A THREE-DIMENSIONAL STUDY OF THE MOTION OF A DROP IN PLANE POISEUILLE FLOW AT FINITE REYNOLDS NUMBERS
A THREE-DIMENSIONAL STUDY OF THE MOTION OF A DROP IN PLANE POISEUILLE FLOW AT FINITE REYNOLDS NUMBERS
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发表时间：
2010-04
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通讯作者：
A. Nourbakhsh;S. Mortazavi
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作者：
A. Nourbakhsh;S. Mortazavi
本文对在有限雷诺数下，在重力可忽略的条件下，两平行平板间中性浮力液滴在平面Poiffille流中的运动进行了三维模拟。完整的Navier-Stokes方程求解的有限差分/前跟踪方法，允许一个完全可变形的界面之间的下降和悬浮介质和列入的表面张力。在小雷诺数（< 1）的限制下，液滴的运动方向取决于液滴流体的粘度与环境流体的粘度的比率。在有限雷诺数下，液滴迁移到壁面和中心线之间的平衡横向位置（Segre-Silberberg效应）。结果是在一个范围内的毛细管数，雷诺数，粘度比和液滴大小。随着雷诺数的增加或毛细管数或粘度比的减小，平衡位置向壁面移动。液滴速度随毛细管数和粘度比的增大而增大，随雷诺数的增大而减小。随着毛细管数或粘度比的增加，液滴的变形更大。在毛细管数不变的情况下，液滴变形随雷诺数的增加而略有增加。三维液滴的平衡位置接近于二维模拟预测的平衡位置。但平移速度不同意定量与二维模拟。
Three-dimensional simulations are presented on the motion of a neutrally buoyant drop between two parallel plates at a finite-Reynolds-number in plane Poiseuille flow, under conditions of negligible gravitational force. The full Navier-Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the drop and the suspending medium and the inclusion of the surface tension. In the limit of a small Reynolds number (< 1), the direction of motion of the drop depends on the ratio of the viscosity of the drop fluid to the viscosity of the ambient fluid. At finite Reynolds numbers, the drop migrates to an equilibrium lateral position about halfway between the wall and the centerline (the Segre-Silberberg effect). Results are presented over a range of capillary number, Reynolds number, viscosity ratio and drop size. As the Reynolds number increases or capillary number or viscosity ratio decreases, the equilibrium position moves closer to the wall. The drop velocity is observed to increase with increasing capillary number and viscosity ratio, but decreases with increasing Reynolds number. The drops are more deformed with increasing the capillary number or viscosity ratio. The drop deformation increases slightly with increasing Reynolds number at constant capillary number. The equilibrium position of the three-dimensional drop is close to that predicted by two-dimensional simulations. But the translational velocities do not agree quantitatively with two-dimensional simulations.