destruction rate (b) of semi-solid foods, and the shear rate exponent (m) of the destruction term.
7. A system for characterizing the thixotropic properties of semi-solid foods, characterized in that, include: The data acquisition unit is used to select the thixotropic process of semi-solid food as the research object, conduct experiments to obtain experimental data on the change of viscosity or shear stress of semi-solid food over time within the observation period; The model building unit is used to establish a structural parameter evolution model characterizing semi-solid food and derive the analytical solution of the model; the viscosity or shear stress expression of semi-solid food is obtained by substituting the analytical solution of the model into the thixotropic constitutive model of semi-solid food. The parameter fitting unit is used to fit the parameters of the constitutive model of thixotropy of semi-solid food by combining experimental data, and the experimental data is quantified by the model. The variation curve acquisition unit is used to simulate the variation curve of viscosity or shear stress of semi-solid food based on the model parameters obtained from the fitting.
8. An electronic device, characterized in that, The invention includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, characterized in that, when the computer program / instructions are executed by the processor, they implement the steps of the method for characterizing the thixotropy of semi-solid foods as described in any one of claims 1-6.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when invoked, are used to perform the steps of the method for characterizing the thixotropy of semi-solid foods as described in any one of claims 1-6.
10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method for characterizing the thixotropy of semi-solid foods as described in any one of claims 1-6.