Effect of interfacial slip on the cross-stream migration of a drop in an unbounded Poiseuille flow.
Effect of interfacial slip on the cross-stream migration of a drop in an unbounded Poiseuille flow.
复制标题
界面滑移对无界泊肃叶流中液滴跨流迁移的影响。
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Chakraborty
中科院分区：
文献类型：
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作者：
Shubhadeep Mandal;A. Bandopadhyay;S. Chakraborty
我们分析了悬浮在无界流体中的浮力液滴的运动和变形，该流体在液滴界面存在滑移的情况下经历小雷诺数的二次剪切流。界面处的边界条件通过简单的纳维滑移条件来解释。考虑到小但有限的界面变形，推导了液滴的速度和形状变形的表达式，并针对沉降、剪切流和泊肃叶流的具体情况给出了结果，并将先前报告的结果作为我们一般表达式的限制情况。发现界面滑移的存在显着影响泊肃叶流中液滴的轴向和横向迁移速度。对于具有较大粘度的液滴，其中液滴速度增加，滑移的影响更为显着。对于任何液滴与介质粘度比，显着的界面滑移的存在总是导致变形液滴向通道的中心线迁移，这与界面处无滑移的情况相反，后者允许液滴根据粘度比向或远离中心线迁移。我们获得了滑移对跨流迁移时间尺度的影响，该时间尺度量化了到达河道中最终稳定径向位置所需的时间。液滴界面处滑移的存在导致跨流迁移时间尺度的减小，这进一步导致液滴在跨流方向上的更快运动。泊肃叶流存在下的重力不仅影响轴向运动，而且影响液滴的跨流迁移速度；界面滑移总是会增加液滴速度。
We analyze the motion and deformation of a buoyant drop suspended in an unbounded fluid which is undergoing a quadratic shearing flow at small Reynolds number in the presence of slip at the interface of the drop. The boundary condition at the interface is accounted for by means of a simple Navier slip condition. Expressions for the velocity and the shape deformation of the drop are derived considering small but finite interface deformation, and results are presented for the specific cases of sedimentation, shear flow, and Poiseuille flow with previously reported results as the limiting cases of our general expressions. The presence of interfacial slip is found to markedly affect axial as well as cross-stream migration velocity of the drop in Poiseuille flow. The effect of slip is more prominent for drops with larger viscosity wherein the drop velocity increases. The presence of significant interface slippage always leads to migration of a deformed drop towards the centerline of the channel for any drop-to-medium viscosity ratio, which is in contrast to the case of no slip at the interface, which allows drop migration towards or away from the centerline depending on the viscosity ratio. We obtain the effect of slip on the cross-stream migration time scale, which quantifies the time required to reach a final steady radial position in the channel. The presence of slip at the drop interface leads to a decrease in the cross-stream migration time scale, which further results in faster motion of the drop in the cross-stream direction. Gravity in the presence of Poiseuille flow is shown to affect not only the axial motion, but also the cross-stream migration velocity of the drop; interfacial slip always increases the drop velocities.