VISCOUS FLOW IN MULTIPARTICLE SYSTEMS - SLOW MOTION OF FLUIDS RELATIVE TO BEDS OF SPHERICAL PARTICLES
VISCOUS FLOW IN MULTIPARTICLE SYSTEMS - SLOW MOTION OF FLUIDS RELATIVE TO BEDS OF SPHERICAL PARTICLES
复制标题
DOI：
10.1002/aic.690040214
复制
发表时间：
1958-01-01
期刊：
影响因子：
3.7
通讯作者：
HAPPEL, J
中科院分区：
文献类型：
--
作者：
HAPPEL, J
一个数学处理的基础上，两个同心球可以作为一个随机组合的球体相对于流体运动的模型。内球包括集合中的一个粒子，外球由具有“自由表面”的流体包层组成。由这些假设产生的适当的边界条件使得能够获得满足省略惯性项的Stokes-Navier方程的封闭解。该解决方案使沉降率或可替代的压降作为一个功能的预测的分数空隙体积。比较的理论与其他关系和文献中报道的数据。特别令人感兴趣的是它与众所周知的卡曼-Kozeny方程的密切一致性，该方程已被广泛用于关联填充床以及颗粒沉降和流化系统的数据。这是值得注意的，因为在填充床中每个颗粒上的力可以是在无扰动介质中施加在单个颗粒上的力的几百倍。
A mathematical treatment is developed on the basis that two concentric spheres can serve as the model for a random assemblage of spheres moving relative to a fluid. The inner sphere comprises one of the particles in the assemblage and the outer sphere consists of a fluid envelope with a “free surface.” The appropriate boundary conditions resulting from these assumptions enable a closed solution to be obtained satisfying the Stokes‐Navier equations omitting inertia terms. This solution enables rate of sedimentation or alternatively pressure drop to be predicted as a function of fractional void volume.Comparison of the theory is made with other relationships and data reported in the literature. Of special interest is its close agreement with the well known Carman‐Kozeny equation which has been widely used to correlate data on packed beds as well as sedimenting and fluidized systems of particles. This is remarkable in view of the fact that the force on each particle in a packed bed can be up to several hundred times that exerted on a single particle in an undistrubed medium.