Research On The Relationship Between Fractal Dimensions Of Organic Powdery Carrier Surface And Carrying Capacity

Powdery carriers are used in multi-industries such as chemical engineering, medicine, foodstuff, and feedstuff so on. Carrying capacity of carriers is an important gist to select carriers and optimize carrying technics, and an important factor for product quality. At present, there has been not still credible, recognized quantificational description approach toward carrying capacity, which directly influences design and operation of the industrialized processing. Carrying capacity of powdery carriers largely rests on microcosmic superficial properties of granule (surface roughness, quantity and size of surface pore), and particle size distribution of grain group, which are researched as a significant region in arisen fractal geometry theory. The citation index showed that powder fractal dimension could be used to quantificationally describe powder granular characters and particle size distribution. However, the data about organic powder fractal were seldom founded, and the investigative literature on organic powdery carrier and its fractal investigation were still scarce.Utilizing predecessor's production on the part of fractal geometry theory, especially measuring method to fractal dimensions, methods to measuring surface fractal dimension and carrying capacity' evaluating indicators of organic powders were set up. Taking corn powders and bran powders, which were commonly used as carriers in feedstuff industry, and taking FeSO₄·H₂O as carrying object, the effect of ranges in particle size and moisture content on carrying capacity of carriers was investigated. And the models between carrying capacity and surface fractal dimensions under different moisture content were founded.At first, utilizing Photoshop, MATLAB, and two different principles which were Hausdorff Dimension and Difference Boxing-counting Dimension, the calculation methods to surface fractal dimensions of the organic powder granules based on the SEM-images were set up. The results showed that the regression equations used to determine surface fractal dimensions of the granules D_S1 (based on Hausdorff Dimension) and D_S2 (based on Difference Boxing-counting Dimension) were highly significant (P < 0.01); The two calculation methods were reliable. With the range from 30 mesh to 100 mesh in particle size, D_S1 were more than 2.6, while D_S2 were less than 2.6, and statistic test indicated that surface fractal dimension D_S1 was larger than D_S2 for the same granule (P < 0.01). The fractal research indicated that the granulesurfaces of corn powders and bran powders were much more irregular and coarser; and their structures were less compact as well as possessing absorption and carrying capacity. Secondly, the effect of ranges in particle size and moisture content on carrying capacity of carriers was investigated. Corn powders with the range from 30 mesh to 80 mesh in particle size, moisture content for 4.80%, 5.83%, 7.50%, 8.41%, the effect on carrying capacity by ranges in particle size was not significant (P > 0.05); the effect on carrying capacity by moisture content and the interaction between ranges in particle size and moisture content was highly significant (P < 0.01). Bran powders with the range from 30 mesh to 80 mesh in particle size, moisture content for 4.45%, 5.69%, 7.09%, 8.38%, the effect on carrying capacity by particle size was significant (P < 0.05); the effect on carrying capacity by moisture content and the interaction between ranges in particle size and moisture content was highly significant (P < 0.01). Using LSD in order to make multiple comparisons, the study showed that there were significant differences between some levels which belonged to significant factors.In the end, the models between carrying capacity and surface fractal dimensions under different moisture content were founded. The static indicated that all of the regression equations and regression coefficients were significant or highly significant.There were corn powders in different moisture content, including 4.80%, 7.50%and 8.41%, and bran powders in moisture content 7.09%. The models between carrying capacity and the surface fractal dimensions D_S1 belonged to linearity, as flows:4.80% moisture content, rj = 91.690 - 27.381D_S1 ; 7.50% moisture content, (?) = 169.000- 52.31LD_S1; 8.41% moisture content, (?) =-282.050 + 98.981D_S1; 7.09% moisture content, (?) = -530.771 + 190.835D_S1.There were com powders in different moisture content, including 5.83% and 7.50%, and bran powders in different moisture content, including 4.45%, 5.69%, and 8.38%. The models between carrying capacity and the surface fractal dimensions D_S2 belonged to quadratic form, as flows:5.83% moisture content, (?) = -137.764D_S2² +672.370D_S2 -805.519 ; 7.50% moisture content, (?) = -124.779D_S2² + 596.494D_S2 - 693.497;4.45% moisture content, (?) =-188.524D_S2² +910.821D_S2 -1082.631 ; 5.69% moisture content, (?) = -70.409D_S2² + 342.846D_S2 - 404.907; 8.38% moisture content, (?) = -74.771D_S2² +333.471D_S2 -359.120.