Spontaneous oscillations in simple fluid networks

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 f...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2013-06
Main Authors: Karst, Nathaniel J, Storey, Brian D, Geddes, John B
Format: Article
Language:English
Subjects:
Bifurcations
Biological control
Blood flow
Computational fluid dynamics
Constituents
Flow velocity
Fluid flow
Fluids
Hopf bifurcation
Inlet flow
Laminar flow
Mathematical models
Newtonian fluids
Nonlinear phenomena
Oscillations
Parameter identification
Parameter sensitivity
Rheological properties
Rheology
Sensitivity analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422