We consider the translation of a rigid, axisymmetric, tightly fitting object through a cylindrical elastic tube filled with viscous fluid, using a combination of theory and direct numerical simulations. The intruding object is assumed to be wider than the undeformed tube radius, forcing solid–solid contact in the absence of relative motion. The motion of the object establishes a thin fluid film that lubricates this contact. Our theory couples lubrication theory to a geometrically nonlinear membrane description of the tube's elasticity, and applies to a slender intruding object and a thin tube with negligible bending rigidity. We show using asymptotic and numerical solutions of the theory, that the thickness of the thin fluid film scales with the square root of the relative speed for small speeds, set by a balance of hoop stresses, membrane tension and fluid pressure. While membrane tension is relatively small at the entrance of the film, it dominates near the exit and produces undulations of the film thickness, even in the limit of vanishing speeds and slender objects. We find that the drag force on the intruding object depends on the slope of its surface at the entrance to the thin fluid film, and scales as the square root of the relative speed. The predictions of the lubricated membrane theory for the shape of the film and the force on the intruder are in quantitative agreement with three-dimensional direct numerical simulations of the coupled fluid–elastic problem.

中文翻译：

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紧配合轴对称物体通过润滑弹性管的运动

我们结合理论和直接数值模拟，考虑通过充满粘性流体的圆柱形弹性管平移刚性、轴对称、紧密配合的物体。假设侵入物体比未变形的管半径更宽，在没有相对运动的情况下迫使固体-固体接触。物体的运动会形成一层薄薄的流体膜来润滑这种接触。我们的理论将润滑理论与管弹性的几何非线性膜描述相结合，并适用于细长的侵入物体和弯曲刚度可忽略不计的细管。我们使用理论的渐近和数值解证明，薄流体膜的厚度与小速度的相对速度的平方根成比例，由环向应力的平衡设定，膜张力和流体压力。虽然薄膜入口处的膜张力相对较小，但它在出口附近占主导地位并产生薄膜厚度的波动，即使在消失速度和细长物体的限制下也是如此。我们发现侵入物体上的阻力取决于其表面在薄流体膜入口处的斜率，并且与相对速度的平方根成比例。润滑膜理论对薄膜形状和入侵者所受力的预测与流体-弹性耦合问题的三维直接数值模拟定量一致。即使在消失速度和细长物体的限制下。我们发现侵入物体上的阻力取决于其表面在薄流体膜入口处的斜率，并且与相对速度的平方根成比例。润滑膜理论对薄膜形状和入侵者所受力的预测与流体-弹性耦合问题的三维直接数值模拟定量一致。即使在消失速度和细长物体的限制下。我们发现侵入物体上的阻力取决于其表面在薄流体膜入口处的斜率，并且与相对速度的平方根成比例。润滑膜理论对薄膜形状和入侵者所受力的预测与流体-弹性耦合问题的三维直接数值模拟定量一致。