论文标题
非牛顿流体结构的相互作用：可变形通道中粘弹性Oldroyd-B流体的流动
Non-Newtonian fluid-structure interaction: Flow of a viscoelastic Oldroyd-B fluid in a deformable channel
论文作者
论文摘要
我们分析了Oldroyd-B流体和可变形通道之间的稳定非牛顿流体结构相互作用。具体而言，我们提供了一个理论框架，用于计算流体粘弹性对流速压力下降关系以及通道弹性壁的变形的领先效应。我们首先确定了在细长和浅道通道中管理流体结构相互作用的特征量表和无量纲参数。在Deborah Number $ de $的功率中，应用流量的润滑近似，并采用扰动扩展，在弱质量固定的限制中，压力的封闭形式表达式是该通道不均匀形状的函数，最高可达$ \ \\ mathrm {o}（o}（de）$。将流体动力压力耦合到弹性变形，我们提供了流体粘弹性与通道对压力和变形场的依从性之间的相互作用的领先效应，以及流速压力降低的关系。对于流量率控制的制度和弱粘弹性极限，我们在分析上表明，变形顶壁的依从性和流体的粘弹性都会降低压力下降。此外，我们揭示了通道依从性的影响与流体粘弹性对变形之间的权衡。尽管通道的依从性增加了变形，但流体的粘弹性降低了它。
We analyze the steady non-Newtonian fluid-structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a theoretical framework for calculating the leading-order effect of the fluid's viscoelasticity on the flow rate-pressure drop relation and on the deformation of the channel's elastic wall. We first identify the characteristic scales and dimensionless parameters governing the fluid-structure interaction in slender and shallow channels. Applying the lubrication approximation for the flow and employing a perturbation expansion in powers of the Deborah number $De$, we derive a closed-form expression for the pressure as a function of the non-uniform shape of the channel in the weakly viscoelastic limit up to $\mathrm{O}(De)$. Coupling the hydrodynamic pressure to the elastic deformation, we provide the leading-order effect of the interplay between the viscoelasticity of the fluid and the compliance of the channel on the pressure and deformation fields, as well as on the flow rate-pressure drop relation. For the flow-rate-controlled regime and in the weakly viscoelastic limit, we show analytically that both the compliance of the deforming top wall and the viscoelasticity of the fluid decrease the pressure drop. Furthermore, we reveal a trade-off between the influence of compliance of the channel and the fluid's viscoelasticity on the deformation. While the channel's compliance increases the deformation, the fluid's viscoelasticity decreases it.
