简单流体网络中的自发振荡
Spontaneous oscillations in simple fluid networks
摘要：
在含有多相或多组分流动的流体网络中，包括多重平衡和自发振荡在内的非线性现象是常见的。在许多系统中，这种行为可能归因于网络的复杂几何形状，组成流体的复杂流变学，或者在微血管血流的情况下，生物控制。在本文中，我们研究了两个例子，一个简单的三节点流体网络包含两个不同粘度的牛顿流体，第一个建模微血管血流和第二个建模分层层流。我们使用分析和数值技术相结合，通过大参数空间识别和跟踪鞍结和Hopf分岔。在这两个模型中，我们记录持续的自发振荡，并为实验相关的参数分析的例子，调查这些振荡的敏感性的组成流体和入口流速之间的粘度对比度的变化。对于分层层流的情况下，我们详细介绍了一个物理上可实现的一组网络参数，表现出丰富的动态。这里开发的工具和结果是通用的，可以应用到其他物理系统。
英文摘要：
Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituent flows. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent fluids, or, in the case of microvascular blood flow, biological control. In this paper we investigate two examples of a simple three-node fluid network containing two miscible Newtonian fluids of differing viscosities, the first modeling microvascular blood flow and the second modeling stratified laminar flow. We use a combination of analytic and numerical techniques to identify and track saddle-node and Hopf bifurcations through the large parameter space. In both models, we document sustained spontaneous oscillations and, for an experimentally relevant example of parameter analysis, investigate the sensitivity of these oscillations to changes in the viscosity contrast between the constituent fluids and the inlet flow rates. For the case of stratified laminar flow, we detail a physically realizable set of network parameters that exhibit rich dynamics. The tools and results developed here are general and could be applied to other physical systems.
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