Fractal Characteristics Study On Capillary Shrinkage And Heat And Mass Transfer Of Porous Media

As the fractal properties of porous media microstructure (mineral, bamboo, wood, fruit, vegetables and so on), the change of fractal dimensions will affect the heat and mass transfer processes of porous media during the hot air drying. On one hand, the temperature gradient drives the moisture transporting from the inside to the outward in the porous media, leading to the change of media volume and shape, such as shrinkage phenomenon. On the other hand, the existence of shrinkage hinders moisture transport, heat and mass transfer further. Therefore, the drying process of the porous media involves the coupling of the shrinkage and heat and mass transfer.In the study of the coupling of the shrinkage and heat and mass transfer at the home and abroad, the determination of the effective diffusivity and thermal conductivity are the key factors in the solving the coupling problem. In the studies about the description of media proliferation, the average moisture content, non-shrinkage and uniform pore size distribution were adopted to simplify the parameters of internal structure, which simplified mathematical model and provided the convenience for simulating the drying process. But the disadvantage is that the relationship between the diffusivity of the fixed point located at the inside of media and the dry moisture content, pore tortuosity, pore connectivity, pore diameter and the drying time at that point cannot be described accurately. The complexity of porous media cannot be described by traditional Euclidean geometry, which compelles a large number of researchers to adopt continuum hypothesis and the concept of average size. So it is difficult to study the influence of inner microstructure of porous media on internal heat and mass transfer, which leads to a number of limitations in the application of the traditional research methods and the theory.The thermal conductivity involved in the investigation is based on the medium thermal method and empirical formula generally. The media is assumed as continuous, isotropic, the average internal pore diameter distribution and the uniform homogenous structure; the thermal resistance of the medium is set as fixed connectivity pattern in advance and the help of the empirical formula is needed, but it can not seek out accurate effective thermal conductivity.In this paper, based on the fractal structure of porous media, combining the coupling relationship between the shrinkage and heat and mass transfer during the drying process, the works have been studied systematically, and the main contents are conducted as follows:First, the porous media was divided into the complete fractal which include fractal solid phase and incomplete fractal which include fractal aggregation, and two simplified unit-cell models were used to exhibit the microstructures. The effective conductivity without thermal resistance and empirical formula is built combined with thermal energy and Fourier’s law of heat conduction during drying. The result shows that effective conductivity has a negative correlation with the tortuosity fractal dimension, porosity, the areal fractal dimension and hot air temperature, whereas it has a positive correlation with the hot air rate and time.Second, the porous media is simulated as the fractal model with the wetting phase and non-wetting phase. The fractal model with wetting phase distribution is established. The local moisture content and the fractal dimension of this model are calculated by box-counting method, and the relationship is developed to express the local shrinkage model with the local moisture content and the fractal dimension. The relationship between the drying rate and the fractal dimension is analyzed based on the fractal structure of porous media and the random diffusion theory of gas. The result showed that the local moisture content can be used to all kinds of the shrinkage model. The drying rate and time are power exponent relationship, while the drying rate and the fractal dimension are index relationship.Third, combined with moisture concentration distribution, shrinkage characteristics and fractal characteristics of porous media during drying, a two-dimensional convection mass diffusion model of moisture transmission was established. It can be observed that in the straight line plot of the effective diffusion coefficient (Deff) versus the square of thickness of media, the axial diffusion coefficient (Dx) is the intercept in the Y axis and the radial diffusion coefficient (Dr) is gradient. Since the value of Dz was higher than the value of Dr, the great difference between the longitudinal direction and lateral direction of water diffusion for the material tested indicated an-isotropic behavior in the physical structure of material. Deff is related with microstructure, experimental conditions, thickness and volume shrinkage of media.Finally, by analyzing the coupling problems on shrinkage、diffusion and thermal conduction, it has been found that temperature of the media is improved by hot air, which leads to the moisture evaporation from the surface and form a temperature gradient inside. Thus the moisture transport phenomena occurres in the inside of media. The water evaporation and the emergence of drying front will generate the shrinkage, and then it will impede the diffusion of water. The increase of media temperature resulted in the decline of thermal conductivity, while the increase of temperature prompted;the enlargement of diffusivity. So the effective diffusivity is inversely proportional to the effective thermal conductivity. The drying curve of porous media is simulated combined with mass transfer processes principles, local shrinkage, local moisture content, the effective diffusivity and thermal conductivity. The result showed that the model combined with shrinkage and fractal is much closer to the experimental data than the no shrinkage and continuum model. Different from the continuous model, the internal pressure distribution does not fall step by step in proportion. The drying process is affected by pore connectivity, shrinkage, porosity, area fractal dimension and the ratio of the minimum and maximum pore diameters, tortuosity fractal dimension, tortuosity, shrinkage, the effective diffusivity and the effective thermal conductivity.