Fluid skimming and particle entrainment into a small circular side pore
Fluid skimming and particle entrainment into a small circular side pore
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流体撇渣和颗粒夹带进入小圆形侧孔
DOI：
10.1017/s0022112091002914
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发表时间：
1991
影响因子：
3.7
通讯作者：
S. Weinbaum
中科院分区：
文献类型：
--
作者：
Zong;A. Acrivos;S. Weinbaum
在流化技术、轴向过滤器和血液微循环中众所周知的观察结果是，通过由大主管供给的小圆形侧孔的颗粒悬浮液的排出浓度可以显著低于供给浓度。两个潜在的机制被认为是负责这种出口浓度缺陷：流体从主管壁处的无颗粒层撇去，以及由于与孔入口的流体动力学相互作用而导致的颗粒筛选。在本文中，我们将只集中注意力于第一种机理，并将提出一个理论，它将排放浓度与通过侧孔的无量纲体积排放速率2πQ（与主管中的壁剪切速率和孔半径成比例）以及在蠕动流动条件下和对于小颗粒浓度的颗粒与孔入口直径的比率联系起来。首先，捕获管的横截面上游的孔隙的形状计算的基础上，一个简化的三维速度场，忽略了传入的剪切流上的孔产生的扰动。令人惊讶的是，这种形状的简单封闭形式表达式可以导出为Q → ∞或Q → 0。此外，利用最近发展的一个精确解，我们可以严格地证明，即使对于小Q，由孔板对剪切流产生的扰动对上游捕获管横截面的影响也很小。这个简化的流场，然后用于构建一个。三维理论的排放浓度缺陷，由于纯流体撇球的稀悬浮液。理论预测的定性特征显示出与微循环中的实验观察相同的趋势，尽管该理论的极限远低于所观察到的血细胞比容浓度并且颗粒被视为刚性球体。
It is a well-known observation in fluidization technology, axial filters and the blood microcirculation that the discharge concentration of a particulate suspension through a small circular side pore which is fed by a large main tube can be significantly lower than the feed concentration. Two underlying mechanisms are believed to be responsible for this exit concentration defect: the fluid skimming from the particle-free layer at the main tube wall and the particle screening due to the hydrodynamic interaction with the pore entrance. In this paper we shall focus our attention only on the first mechanism and shall present a theory which relates the discharge concentration to the dimensionless volume discharge rate 2πQ through the side pore (scaled to the wall shear rate in the main tube and the pore radius) and the ratio of the particle to pore entrance diameters, under creeping flow conditions and for small particle concentrations. First, the shape of the capture tube cross-section upstream of the pore is computed on the basis of a simplified three-dimensional velocity field which neglects the disturbance produced by the orifice on the incoming shear flow. Surprisingly simple closed-form expressions for this shape are derived as Q → ∞ or as Q → 0. Also, using a recently developed exact solution for the simple shear flow past an orifice (Davis 1991), we are able to rigorously demonstrate that, even for small Q, the disturbance produced by the orifice on the shear flow has only a minor effect on the capture tube cross-section far upstream. This simplified flow field is then used to construct a. three-dimensional theory for the discharge concentration defect due to pure fluid skimming for a dilute suspension of spheres. The qualitative features of the theoretical predictions show the same trends as the experimental observations in the microcirculation, although the limits of this theory are well below the observed hematocrit concentrations and the particles are taken as rigid spheres.