Derivation of a Segregation-Mixing Equation for Particles in a Fluid Medium
-
摘要: 主要目的是从基本原理(即,基本的物理)出发,推导出流体中纤细的、单个分散微粒的分离-混合方程的重力项.推出的微粒重力驱动通量,直接导致Richardson-Zaki相互关系式的最简单情况.仅仅依靠推导,自然地引出由微粒和流体的物理参数表达的Stokes速度.从基本物理原理出发的推导在以前的文献中还没有出现过.它可应用于低浓度的纤细微粒.Abstract: The main purpose is to show that the gravity term of the segregation-mixing equation of fine mono-disperse particles in a fluid can be derived from elementary physics(i.e.first principles).The derivation of the gravity-driven flux of particles leads to the simplest case of the Richaidson and Zald correlation.Stokes velocity also naturally appears from the physical parameters of the particles and fluid by means of derivation only,for the first time.This derivation fmm first principle physics has never been presented before.It is applicable in small concentrations of fine particles
-
[1] Smallwood R H, Tindale W B,Trowbridge E A.The physics of red cell sedimentation[J].Phys Med Biol,1985,30(2):125-137. doi: 10.1088/0031-9155/30/2/002 [2] Dolgunin V N, Ukolov A A.Segregation modeling of particle rapid gravity flow[J].Powder Technol,1995,83(2):95-103. doi: 10.1016/0032-5910(94)02954-M [3] Batchelor G K.Sedimentation in a dilute dispersion of spheres[J].J Fluid Mech,1972,52(2):245-268. doi: 10.1017/S0022112072001399 [4] Batchelor G K.Sedimentation in a dilute polydisperse system of interacting spheres—part 1:general theory[J].J Fluid Mech,2006,119:379-408. [5] Masliyah J H.Hindered settling in a multiple-species particle system[J].Chem Eng Sci,1979,34:1166-1168. doi: 10.1016/0009-2509(79)85026-5 [6] Kynch G J.A theory of sedimentation[J].Trans Faraday Soc,1952,48:166-176. doi: 10.1039/tf9524800166 [7] Shojaei A,Arefinia R.Analysis of the sedimentation process in reactive polymeric suspensions[J].Chem Eng Sci,2006,61(23):7565-7578. doi: 10.1016/j.ces.2006.08.050 [8] Garrido P, Bürger R, Concha F.Settling velocities of particulate systems—11:Comparison of the phenomenological sedimentation-consolidation model with published experimental results[J].Int J Miner Process,2000,60(3/4): 213-227. doi: 10.1016/S0301-7516(00)00014-4 [9] Bürger R, Damasceno J J R,Karlsen K H.A mathematical model for batch and continuous thickening of flocculated suspensions in vessels with varying cross-section[J].Int J Miner Process,2004,73(2/4):183-208. doi: 10.1016/S0301-7516(03)00073-5 [10] Richardson J F,Zaki W N.Sedimentation and fluidization—part Ⅰ[J].Chem Eng Res Des,1954,32:35-53. [11] Gray J,Chugunov V A.Particle-size segregation and diffusive remixing in shallow granular avalanches[J].J Fluid Mech,2006,569: 365-398. doi: 10.1017/S0022112006002977 [12] Savage S B,Lun C K K.Particle size segregation in inclined chute flow of dry cohesionless granular solids[J].J Fluid Mech,1988,189: 311-335. doi: 10.1017/S002211208800103X [13] Carslaw H S,Jaeger J C.Conduction of Heat in Solids[M].Oxford:Clarenden Press,1959. [14] Mazo R M.Brownian Motion: Fluctuations, Dynamics, and Applications[M].Oxford:Oxford University Press,2002. [15] Nelson E.Dynamical Theories of Brownian Motion[M].Princeton, NJ:Princeton University Press,1967. [16] Firoozabadi A.Thermodynamics of Hydrocarbon Reservoirs[M].McGraw-Hill,1999. [17] Boyd C E.Water Quality: An Introduction[M].Kluwer Academic Pub,2000. [18] Yoo K H,Boyd C E.Hydrology and Water Supply for Pond Aquaculture[M].New York,London:Springer,1994. [19] Bürger R, García A, Karlsen K H,et al.A kinematic model of continuous separation and classification of polydisperse suspensions[J].Comput Chem Eng,2008,32(6):1173-1194. doi: 10.1016/j.compchemeng.2007.04.019
点击查看大图
计量
- 文章访问数: 1157
- HTML全文浏览量: 42
- PDF下载量: 664
- 被引次数: 0