Theoretical Models of Light Scattering Applied in Sizing Particles in Coal Water Slurry

Journal of China University of Mining & TechnologyVol 14 No. 1Theoretical Models of lightScattering Applied in Sizing Particlesin Coal Water SlurryWANG Ren-zhe(王仁哲), ZHANG Rong-zeng(張榮曾), XU Zhi-qin(徐志強)(School of Chemical and Environmental Engineering. CUMT. Beijing 100083, China.Abstract: Advantges and disadvantage of Mie scattering model and Fraunhofer diffraction model are discussed. Theresult shows that 1) the Fraunhofer diffraction model is simple in design and fast in operation, which is quitesuitable for on-line control and 2)the intensity and energy distribution of diffracted light of both the Mie scatteriodel and the Fraunhofer theoretical model are compared and researched. Feasibility of using the Fraunhoferdiffraction model to replace the Mie scattering model in measuring particles in coal water slurry is demonstratedKey words: coal water slurry light scattering model; Mie scattering model; diffractionCLC number: (043 Document code :a Article Id: 1006-1266(2004)01-0064-03Distribution of Particles in Coal Water solid particle and the reasonable size graduation canSlurryssure the accumulation efficiency valid. Thesmaller the gap between coal granules is, the higherChina is abundant in coal and consumes coal intities. The develoaccumulated, the gaps between granules are verylurry is a main task for the rational use of coalrecent years. The coal water slurry fuel is a fluid Small and are filled with fine particles. The particlesare separated by water and the solid particles cancoal-based industrial fuel. which is consisted ofwater,coal, and additive, with each of which not contact each other, making the coal wateraccounting approximately for about 35%, 65. slurry have a good fluidizability (Fig. 1)Therefore, particle size measurement of slurry onand 1%-2%, respectively n.stream is one of the important methods to monitorThe size graduation is one of the key techniquesthe quality of slurryof preparing the coal water slurry. The small size ofFig. 1 Schematic diagram中國煤化工The coal water slurry has a wide range of sizemCNMHOf particledistribution, with the upper limit of particles being range of 20 to 75 microns 2-3.500 microns and the lower limit being less than 1Received date: 2003-12-3Biograph Ay F Ren-zhe(1967-). male, from Huaibei. AnHui province. associate professor, engaged in the research on mineraWANG Ren-zhe et alTheoretical Models of Light Scattering Applied in Sizingwhen improved Mie algorithms are used2 Models of Light Scattering2.2 Fraunhofer modelIn practice, we have employed many methodsThe Fraunhofer approximation assumes thaand several techniques to measure particle size, the scatteringndependent of the relativeincluding sieves, sedimentation, microscopic refractive index, which means that measurementsevaluation, and light scattering 4-5. Light scattering do not require knowledge of the material or mediuminstrumentation has many advantages compared optical properties. The following assumptions areth othesImlconvenient in operation, fast in data processing, andight does not pae pagood in repeatability, etc. Therefore, it has become itself. Light that falls onto the particle is absorbedthe preferred equipment in many coal water slurry and can be ignoredplants for quality control2) Particles are assumed to be sphericalModel of light scattering is the basis of particleUnder this approximation the scattering due toanalysis. The existing mathematical models are as a single particle of radius a(or, for nonspheres, offollowsequivalent radius a) at an angle b takes the following2. 1 Mie modelforGustav Mie gave a unified mathematicalI(0)=Cloa2,(kasino)deof light scattering by spheres inThe Mie model is a solution of the Maxwellhere k=2/A, a is the wavelength of light; C is aconstant; 8 is the scattering angle measured fromelectromagnetic wave of light in space. Mie obtainedthe direction of the incident light to the direction ofthe solution for a plane wave incident on athe scattered light; Io is the intensity of the incidenthomogeneous sphere. The Mie model is valid for beam, and J, is the first-order Bessel function of theparticles any diameter and refractive indexesfirst kindThe angular distribution of irradiance intensity2. 3 Rayleigh modelis represented by()=I1()+I(),wavelength of light )particles was first explained bywhere 0 is the scattering angle measured from the Lord Rayleigh in 1881 8. When a particle is smallerdirection of the incident light to the direction of the than one-tenth of the light wavelength, it behavesas a single electric dipole oscillating in phase withscattered light: I(0) is the scattered intensity the electric field of theperpendicular to the scattering plane; and I/(0)ise incident light wave.the scattered intensity parallel to the scattering2. 4 Van de Helst modelsAs the large particle with the refractive indexplane, that isclose to that of the2n+1n(n+\(a, (coso)+b, tn(coso))shifts the phase of the ray. The phase shift is theⅠ(∑2+1(a()+bx(os)of the difference between the refractive indices ofwhere both a, and bm are scattering coefficients; Tn the particle and the surrounding medium. Thus theand t. aree ang中國煤化工he particle can be easilyexpressions are complicated and formidableTHCNMHGThe Mie solution of Maxwell equations is aslowly converging series, and before the advent of3 Data Analysiscomputers, Mie computations were rarely done.As what mentioned in the preceding section, itit was onlyesstall particles before. Today a PC is obvious that the Mie model is undoubtedlycan be used to calculate the Mie series, especially appropriate to spherical particles. But many defects66Journal of China University of Mining & TechnologyVol 14 No. 1re presented when we calculate the irradiance energy detected by the 40-ring photoelectricintensity of pattern scattered by the very large detector approximately corresponding to theparticle, including very slowly velocity of calculation scattering angle through o degree to 30 degrees.and the need of refractive index of many materials As shown in Fig. 3, the smaller the radius ofbeing measured. Nowadays instruments are mostly particles is, the lower the scattering energy isused in a combination of Fraunhofer model with the According to the distribution of scattered energyMie scattering theory, which deals properly with only when the radius of particle is longer than 1fine particles, but some error will come from micron, Fraunhofer diffraction energy and Miedifference of models appliedscattering energy are approximately the same WithIn the water coal slurry, the coal particles the radius of particle decreasing the scatteredbelong to the material absorbing light and refractive energy is very weak and the distributions areindex of which has a value of 1. 52+i0. 67. To obviously differentcompare the difference between the Fraunhofermodel and the mie model, the author calculated a600 F Fraunhoseries of intensity and energy corresponding tovarious particle sizes, respectively.ese curves areshown in Figs. 2 andRing number(a)r-I0 u m(b)r=5 wmFraunhoferc)r=l um(d)r=0.5pmFraunhoferFig 3 Fraunhofer diffracting energy comparwith Mie scattering energyS Fraunhofer(A=0.6328m,n=1.52+10.67)0203040Scattering angle/(Scattering angle/()4 Conclusions(c)r=l umFig 2 Fraunhofer diffracting intensity comparedFrom the above comparison between the resultswith Mie scattering intensityof mie theory and that of Fraunhofer approximation(A=0.6328m,n=1.52+10.67)theory, some conclusions are derived as follows.1) The Fraunhofer theory can be used as anAs shown in Fig. 2, the intensity of scattereapproximately substitute for the Mie theory. It canlight graduallyecrease oalso be used for analyzing and calculating theparticle radius, and the point of the first minimumis gradually moving to the direction of enlargementdistributions of intensity and energy scattered bycarbon particles in water coal slurry.um versus 40 degrees ) as the radius of particledistribution of particles with theer sizes smallerdecrease to 0. 5 um, the distribution of theirintensity are obviously dissimilar.ig. 3 shows the distribution of scatteredTHtto t中國煤化工their sizes larger than 1CNMHGg Lui ve illig and interpolation(Transferred to Page 81)ZHAI Hong-xin et al.Integral Optimization of Systematic Parameters ofin existing ones (e. g. around 200 mm, determinesame tendency, showing significant influence ofin view of structure mainly ) demonstrating the technology conditions on screeningdifference between systematic and structure points5)There are also some agreements with thedata at present used, such as e(6 mm) and one of3)The n-value should be as low as 550 min the specifications B.L(2.0X8.8 m2)instead of 600-700 min normally used, which is6) The proposed method of synthetic index Kuseful to reduce mechanical vibration in unfavorable has been here used in the first time, and will bedyhopefully introducedevaluation of different4)K, values increases with K increasing in the screensReferences1] Zuber J. 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