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Mar 2013

Volume 25, Issue 3, Articles (03xxxx)

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Phys. Fluids 25, 031302 (2013); http://dx.doi.org/10.1063/1.4793543 (13 pages)

Gretar Tryggvason, Sadegh Dabiri, Bahman Aboulhasanzadeh, and Jiacai Lu
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back to top Laminar Flows

Laminar flow of two miscible fluids in a simple network

Casey M. Karst, Brian D. Storey, and John B. Geddes

Phys. Fluids 25, 033601 (2013); http://dx.doi.org/10.1063/1.4794726 (17 pages)

Online Publication Date: 11 March 2013

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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.
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47.15.Fe Stability of laminar flows
47.51.+a Mixing
47.55.-t Multiphase and stratified flows
47.55.Hd Stratified flows
64.75.Ef Mixing
47.10.ad Navier-Stokes equations
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Inertial particle trapping in viscous streaming

Kwitae Chong, Scott D. Kelly, Stuart Smith, and Jeff D. Eldredge

Phys. Fluids 25, 033602 (2013); http://dx.doi.org/10.1063/1.4795857 (21 pages)

Online Publication Date: 28 March 2013

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The motion of an inertial particle in a viscous streaming flow of Reynolds number order 10 is investigated theoretically and numerically. The streaming flow created by a circular cylinder undergoing rectilinear oscillation with small amplitude is obtained by asymptotic expansion from previous work, and the resulting velocity field is used to integrate the Maxey–Riley equation with the Saffman lift for the motion of an inertial spherical particle immersed in this flow. It is found that inertial particles spiral inward and become trapped inside one of the four streaming cells established by the cylinder oscillation, regardless of the particle size, density and flow Reynolds number. It is shown that the Faxén correction terms divert the particles from the fluid particle trajectories, and once diverted, the Saffman lift force is most responsible for effecting the inward motion and trapping. The speed of this trapping increases with increasing particle size, decreasing particle density, and increasing oscillation Reynolds number. The effects of Reynolds number on the streaming cell topology and the boundaries of particle attraction are also explored. It is found that particles initially outside the streaming cell are repelled by the flow rather than trapped.
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47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
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