Elastic Instabilities of Polymer Solutions in Cross-Channel Flow

Arratia, Paulo E.; Thomas, Catherine; DiOrio, James P.; Gollub, Jerry P.

doi:10.1103/physrevlett.96.144502

Cited by 231 publications

(245 citation statements)

References 28 publications

Supporting

Mentioning

202

Contrasting

Order By: Relevance

“…Moreover, anomalies are known to occur for fluids of high extensional viscosity in the vicinity of the stagnation points in different flow geometries. [16][17][18][19] For viscoelastic fluids flowing in orthogonal channels, elastic instabilities have indeed been observed experimentally 20 and flow asymmetries have been predicted numerically. 21 The recirculation cells appearing at low α values will control the exchange of solute (or other passive or reactive species) between the two injected fluids: this exchange involves a combination of transverse molecular diffusion between the cells and the two flows (and from one cell to another) and convective transport by the circulation within the cells.…”

mentioning

confidence: 94%

Stokes flow paths separation and recirculation cells in X-junctions of varying angle

Cachile¹,

Talon

Gomba

et al. 2012

Physics of Fluids

View full text Add to dashboard Cite

Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle α in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing channels of the junction. Planar laser induced fluorescence (PLIF) measurements show that the largest part of each injected fluid “bounces back” preferentially into the outlet channel at the lowest angle to the injection; this is opposite to the inertial case and requires a high curvature of the corresponding streamlines. The proportion of this fluid in the other channel decreases from 50% at α = 90° to 0% at a threshold angle. These counterintuitive features reflect the minimization of energy dissipation for Stokes flows. Finite elements numerical simulations of a 2D Stokes flow of equivalent geometry confirm these results and show that, below the threshold angle αc = 33.8°, recirculation cells are present in the center part of the junction and separate the two injected flows of the two solutions. Reducing further α leads to the appearance of new recirculation cells with lower flow velocities.

show abstract

mentioning

confidence: 94%

Stokes flow paths separation and recirculation cells in X-junctions of varying angle

Cachile¹,

Talon

Gomba

et al. 2012

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…At the higher extensibility the FENE-P model has a much stronger tendency to yield a non-steady end-state flow: while for the FENE-CR model the flow bifurcates but remains steady up to De ≈ 1, for the FENE-P model the results suggest that a slightly fluctuating bifurcated-flow regime tends to set in at much lower levels of Deborah number. In order to illustrate this unsteady phenomenon, which was also observed by Arratia et al [9] in the microfluidic apparatus when this bifurcation was measured for the first time, the FENE-P model predictions of DQ at De = 0.46 are plotted in Fig. 13 where a periodic evolution of the asymmetry is shown with a period of about 50 time units (d/U).…”

Section: Effect Of Viscoelastic Modelmentioning

confidence: 99%

“…Arratia et al [9] visualized the flow of a flexible polyacrylamide solution in a microfabricated geometry formed by the crossing of two rectangular cross-section channels and observed that, even for the very low Reynolds number of their experiments, the polymer solution flow tended to evolve to a non-symmetric pattern while the corresponding Newtonian flow remained perfectly symmetric regardless of flow rate. That asymmetric flow pattern, with the incoming flow tending to be preferentially diverted to one of the outlet arms of the cross, was found to be steady at small to moderate Deborah numbers (De), thus corresponding to a supercritical pitchfork bifurcation (Larson [10]).…”

Section: Introductionmentioning

confidence: 99%

“…Such bifurcation phenomena had never been predicted in previous studies concerned with the cross-slot flow, in which most researchers adopted for the solution domain only one quarter of the full geometry, in the belief that the resulting flow would follow the symmetry imposed by that same solution domain, and thus sparing useful computational resources. However, motivated by the thought-provoking observations of Arratia et al [9], Poole et al [11] simulated the complete cross-slot geometry using the simplest of the available differential constitutive models, the upper-convected Maxwell (UCM) model, and were able to reproduce the main features of the experiments. Their predictions were in qualitative agreement with all the experimental observations: a supercritical bifurcation was found to occur at a critical Deborah number of De cr ≈ 0.31, under creeping-flow conditions, and at higher De the flow became unsteady.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Extensibility Effects in the Cross-slot Flow Bifurcation

Rocha

Poole

Alves

et al. 2008

AIP Conference Proceedings

View full text Add to dashboard Cite

a b s t r a c tThe flow of finite-extensibility models in a two-dimensional planar cross-slot geometry is studied numerically, using a finite-volume method, with a view to quantifying the influences of the level of extensibility, concentration parameter, and sharpness of corners, on the occurrence of the bifurcated flow pattern that is known to exist above a critical Deborah number. The work reported here extends previous studies, in which the viscoelastic flow of upper-convected Maxwell (UCM) and Oldroyd-B fluids (i.e. infinitely extensionable models) in a cross-slot geometry was shown to go through a supercritical instability at a critical value of the Deborah number, by providing further numerical data with controlled accuracy. We map the effects of the L 2 parameter in two different closures of the finite extendable non-linear elastic (FENE) model (the FENE-CR and FENE-P models), for a channel-intersecting geometry having sharp, "slightly" and "markedly" rounded corners. The results show the phenomenon to be largely controlled by the extensional properties of the constitutive model, with the critical Deborah number for bifurcation tending to be reduced as extensibility increases. In contrast, rounding of the corners exhibits only a marginal influence on the triggering mechanism leading to the pitchfork bifurcation, which seems essentially to be restricted to the central region in the vicinity of the stagnation point.

show abstract

“…However it is precisely at these points in the flow that interesting dynamics arise. Instabilities have been found in experiments at internal stagnation points [1,2,3,4,5], and related numerical instabilities are found in similar geometries [6,7,8,9,10,11]. It is unclear what is driving these instabilities, but it is reasonable to conjecture that they are related to the large polymer stresses and stress gradients which accumulate along the incoming and outgoing streamlines of these internal stagnation points.…”

Section: Introductionmentioning

confidence: 87%

Equilibrium circulation and stress distribution in viscoelastic creeping flow

Biello¹,

Thomases²

2016

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both as an asymptotic parameter and a regularization parameter. The structure of the singular part of the polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point; a smoothed δ-distribution whose width is proportional to the square-root of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number, and although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order velocity response to this stress island is constructed and shown to be independent of the diffusion coefficient in the limit. The secondary circulation counteracts the forced flow and has a vorticity jump at the location of the stress islands, essentially expelling the background vorticity from the location of the birefringent strands. The analytic solutions are shown to be in excellent quantitative agreement with full numerical simulations, and therefore, the analytic solutions elucidate the salient mechanisms of the flow response to viscoelasticity and the mechanism for instability.

show abstract

Elastic Instabilities of Polymer Solutions in Cross-Channel Flow

Cited by 231 publications

References 28 publications

Stokes flow paths separation and recirculation cells in X-junctions of varying angle

Stokes flow paths separation and recirculation cells in X-junctions of varying angle

On Extensibility Effects in the Cross-slot Flow Bifurcation

Equilibrium circulation and stress distribution in viscoelastic creeping flow

Contact Info

Product

Resources

About