Laminar Flow of Two Miscible Fluids in a Simple Network
© 2012 American Institute of Physics. This article was published in Physics of Fluids, vol. 29, iss. 3 and can be found here.
When a ﬂuid comprised of multiple phases or constituents ﬂows through a network, nonlinear phenomena such as multiple stable equilibrium states and spontaneous oscillations can occur. Such behavior has been observed or predicted in a number of networks including the ﬂow of blood through the microcirculation, the ﬂow of picoliter droplets through microﬂuidic devices, the ﬂow of magma through lava tubes, and two-phase ﬂow in refrigeration systems. While the existence of nonlinear phenomena in a network with many inter-connections containing ﬂuids with complex rheology may seem unsurprising, this paper demonstrates that even simple networks containing Newtonian ﬂuids in laminar ﬂow can demonstrate multiple equilibria. The paper describes a theoretical and experimental investigation of the laminar ﬂow of two miscible Newtonian ﬂuids of different density and viscosity through a simple network. The ﬂuids stratify due to gravity and remain as nearly distinct phases with some mixing occurring only by diffusion. This ﬂuid system has the advantage that it is easily controlled and modeled, yet contains the key ingredients for network nonlinearities. Experiments and 3D simulations are ﬁrst used to explore how phases distribute at a single T-junction. Once the phase separation at a single junction is known, a network model is developed which predicts multiple equilibria in the simplest of networks. The existence of multiple stable equilibria is conﬁrmed experimentally and a criterion for existence is developed. The network results are generic and could be applied to or found in different physical systems.