Peristaltic pumping of rigid objects in an elastic tube
Peristaltic pumping of rigid objects in an elastic tube
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弹性管中刚性物体的蠕动泵送
DOI：
10.1017/s0022112010005926
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发表时间：
2011
影响因子：
3.7
通讯作者：
N. Balmforth
中科院分区：
文献类型：
--
作者：
D. Takagi;N. Balmforth
建立了长蠕动波推动悬浮刚体沿充液轴对称管内运动的数学模型。流体的流动用润滑理论来描述，管的变形用线弹性来描述。该物体可以是一根半径不变的无限长棒，也可以是一个有限长度的抛物线形菱形。该系统由施加在管壁上的径向力驱动，该力沿管轴匀速向下转换，并选择一种形式来产生周期波列或孤立波。这些波对封闭的物体施加牵引力，迫使它运动起来。周期波驱动无限棒的速度在中等强迫振幅下达到最大值，在大振幅极限下接近波速的大约四分之一。如果力足够强，有限菱形可以以与孤立波或周期波列相同的速度被夹带和驱动。对于较弱的强迫，菱形要么留在孤立波后面，要么与周期性序列中的波反复相互作用，产生断断续续的前进。夹带的阈值强迫幅值随被封闭物体的径向跨度而微弱增加，但随轴向长度而强烈增加，如果物体太长则不可能夹带。
A mathematical model is developed for long peristaltic waves propelling a suspended rigid object down a fluid-filled axisymmetric tube. The fluid flow is described using lubrication theory and the deformation of the tube using linear elasticity. The object is taken to be either an infinitely long rod of constant radius or a parabolic-shaped lozenge of finite length. The system is driven by a radial force imposed on the tube wall that translates at constant speed down the tube axis and with a form chosen to generate a periodic wave train or a solitary wave. These waves exert a traction on the enclosed object, forcing it into motion. Periodic waves drive the infinite rod at a speed that attains a maximum at a moderate forcing amplitude and approaches approximately one quarter of the wave speed in the large-amplitude limit. The finite lozenge can be entrained and driven at the same speed as a solitary wave or periodic wave train if the forcing is sufficiently strong. For weaker forcing, the lozenge is either left behind the solitary wave or interacts repeatedly with the waves in the periodic train to generate stuttering forward progress. The threshold forcing amplitude for entrainment increases weakly with the radial span of the enclosed object, but strongly with the axial length, with entrainment becoming impossible if the object is too long.