Spontaneous oscillations in simple fluid networks

TL;DR

This paper investigates spontaneous oscillations in simple fluid networks with two miscible Newtonian fluids, using analytic and numerical methods to identify bifurcations and analyze the sensitivity of oscillations to system parameters.

Contribution

It introduces a combined analytic and numerical approach to identify bifurcations and analyze oscillations in simple fluid networks, applicable to various physical systems.

Findings

Documented sustained spontaneous oscillations in both models.

Identified saddle-node and Hopf bifurcations in parameter space.

Demonstrated sensitivity of oscillations to viscosity contrast and flow rates.

Abstract

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.