水果在热风干燥中的水分扩散分形模型

    Diffusion fractal model of fruit moisture in hot air drying

    • 摘要: 为了探讨水果在热风干燥过程中微观结构变化对水分扩散规律和干燥速率快慢的影响,该文用迂曲分形维数描述了香蕉内部孔道分布的联通性,用面积分形维数描述了内部孔道的不均匀性。研究表明,在有效扩散系数-香蕉厚度平方线形变化关系图中,轴向扩散系数大小为直线在Y轴上截距,径向扩散系数大小为直线斜率,并且轴向扩散系数远大于径向扩散系数,水分扩散系数在干燥样本中径向与轴向的巨大差异表明了香蕉在结构上具有异质性。随着面积分形维数的增大,导致干燥时间减小和有效扩散系数增大。由孔隙率与孔径比的变化而导致干燥时间和有效扩散系数的变化与面积分形变化引起的规律相近。随着迂曲分形维数的增大,使得干燥时间增加和有效扩散系数减小。扩散系数随体积变化率成对数增加。该研究可为脱水果蔬干燥技术研究提供参考。

       

      Abstract: Abstract: In order to understand the change of food microstructure impact on moisture diffusion and drying rate during the process of hot air drying, using a tortuosity fractal dimension to describe the interconnectivity of banana pore distribution, and using areal fractal dimension to describe the internal non-uniformity of pore sizes and shapes, considering the area shrinkage of the material and the pore shrinkage during the hot air drying, a two-dimensional diffusion model was built based on Crank's equation, and the coefficient of diffusion was determined. The experiment was carried out for hot air drying banana in order to validate the model. The results showed that the simulation was in good agreement with the results, so the model was found to describe the variation of the effective diffusion coefficient very satisfactorily. It can be observed that the plot of the effective diffusion coefficient (Deff) versus the square of thickness of banana needed to be a straight line with the axial diffusion coefficient (Dr) as the intercept in the Y axis and the radial diffusion coefficient (Dz) as the gradient. The value of Dz was higher than the value of Dr, the difference from the longitudinal direction of moisture diffusion compared with the lateral direction of water diffusion for the tested material indicated isotropic and random behavior in the physical structure of banana. The thicknesses of banana varying from 0.0075 to 0.012 in the experiment, the effective diffusion coefficients had been found to increase with the thicknesses and the drying time, which indicated that the hot air drying had a greater impact on the thick material. The value of drying time (t) decreased and the value of Deff increased with the increasing of the areal fractal dimension in the same porosity, which showed that the bigger areal fractal dimension made the moisture transfer more difficult. The t decreased and the Deff increased with the increasing of porosity and pore diameter rate in conformity with the areal fractal dimension, which showed that big pores diffuse easier. The t increased and the Deff decreased with the tortuosity fractal dimension increased in the same porosity, which indicated that the tortuosity resisted the moisture diffusion process. A logarithmic increase can be presented from the plot of the Deff versus the volume change rate, which showed that shrinkage leads to more tortuous pore and increased resistance. The research can provide a reference for the study of the drying technology of dehydrated fruits and vegetables.

       

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