The motion of long bubbles in polygonal capillaries. Part 1. Thin films
The motion of long bubbles in polygonal capillaries. Part 1. Thin films
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DOI：
10.1017/s0022112095001443
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发表时间：
1995-06
影响因子：
3.7
通讯作者：
H. Wong;C. Radke;S. Morris
中科院分区：
文献类型：
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作者：
H. Wong;C. Radke;S. Morris
多孔介质中的泡沫表现出异常高的表观粘度，使其在许多工业过程中非常有用。然而，泡沫的流变学是复杂的，并且没有很好地理解。以前的泡沫孔级模型主要是基于圆形毛细管中气泡流动的研究。然而，圆形毛细管缺少表征孔的几何形状的拐角。本文研究了多边形毛细管中泡状流的压力-速度关系。多边形毛细管中的长气泡充当泄漏活塞。由于毛细管侧壁施加的大阻力，“活塞”不愿移动。因此，毛细管中的液体以比气泡高一个数量级的速度绕过气泡通过泄漏的角落。因此，压力功主要通过流体的运动而不是气泡的运动来耗散。这与基于圆形毛细管中气泡流的结论相反。这种新的流动状态的发现调和两组矛盾的泡沫流动实验。本文的第一部分研究了在Ca → 0（Ca = μU/σ，其中μ为流体粘度，U为气泡速度，σ为表面张力）极限条件下毛细管壁上的流体膜。第2部分（Wong等1995）使用后端的膜轮廓来计算气泡的阻力。由于气泡长度是任意的，因此这里将膜轮廓确定为无量纲下游距离x的一般函数。对于1 [Lt ] x [Lt ] Ca−1，膜轮廓被冻结，中心处的厚度为Ca 2/3量级，侧面处的厚度为Ca量级。对于x <$Ca−1，表面张力使中心的膜重新排列成抛物线形状，而侧面的膜变薄为Ca 4/3。对于x [Gt ] Ca−1，膜仍然是抛物线，但高度随着膜流体通过侧收缩泄漏而减小。对于x <$Ca−5/3，抛物线的高度为Ca 2/3阶。最后，对于x [Gt ] Ca−5/3，高度以Ca 1/4x−1/4的形式减小。
Foam in porous media exhibits an unusually high apparent viscosity, making it useful in many industrial processes. The rheology of foam, however, is complex and not well understood. Previous pore-level models of foam are based primarily on studies of bubble flow in circular capillaries. A circular capillary, however, lacks the corners that characterize the geometry of the pores. We study the pressure–velocity relation of bubble flow in polygonal capillaries. A long bubble in a polygonal capillary acts as a leaky piston. The ‘piston’ is reluctant to move because of a large drag exerted by the capillary sidewalls. The liquid in the capillary therefore bypasses the bubble through the leaky corners at a speed an order higher than that of the bubble. Consequently, the pressure work is dissipated predominantly by the motion of the fluid and not by the motion of the bubble. This is opposite to the conclusion based on bubble flow in circular capillaries. The discovery of this new flow regime reconciles two groups of contradictory foam-flow experiments. Part 1 of this work studies the fluid films deposited on capillary walls in the limit Ca → 0 (Ca ≡ μU/σ, where μ is the fluid viscosity, U the bubble velocity, and σ the surface tension). Part 2 (Wong et al. 1995) uses the film profile at the back end to calculate the drag of the bubble. Since the bubble length is arbitrary, the film profile is determined here as a general function of the dimensionless downstream distance x. For 1 [Lt ] x [Lt ] Ca−1, the film profile is frozen with a thickness of order Ca2/3 at the centre and order Ca at the sides. For x ∼ Ca−1, surface tension rearranges the film at the centre into a parabolic shape while the film at the sides thins to order Ca4/3. For x [Gt ] Ca−1, the film is still parabolic, but the height decreases as film fluid leaks through the side constrictions. For x ∼ Ca−5/3, the height of the parabola is order Ca2/3. Finally, for x [Gt ] Ca−5/3, the height decreases as Ca1/4x−1/4.