# Simulation Study of Xylitol-Mediated Effect on NaCl Diffusion Behavior in Cured Pork Tenderloin

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−9}m

^{2}·s

^{−1}, 1.22 × 10

^{−9}m

^{2}·s

^{−1}, 1.2 × 10

^{−9}m

^{2}·s

^{−1}, and 1.15 × 10

^{−9}m

^{2}·s

^{−1}when the amount of xylitol added was 0%, 4%, 8%, and 12% (w/w), respectively. This result agrees with the predicted values from the power function time-varying model. Moreover, a three-dimensional simulating model of mass transfers constructed using COMSOL Multiphysics was developed to evaluate the NaCl diffusion in pork tenderloin during the curing process. This model has high accuracy and can be used to describe the diffusion of NaCl in curing. Overall, this study provided a foundation for NaCl diffusion and distribution during the curing process.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

#### 2.2.1. Cured Pork Tenderloin Sample Preparation

#### 2.2.2. Measurements of Moisture and NaCl Contents

#### 2.2.3. Evaluation of Changes in Water, Salt, and Total Weight

#### 2.2.4. Construction of Mass Transfer Kinetic Model

_{1}was used to describe the parameters at the initial stage of curing. The slope k

_{2}was associated with the mass transfer kinetics of the diffusion mechanism of mass transfer kinetics about the curing.

#### 2.2.5. NaCl Diffusion Coefficient (De)

#### 2.2.6. Evaluation of the Link between NaCl Content and Diffusion Distance

#### 2.3. One-Way Model Simulations of the Kinetics of NaCl Diffusion

#### 2.4. Statistical Analysis

## 3. Results and Discussion

#### 3.1. Total Weight, Moisture, and NaCl Contents

^{+}and Cl

^{−}was higher than that in water molecules [22].

#### 3.2. Application of Predictive Models to Detect Changes

^{−9}m

^{2}·s

^{−1}. This result indicates that xylitol slightly affected the diffusion coefficient of NaCl. Moreover, the De values obtained in this study were smaller than experimental results previously described [31]. This may be related to several parameters, such as the material–liquid ratio, NaCl content of the brine, xylitol concentration, and curing temperature [32].

_{1}and k

_{2}are shown in Table 1b. The intercept parameter K

_{1}is used to describe the initial stage of curing, which is mainly affected by the salt concentration gradient, water gradient, pressure gradient, and other factors during the initial stage of curing. The slope parameter K

_{2}is related to diffusion kinetics and is affected by the type of additive [33]. The changes in weight, moisture content, and NaCl content of tenderloin had good linear relationships (R

^{2}≥ 0.9000) with curing time (t

^{0.5}) under different xylitol concentrations. These results suggest that the model can be applied to simulate xylitol-mediated mass transfer during the curing process. Table 1b shows that the concentration of xylitol has a significant impact on K

_{2}; this is because the xylitol-mediated curing can significantly reduce the mass, moisture content, and NaCl content. However, the addition of xylitol had no significant impact on the NaCl concentration under the initial curing conditions, so the change in K

_{1}was not significant.

#### 3.3. Link between NaCl Content and Diffusion Distance

#### 3.4. Simulating Model

^{2}and De under these prediction models are shown in Table 2. The R

^{2}cases for the relationship between the NaCl content in the aqueous phase of the tenderloin and the curing time can be obtained as follows: power function time-varying model > exponential function time-varying model > linear function time-varying model. The power and exponential functions (R

^{2}> 0.9500) are good for correlations when the linear function is poor (R

^{2}< 0.7). The results obtained in this study agree with previous studies [39], which proves that the data predicted by the power function time-varying model are closer to the De value calculated using the experimental method, and the experimental data were a good fit with predicted values. Additionally, when xylitol was added (0–12%), the experimentally calculated De values were 1.29 × 10

^{−9}m

^{2}·s

^{−1}, 1.22 × 10

^{−9}m

^{2}·s

^{−1}, 1.2 × 10

^{−9}m

^{2}·s

^{−1}, and 1.15 × 10

^{−9}m

^{2}·s

^{−1}(Figure 2d). The power function time-varying model was 1.29 × 10

^{−9}m

^{2}·s

^{−1}, 1.21 × 10

^{−9}m

^{2}·s

^{−1}, 1.14 × 10

^{−9}m

^{2}·s

^{−1}, and 1.04 × 10

^{−9}m

^{2}·s

^{−1}(Table 2). However, no significant differences were observed between the experimental conditions (p > 0.05). Andrés et al. showed that the change in mass transfer during curing was related to the square root of time. The square root time-varying model is a subset of the power function time-varying model, so the power function time-varying model is used to predict the NaCl content in the water phase of the pig ridge at different treatment times and calculate the diffusion coefficient of NaCl [40]. Therefore, the power function time-varying model was subsequently chosen as the prediction equation for Z

^{NaCl}in the simulation model, and De was calculated. The unidirectional model simulation simulated the kinetics of NaCl diffusion during the curing process.

^{®}software (version 5.5, COMSOL Inc, Stockholm, Sweden), applying the “Porous media dilute material transfer module” physical interface standard. The model’s dimensions were designed according to the actual dimensions of the experimental samples (30 mm × 30 mm × 10 mm (length × width × height)) to build a rectangular lattice geometry model for analysis. Figure 3b shows the biosolid generated by the COMSOL, with all simulations made with 3D geometry modeling with the volume subdivided into a mesh of tetrahedral finite elements consisting of the model solution domain divided by finite mesh division, generating 10,789 domain cell numbers, 8 vertex cell numbers, 120 edge cell numbers, and a minimum cell mass of 0.2608.

^{−3}. The high NaCl concentrations in the tenderloin surface might induce structural changes to the tenderloin matrix, which lead to increased NaCl diffusion [41] The results showed that most NaCl was present in the surface layer of the tenderloin (Figure 2a). During the curing, the NaCl content in the surface layer of the meat increased. However, a slow increase was detected in this content when the diffusion distance increased.

## 4. Conclusions

_{2}but has no significant impact on K

_{1}. The one-way model diffusion coefficient of NaCl was reduced from 1.29 × 10

^{−9}m

^{2}·s

^{−1}to 1.22 × 10

^{−9}m

^{2}·s

^{−1}, 1.2 × 10

^{−9}m

^{2}·s

^{−1}, and 1.15 × 10

^{−9}m

^{2}·s

^{−1}. The results also demonstrated that the power function time-varying model had a higher correlation with experimental data (R

^{2}> 0.9500). The NaCl diffusion coefficients calculated by the power function time-varying model were similar to the experimental method. The variation in NaCl distribution with position and time was solved and predicted by the COMSOL Multiphysics porous media module to analyze the diffusion process of NaCl during the curing process more intuitively. At the beginning of curing, the NaCl content in the pork tenderloin surface increased rapidly, increasing from 0 mol·m

^{−3}to 1350 mol·m

^{−3}from 0 to 12 h. Furthermore, the NaCl content increased slowly when the diffusion distance was enhanced. The NaCl penetrated to a position 10 mm from the meat surface, observed after 12 h. Based on the simulation results, a more accurate understanding of the diffusion mechanism was obtained. The model’s predicted values were validated against the experimental values, indicating that the model is reasonable. Overall, this research work suggests that using COMSOL Multiphysics to describe the spatial distribution of NaCl is a very economical and fast method, and no expensive instruments were required to achieve these results. Therefore, this study provides a new idea for achieving intelligent production in the food industry. In future studies, it is also necessary to develop other studies to evaluate the physicochemical properties during dry-ripening and the characterization of final product quality (oxidative status, physicochemical properties, and sensory properties).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The weight change amount (

**a**), moisture change amount (

**b**), and NaCl change amount (

**c**) of pork tenderloin with different xylitol concentrations, and driving force (1 − Y

_{t}

^{NaCl}) versus curing time (t

^{0.5}/l) (

**d**). Note: different capital letters indicate significant differences between the treatment groups with different concentrations of xylitol (p < 0.05); different small letters indicate significant differences between the treatment groups with different curing processes (p < 0.05).

**Figure 2.**Variation in NaCl content with diffusion distance in pork tenderloin cured for 6 h (

**a**), 12 h (

**b**), and 24 h (

**c**) based on different concentrations of xylitol, and the effect of the xylitol concentration and curing time on the diffusion coefficient De of NaCl (

**d**) (×10

^{−9}m

^{2}·s

^{−1}). Note: different capital letters indicate significant differences between the treatment groups with different concentrations of xylitol (

**a**–

**c**), and curing times (

**d**) (p < 0.05); different small letters indicate significant differences between the treatment groups with different diffusion distances (

**a**–

**c**) and different concentrations of xylitol (

**d**) (p < 0.05).

**Figure 3.**Fitted equations of time and NaCl content with 4% xylitol in pork tenderloin (

**a**) and 3D grid model of pork tenderloin (

**b**).

**Figure 4.**The unidimensional (

**a**), 2D (

**b**,

**c**), 3D (

**d**,

**e**) simulation diagram of NaCl diffusion at different curing times with 4% xylitol, and the experimental vs. simulated values of NaCl content with 4% xylitol in pork tenderloin (

**f**).

**Table 1.**Kinetic parameters and fitting correlation coefficients of pork tenderloin cured in different xylitol concentrations.

a. Kinetic Parameters of Pork Tenderloin Cured in Different Xylitol Concentrations | ||||

Addition of Xylitol/(w/w) | De/(10^{−9} m^{2} s^{−1}) | K | R2 | |

0% | 2.58 ± 0.12 | −0.1060 | 0.9569 | |

4% | 2.25 ± 0.10 | −0.1272 | 0.9327 | |

8% | 2.20 ± 0.03 | −0.1697 | 0.9065 | |

12% | 2.35 ± 0.08 | −0.2088 | 0.9001 | |

b. Kinetic Parameters for Δ${M}_{t}^{0}$, Δ${M}_{t}^{w}$, and Δ${M}_{t}^{NaCl}$ and Fitting Correlation Coefficients | ||||

Variables | Addition of xylitol/(w/w) | K1 | K2 | R2 |

Δ${M}_{t}^{0}$ | 0% | 0.94972 | 0.066870 | 0.9464 |

4% | 0.95896 | 0.056627 | 0.9533 | |

8% | 0.98067 | 0.047707 | 0.9775 | |

12% | 0.96797 | 0.032758 | 0.9160 | |

Δ${M}_{t}^{w}$ | 0% | 0.95202 | 0.060436 | 0.9403 |

4% | 0.97873 | 0.047178 | 0.9669 | |

8% | 0.98555 | 0.036387 | 0.9650 | |

12% | 0.97978 | 0.029523 | 0.9500 | |

Δ${M}_{t}^{NaCl}$ | 0% | 0.99072 | 0.010715 | 0.9189 |

4% | 0.99204 | 0.009633 | 0.9246 | |

8% | 0.99316 | 0.008951 | 0.9302 | |

12% | 0.99345 | 0.008060 | 0.9232 |

Predictive Model | Addition of Xylitol (w/w) | Equation | R^{2} | De (10^{−9} m^{2}·s^{−1}) |
---|---|---|---|---|

linear function time-varying model | 0% | Z^{NaCl} = 0.0014143t + 0.0294540 | 0.6238 | 1.57 |

4% | Z^{NaCl} = 0.0013564t + 0.028745 | 0.6117 | 1.47 | |

8% | Z^{NaCl} = 0.0013992t + 0.0280392 | 0.6313 | 1.5 | |

12% | Z^{NaCl} = 0.0013282t + 0.0262829 | 0.6461 | 1.36 | |

Power function time-varying model | 0% | Z^{NaCl} = 0.026587t^{0.212376} + 0.005467 | 0.98558 | 1.29 |

4% | Z^{NaCl} = 0.025606t^{0.212376} + 0.005471 | 0.981743 | 1.21 | |

8% | Z^{NaCl} = 0.024312t^{0.212376} + 0.005456 | 0.978139 | 1.14 | |

12% | Z^{NaCl} = 0.022290t^{0.212376} + 0.005470 | 0.981368 | 1.01 | |

Exponential function time-varying model | 0% | Z^{NaCl} = 0.053269(1 − e^{−0.408018t}) | 0.952283 | 1.21 |

4% | Z^{NaCl} = 0.051846(1 − e^{−0.3930302t}) | 0.962545 | 1.16 | |

8% | Z^{NaCl} = 0.0523298(1 − e^{−0.3473287t}) | 0.968102 | 1.23 | |

12% | Z^{NaCl} = 0.04943(1 − e^{−0.33598t}) | 0.960972 | 1.14 |

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## Share and Cite

**MDPI and ACS Style**

Chen, D.; Zhu, Q.; Zhou, Y.; Wan, J.; Deng, L.; Wang, L.; Liu, L.; Gu, S.; Huang, Y.; Zhou, Y.;
et al. Simulation Study of Xylitol-Mediated Effect on NaCl Diffusion Behavior in Cured Pork Tenderloin. *Foods* **2023**, *12*, 1451.
https://doi.org/10.3390/foods12071451

**AMA Style**

Chen D, Zhu Q, Zhou Y, Wan J, Deng L, Wang L, Liu L, Gu S, Huang Y, Zhou Y,
et al. Simulation Study of Xylitol-Mediated Effect on NaCl Diffusion Behavior in Cured Pork Tenderloin. *Foods*. 2023; 12(7):1451.
https://doi.org/10.3390/foods12071451

**Chicago/Turabian Style**

Chen, Dan, Qiujin Zhu, Ying Zhou, Jing Wan, Li Deng, Lei Wang, Linggao Liu, Sha Gu, Yanpei Huang, Yeling Zhou,
and et al. 2023. "Simulation Study of Xylitol-Mediated Effect on NaCl Diffusion Behavior in Cured Pork Tenderloin" *Foods* 12, no. 7: 1451.
https://doi.org/10.3390/foods12071451