We analyze the dynamic behavior of viscoelastic fluids in elastic tubes subject to pulsatile pressure gradients. In particular, we study the dynamic permeability, a response function that relates linearly flow and pressure gradient in frequency domain. We have found resonances that can be associated to the elasticity of the tube and resonances that can be associated to the elasticity of the fluid. There is a rich phenomenology that includes cooperation and competition of both elasticities. Tuning of the system parameters allows for the excitation of the different modes in the system, sometimes giving responses that are larger than the ones of the corresponding systems with elasticity in only one of its elements. This behavior is similar to the one of two coupled oscillators. Our results are relevant for small confining geometries with low Young moduli. For example, for a microtube with a radius of a few hundred microns with the elasticity of polydimethylsiloxane (PDMS), in which a viscoelastic fluid, with the rheological parameters of blood, is driven by a pulsatile pressure gradient, resonance frequencies on the sound range are predicted. In a wide frequency range, the dynamic permeability is much lower than the one of the same fluid flowing in a poly(methyl methacrilate) (PMMA) tube. Our results are potentially useful for tailoring composite laboratory-on-a-chip devices, where introducing materials with different parameters in a device would induce an increase or decrease of the amplitude of the longitudinally averaged flow. We demonstrate that the magnitude of the dynamic permeability for a composite tube, at a given frequency of the driving pressure drop, determines the amplitude of the average flow along the composite tube.

中文翻译：

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粘弹性流体与弹性微管在脉动强迫作用下的合作与竞争

我们分析了受脉动压力梯度影响的弹性管中粘弹性流体的动力学行为。特别是，我们研究了动态渗透率，这是一个在频域内线性关系流量和压力梯度的响应函数。我们已经发现可以与管的弹性相关的共振以及可以与流体的弹性相关的共振。有丰富的现象学，包括两种弹性的合作与竞争。系统参数的调整允许激发系统中的不同模式，有时所产生的响应要比相应系统的响应大，并且仅在其元素之一中具有弹性。此行为类似于两个耦合振荡器之一。我们的结果与低杨氏模量的小约束几何有关。例如，对于半径为几百微米的具有聚二甲基硅氧烷（PDMS）弹性的微管，其中具有血液流变学参数的粘弹性流体由脉动压力梯度驱动，共振频率在声范围内被预测。在较宽的频率范围内，动态渗透率远低于在聚甲基丙烯酸甲酯（PMMA）管中流动的相同流体之一。我们的结果对于定制复合片上实验室设备可能有用，在这种设备中，将具有不同参数的材料引入设备将导致纵向平均流量的幅度增加或减少。我们证明了复合管的动态渗透率的大小，