Motion and Deformation of a Viscous Drop in Stokes Flow Near a Rigid Wall
-
摘要: 发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示，由于环境流动和浮力的作用，随着时间的推进，液滴在轴向压缩，在径向拉伸．当环境流动的作用弱于浮力作用时，随着时间的推移，液滴上升并向上弯，固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时，随着时间的推移，液滴变得越来越扁．在这种情形，当大初始间距时，壁面上的应力随液滴的演变而增大；当小初始间距时，由环境流动、浮力及壁面对流动的较强作用的联合影响，此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内，且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．Abstract: A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall.Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall,viscosity ratios,combined surface tension and buoyancy parameters and ambient flow parameters.Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes.When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances.When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes.In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow,buoyancy and the stronger wall action to the flow.The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis,which increases when the initial stand-off distance increases.When the initial stand-off distance increases the stress induced by drop motion decreases substantially.The surface tension effects resist the deformation and smooth the profile of the drop surfaces.The drop viscosity will reduce the deformation and migration of the drop.
-
Key words:
- viscous drop /
- axisymmetric Stokes flow /
- rigid wall /
- motion and deformation /
- stress /
- boundary integral method
-
[1] Ladyzhenskaya O A.The Mathematical Theory of Viscous Incompressible Flow[M].Gordon & Breach，1963. [2] Youngren G K,Acrivos A. On the shape of a gas bubble in a viscous extensional flow[J].J Fluid Mech,1976,76:433—442. doi: 10.1017/S0022112076000724 [3] Rallison J M,Acrivos A.A numerical study of the deformation and burst of a viscous drop in an extensional flow[J].J Fluid Mech,1978,89:191—200. doi: 10.1017/S0022112078002530 [4] Chi B K,Leal L G.A theoretical study of the motion of a viscous drop toward a fluid interface at low Reynolds number[J].J Fluid Mech,1989,201:123—146. doi: 10.1017/S0022112089000868 [5] Pozrikidis C.The instability of a moving viscous drop[J].J Fluid Mech,1990,210:1—21. doi: 10.1017/S0022112090001203 [6] Pozrikidis C.The deformation of a liquid drop moving normal to a plane wall[J].J Fluid Mech,1990,215:331—363. doi: 10.1017/S0022112090002671 [7] Pozrikidis C.Computation of the pressure inside bubbles and pores in Stokes flow[J].J Fluid Mech,2003,474:319—317. [8] 陈建国.可变形液滴入孔问题研究[D].硕士研究生毕业论文.北京：北京大学,1992. [9] Stround A H,Secrest D.Gaussian Quadrature Formulas[M].Englewood,Cliffs N J:Prentice Hall,1966. [10] 严宗毅.低雷诺数流理论[M].北京：北京大学出版社,2002. -
计量
- 文章访问数: 2636
- HTML全文浏览量: 125
- PDF下载量: 472
- 被引次数: 0
下载:
渝公网安备50010802005915号