Upstream vortex and elastic wave in the viscoelastic flow around a confined cylinder

Abstract

The viscoelastic flow past a cylinder is a classic benchmark problem that is not completely understood. Using novel 3D holographic particle velocimetry, we report three main discoveries of the elastic instability upstream of a single cylinder in viscoelastic channel flow. First, we observe that upstream vortices initiate at the corner between the cylinder and the wall and grow with increasing flow rate. Second, beyond a critical Weissenberg, the flow upstream becomes unsteady and switches between two bistable configurations, leading to symmetry breaking in the cylinder axis direction that is highly three-dimensional in nature. Lastly, we find that the disturbance of the elastic instability propagates relatively far upstream via an elastic wave, and is weakly correlated with that in the cylinder wake. The wave speed and the extent of the instability increase with Weissenberg number, indicating an absolute instability in viscoelastic fluids.

Pore‐Scale Flow Characterization of Polymer Solutions in Microfluidic Porous Media

“…Single‐molecule imaging of fluorescently labeled DNA provides evidence that polymers are stretched and have hysteretic conformations as they flow around the cylinder in a manner similar to coil‐stretch hysteresis (Section ). Thus, similar to the case of flow through a constriction, upstream eddies form during polymer solution flow around a cylinder in a narrow channel, growing in size and becoming unstable as Wi increases . Holographic imaging enables full characterization of the complex 3D structure of these eddies ( Figure ).…”

“…Holographic imaging enables full characterization of the complex 3D structure of these eddies ( Figure ). Intriguingly, the vertical location of the eddy can exhibit discrete switching between the top and bottom walls of the channel, suggesting a possible connection to bistable polymer conformations (described in the context of the coil‐stretch transition in Section ). Exploring this connection will be a valuable direction for future work.…”

“…The vertical location of the eddy switches between the top and bottom walls over time. Reproduced with permission . Copyright 2019, Cambridge University Press.…”

Three-dimensional viscoelastic instabilities in microchannels

“…Purely elastic instabilities (Shaqfeh 1996) driven by elastic normal stresses have been widely observed in the absence of significant inertial effects, in both viscometric flows, that imparts steady shearing motion on each fluid particle (Larson, Shaqfeh & Muller 1990), and more general non-viscometric flow geometries (Pakdel & McKinley 1996). In addition to the usual material properties of density ρ and dynamic viscosity η which characterise single-phase Newtonian flows, dilute polymeric solutions, like those used by Qin et al (2019) and most other studies in this area, are also characterised by a 'relaxation' time (Bird, Armstrong & Hassager 1987). The Deborah number De, which is a measure of this relaxation time relative to a characteristic residence time of the flow, must become unimportant in fully developed, steady viscometric flows as the characteristic residence time tends to infinity.…”

“…These two parameters are often thought of as essentially interchangeable although, in general, they represent subtly different properties of the flow: one quantifying inherently Lagrangian unsteady effects (De) and the other the 'strength' of the flow (Wi). In the problem studied by Qin et al (2019) of flow past a cylinder of diameter d in an approximately square channel of height H, the characteristic time scale of the flow can be estimated as the time taken for a fluid particle to circumvent half the cylinder (i.e. πd/2U ∼ d/U ∼ H/U as d ∼ H).…”