基于反演法计算不同温度下小麦面团的水分扩散系数

李望铭; 马荣琨; 贾庆超; 张杰; 赵学伟

doi:10.13386/j.issn1002-0306.2022070354

基于反演法计算不同温度下小麦面团的水分扩散系数

doi: 10.13386/j.issn1002-0306.2022070354

1.
郑州科技学院食品科学与工程学院，河南郑州 450064
2.
郑州轻工业大学食品与生物工程学院，河南郑州 450002

详细信息

作者简介:
李望铭（1994−），男，硕士，助教，研究方向：速冻面制品加工，食品加工过程模拟，E-mail：a551722069@163.com

中图分类号: TS213.2
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- 文章访问数: 79
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- PDF下载量: 6
- 被引次数: 0
出版历程
- 收稿日期: 2022-08-02
- 网络出版日期: 2023-04-20
- 刊出日期: 2023-06-01

Calculation of Moisture Diffusivity of Wheat Dough at Different Temperatures Based on Inversion Method

1.
College of Food Science and Engineering, Zhengzhou Institute of Science and Technology, Zhengzhou 450064, China
2.
Food and Bioengineering Department, Zhengzhou University of Light Industry, Zhengzhou 450002, China

摘要

摘要: 水分扩散系数是食品加工过程中重要的物理参数。估算水分扩散系数的主要方法是基于第二菲克定律，但在应用这些定律的方式上存在显著差异。本研究采用Peleg、Weibull、双指数这三种常用的食品水分吸附动力学模型拟合了冻干面团在20、30及40 ℃时的吸湿曲线。在此基础上，通过COMSOL软件分别建立了瞬时平衡、对流、平行指数边界三种条件下的面团吸湿模型，并通过反演法计算出对应模型下的水分扩散系数。结果表明，Weibull模型和双指数模型决定系数均在0.999以上，较为适合冻干面团吸湿曲线的拟合；平行指数边界模型能较好的模拟出不同温度条件下冻干面团的吸附水分变化规律。同时证明了水分扩散系数随温度升高而变大，且不能被当作一个常数。
- 面团 /
- 水分扩散系数 /
- 反演法 /
- 吸附水分 /
- 冷冻
Abstract: Moisture diffusivity is an important physical parameter in food proceeding. The primary method used to estimate the water diffusion coefficient is based on the second Fick’s law, but there are significant differences in the way in which these laws are applied. In this work, three commonly used food moisture adsorption kinetic models, Peleg, Weibull and double exponential, were used to simulate the moisture absorption curve of freeze-dried dough at 20, 30 and 40 ℃. On this basis, the moisture absorption models of dough under three conditions, such as instantaneous equilibrium, convection, and parallel exponential boundary, were established by COMSOL software. The moisture diffusivity under the corresponding models was calculated using the inversion method. The results showed that the coefficients of determination of Weibull model and double exponential model were above 0.999, which were more suitable for fitting the moisture absorption curve of freeze-dried dough than other models. The variation law of adsorbed moisture of freeze-dried dough under varying temperature conditions was better simulated by the parallel exponential boundary model. Meanwhile, it was proved that the moisture diffusivity increased as the temperature went up and could not be regarded as a constant.
- dough /
- moisture diffusivity /
- inversion method /
- adsorption water /
- freezing

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1 冻干圆柱体面团在不同温度下的吸湿曲线及三个模型的拟合曲线

1. Moisture absorption curves of freeze-dried cylindrical dough at different temperatures and fitted curves of three models

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图 2 三种模型在不同温度下水分含量的变化

Figure 2. Variation of moisture content of three models at different temperatures

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图 3 不同温度下平行指数模型的水分扩散系数随面团内水分浓度的变化

Figure 3. Variation of moisture diffusivity under parallel exponential model with water concentration in dough at different temperatures

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图 4 平行指数模型（20 ℃）在0、15000、30000、57600 s的水分分布

Figure 4. Water distribution of parallel exponential model (20 ℃) at 0, 15000, 30000, 57600 s

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图 5 水分扩散系数为常数对吸附水分的影响

Figure 5. Effects of constant moisture diffusivity on adsorbed water

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表 1 3种模型拟合吸湿曲线所得的参数及分析指标

Table 1. Parameters and analytical indexes obtained by fitting the moisture absorption curves of three models

模型	参数	温度（℃）
模型	参数	20	30	40
Peleg	M_e（kg）	6.19×10⁻⁵	6.63×10⁻⁵	7.07×10⁻⁵
	k	14302.69	8024.52	5940.25
	R²	0.9948	0.9943	0.9933
	SSE	8.85×10⁻¹⁰	7.32×10⁻¹⁰	9.54×10⁻¹⁰
Weibull	M_e（kg）	5.18×10⁻⁵	5.18×10⁻⁵	6.01×10⁻⁵
	a	1.08	0.99	0.98
	b	15362.95	10129.42	7866.26
	R²	0.9999	0.9998	0.9997
	SSE	1.98×10⁻¹¹	2.07×10⁻¹¹	3.97×10⁻¹¹
双指数	k/a	11.65	11.65	11.65
	b	5.83×10⁻⁵	4.94×10⁻⁵	5.70×10⁻⁵
	c	-9.08×10⁻¹²	2.33×10⁻¹²	4.27×10⁻¹²
	d	5.73×10⁻⁵	1.02×10⁻⁴	1.33×10⁻⁴
	R²	0.9999	0.9999	0.9998
	SSE	2.33×10⁻¹¹	1.61×10⁻¹¹	2.78×10⁻¹¹

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表 2 三种边界条件模型参数值

Table 2. Values of some parameters in the three boundary models

温度（℃）	瞬时边界		对流边界			平行指数边界
温度（℃）	D₀（m²/s）	k	D₀（m²/s）	k	k_v	D₀（m²/s）	k	τ
20	1.04×10⁻⁸	0.0311	1.18×10⁻⁸	0.0329	0.0009	5.83×10⁻⁸	0.0252	14548
30	1.72×10⁻⁸	0.0336	1.29×10⁻⁸	0.0416	0.0011	7.72×10⁻⁸	0.0305	9589
40	4.83×10⁻⁸	0.0409	1.8×10⁻⁸	0.0429	0.0012	9.49×10⁻⁸	0.0319	7158

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