Observations of spontaneous oscillations in simple two-fluid networks

Storey, Brian D.; Hellen, Deborah; Karst, Nathaniel J.; Geddes, J

doi:10.1103/physreve.91.023004

Cited by 4 publications

(4 citation statements)

References 29 publications

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“…Oscillations similar to our finding were recently discovered in a stratified flow of two miscible liquids in a narrowing loop [32]. It suggests a possible existence of a common mechanism of oscillations caused by flow of complex fluids through parallel, narrowing ducts.…”

Section: Discussionsupporting

confidence: 90%

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks

2015

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The simplest microfluidic network (a loop) comprises two parallel channels with a common inlet and a common outlet. Recent studies that assumed a constant cross section of the channels along their length have shown that the sequence of droplets entering the left (L) or right (R) arm of the loop can present either a uniform distribution of choices (e.g., RLRLRL...) or long sequences of repeated choices (RRR...LLL), with all the intermediate permutations being dynamically equivalent and virtually equally probable to be observed. We use experiments and computer simulations to show that even small variation of the cross section along channels completely shifts the dynamics either into the strong preference for highly grouped patterns (RRR...LLL) that generate system-size oscillations in flow or just the opposite-to patterns that distribute the droplets homogeneously between the arms of the loop. We also show the importance of noise in the process of self-organization of the spatiotemporal patterns of droplets. Our results provide guidelines for rational design of systems that reproducibly produce either grouped or homogeneous sequences of droplets flowing in microfluidic networks.

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Section: Discussionsupporting

confidence: 90%

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks

2015

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“…Our findings are consistent with experimental results reported by Storey et al. ( 2015 ). They conducted experiments involving mixtures of two fluids in slightly different network geometries and found that imposing flux boundary conditions produced a larger region of instability than imposing pressure boundary conditions.…”

Section: Characterising the Steady And Dynamic Behaviours Of A Three-...supporting

confidence: 94%

Structural Features of Microvascular Networks Trigger Blood Flow Oscillations

et al. 2022

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We analyse mathematical models in order to understand how microstructural features of vascular networks may affect blood flow dynamics, and to identify particular characteristics that promote the onset of self-sustained oscillations. By focusing on a simple three-node motif, we predict that network “redundancy”, in the form of a redundant vessel connecting two main flow-branches, together with differences in haemodynamic resistance in the branches, can promote the emergence of oscillatory dynamics. We use existing mathematical descriptions for blood rheology and haematocrit splitting at vessel branch-points to construct our flow model; we combine numerical simulations and stability analysis to study the dynamics of the three-node network and its relation to the system’s multiple steady-state solutions. While, for the case of equal inlet-pressure conditions, a “trivial” equilibrium solution with no flow in the redundant vessel always exists, we find that it is not stable when other, stable, steady-state attractors exist. In turn, these “nontrivial” steady-state solutions may undergo a Hopf bifurcation into an oscillatory state. We use the branch diameter ratio, together with the inlet haematocrit rate, to construct a two-parameter stability diagram that delineates regimes in which such oscillatory dynamics exist. We show that flow oscillations in this network geometry are only possible when the branch diameters are sufficiently different to allow for a sufficiently large flow in the redundant vessel, which acts as the driving force of the oscillations. These microstructural properties, which were found to promote oscillatory dynamics, could be used to explore sources of flow instability in biological microvascular networks.

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“…This approach has proved fruitful in the past. Prior theoretical work using similar network models, but different constitutive laws for stratified flow of Newtonian fluids with different viscosity (Karst et al 2014) led to experiments which confirmed the existence of oscillations (Storey et al 2015). Here, however, the predictions of observable oscillatory behavior with blood flow occur over a relatively narrow range of parameters.…”

Section: Discussionmentioning

confidence: 55%

Oscillations and Multiple Equilibria in Microvascular Blood Flow

2015

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We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through a combination of analytic and numeric techniques, we predict in a series of two-parameter bifurcation diagrams a range of dynamical behaviors, including multiple equilibria flow configurations, simple oscillations in volumetric flow rate, and multiple coexistent limit cycles at physically realizable parameters. We show that complexity in network topology is not necessary for complex behaviors to arise and that nonlinear rheology, in particular the plasma skimming effect, is sufficient to support oscillatory dynamics similar to those observed in vivo.

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Observations of spontaneous oscillations in simple two-fluid networks

Cited by 4 publications

References 29 publications

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks

Structural Features of Microvascular Networks Trigger Blood Flow Oscillations

Oscillations and Multiple Equilibria in Microvascular Blood Flow

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