Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels

Abstract

We investigate the stability of steady planar stagnation flows of a dilute polyethylene oxide (PEO) solution using T-shaped microchannels. The precise flow rate control and well-defined geometries achievable with microfluidic fabrication technologies enable us to make detailed observations of the onset of elastically-driven flow asymmetries in steady flows with strong planar elongational characteristics. We consider two different stagnation flow geometries; corresponding to T-shaped microchannels with, and without, a recirculating cavity region. In the former case, the stagnation point is located on a free streamline, whereas in the absence of a recirculating cavity the stagnation point at the separating streamline is pinned at the confining wall of the microchannel. The kinematic differences in these two configurations affect the resulting polymeric stress fields and control the critical conditions and spatiotemporal dynamics of the resulting viscoelastic flow instability. In the free stagnation point flow, a strand of highly-oriented polymeric material is formed in the region of strong planar extensional flow. This leads to a symmetry-breaking bifurcation at moderate Weissenberg numbers followed by the onset of three-dimensional flow at high Weissenberg numbers, which can be visualized using streak-imaging and microparticle image velocimetry. When the stagnation point is pinned at the wall this symmetry-breaking transition is suppressed and the flow transitions directly to a threedimensional time-dependent flow at an intermediate flow rate. The spatial characteristics of these purely elastic flow transitions are compared quantitatively to the predictions of two-dimensional viscoelastic numerical simulations using a single-mode simplified PhanThien-Tanner (SPTT) model.

Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

“…2. It is currently widely accepted that the underlying mechanism for the onset of purely elastic flow instabilities is related to streamline curvature, and the development of large hoop stresses, which generates tension along fluid streamlines leading to flow destabilization (Larson et al 1990;Pakdel and McKinley 1996;McKinley et al 1996;Soulages et al 2009). McKinley (1996, 1998) showed that the critical conditions for the onset of purely elastic instabilities can be described for a wide range of flows by a single dimensionless parameter (M), which accounts for elastic normal stresses and streamline curvature: where k is the relaxation time of the fluid, v is the local streamwise fluid velocity, s 11 is the local tensile stress in the flow direction, s 12 is the shear stress ðs 12 ¼ g_ cÞ and < is the streamline local radius of curvature.…”

Accurate control of hyperbolic trajectories in any dimension

“…A classical example from fluid mechanics is the concept of a fluidic device which achieves droplet manipulation through positioning at the hyperbolic trajectory location [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In the paradigmatic two-dimensional device with a hyperbolic point with attached one-dimensional stable and unstable manifolds, droplet elongation in the unstable direction is achieved by this process.…”

“…Thus, if hyperbolic trajectories with a heteroclinic manifold connecting them are made to move in a judiciously chosen manner, it will be possible to break apart the heteroclinic manifold into intersecting stable and unstable manifolds, thereby causing complicated (i.e., chaotic) mixing. Thus, controlling hyperbolic trajectories is a yet-unexplored avenue in the topic of controlling and optimizing mixing which is eliciting much recent interest [23,24,[38][39][40][41][42][43][44][45][46][47][48][49][50].…”

Controlling the Unsteady Analogue of Saddle Stagnation Points

“…Their stable and unstable manifolds separate the flow regime into regions of fluid which do not mix. Analysis of saddle stagnation points is well established in fluid applications ranging from groundwater modeling [29,46], macro-and micromixing devices [17,2,6,50,42,21], and oceanographic flows [48,3,36,11,9,40]. The analogous entity in unsteady flows is that of a hyperbolic trajectory, a specific type of time-varying fluid parcel trajectory which possesses time-varying stable and unstable manifolds, whose locations govern fluid transport; cf.…”