圆孔外Stokes流中球形粒子的运动*

在研究悬浮液入孔问题时,粒子在孔外任意位置所受的力和力矩是所需的最基本数据.本文在严宗毅等(1987)算出的有限个离散数据的基础上.首次给出了球在圆孔外的全部十二个力和力矩系数的近似解析表达式.我们应用这些系数计算零雷诺数下球形粒子入孔时的轨道和旋转角速度,结果与现有实验数据完全一致.分析不同系数的相对重要性表明,在孔口和孔壁附近不能忽略旋转效应.在靠近孔口边缘的局部区域必须计及侧向力效应.以往的理论结果在孔口附近与实验不符,正是由于忽略了这些因素.本文还详细讨论了粒子和孔口尺寸的相对大小以及重力和浮力对于粒子运动轨道、速度分布和旋转的影响,指出用大粒子做中性悬浮实验时,对其密度的要求特别严格.本文所提供的力和力矩系数,考虑因素全面、比较准确,便于计算,为进一步研究各种涉及粒子入口的问题提供了良好的前提.

The Motion of a Spherical Particle in the Stokes Flow Outside a Circular Orifice

For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, This paper for the first lime presents approximate analytical expressions (in closed form) of all the twelve force and moment coefficienis for a sphere outsied a circular orifice, on the basis of a number of discrete data computed by Yan et al(1987).These coefficients are then applied to calculate the trajectory and angular velocity of a spherical particle approaching the pore at zero Reynolds number.The trajectory is in excellent agreement with the available experimental results.An analysis of the relative importance of the coefficients shows that the rotation effect cannot be neglected near the pore opening or near the wall, and that the lateral force effect must be taken into account in the neighborhood of the edge of the pore opening.It is due to neglecting these factors that previous theoretical results deviate from the experimental ones near the pore opening.The effects of the ratio of the particle to pore radii as well as the influences of the graritytbuoyance on the particle trajectory, velocity distribution and rotation are discnssed in detail.It is pointed out that in the experiments of neutrally-buoyant suspensions, the restriction on the density of the particle is most demanding for a large particle size.The expressions of forces and moments presenled herein are complete, relatively accurate and convenient, thus providing a good prerequisite for further studies of any problems involving the entrance of particles to a pare.