scholarly journals Control of a purely elastic symmetry-breaking flow instability in cross-slot geometries

2019 ◽  
Vol 881 ◽  
pp. 1123-1157 ◽  
Author(s):  
Mahdi Davoodi ◽  
Allysson F. Domingues ◽  
Robert J. Poole
Keyword(s):  
Symmetry Breaking ◽  
Stagnation Point ◽  
Passive Control ◽  
Flow Instability ◽  
Extensional Flow ◽  
Creeping Flow ◽  
Viscous Force ◽  
Benchmark Problems ◽  
Blockage Ratio ◽  
The Cross

The cross-slot stagnation point flow is one of the benchmark problems in non-Newtonian fluid mechanics as it allows large strains to develop and can therefore be used for extensional rheometry measurements or, once instability arises, as a mixing device. In such a flow, beyond a critical value for which the ratio of elastic force to viscous force is high enough, elasticity can break symmetry even in the absence of significant inertial forces (i.e. creeping flow), which is an unwanted phenomenon if the device is to be used as a rheometer but beneficial from a mixing perspective. In this work, a passive control mechanism is introduced to the cross-slot by adding a cylinder at the geometric centre to replace the ‘free’ stagnation point with ‘pinned’ stagnation points at the surface of the cylinder. In the current modified geometry, effects of the blockage ratio (the ratio of the diameter of the cylinder to the width of the channel), the Weissenberg number (the ratio of elastic forces to viscous forces) and extensibility parameters ($\unicode[STIX]{x1D6FC}$ and $L^{2}$) are investigated in two-dimensional numerical simulations using both the simplified Phan-Thien and Tanner and finitely extensible nonlinear elastic models. It is shown that the blockage ratio for fixed solvent-to-total-viscosity ratio has a stabilizing effect on the associated symmetry-breaking instability. The resulting data show that the suggested modification, although significantly changing the flow distribution in the region near the stagnation point, does not change the nature of the symmetry-breaking instability or, for low blockage ratio, the critical condition for onset. Using both numerical and physical experiments coupled with a supporting theoretical analysis, we conclude that this instability cannot therefore be solely related to the extensional flow near the stagnation point but it is more likely related to streamline curvature and the high deformation rates towards the corners, i.e. a classic ‘curved streamlines’ purely elastic instability. Our work also suggests that the proposed geometric modification can be an effective approach for enabling higher flow rates to be achieved whilst retaining steady symmetric flow.

Instabilities of Pre-Stretched Viscoelastic Flow in Microfluidic Cross-Slot Devices

2019 ◽  
Author(s):  
Meng Zhang ◽  
Wu Zhang ◽  
Zhengwei Wu ◽  
Weihua Cai ◽  
Zhiying Zheng ◽  
...  
Keyword(s):  
Equilibrium State ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Elastic Energy ◽  
Extensional Flow ◽  
Weissenberg Number ◽  
Viscoelastic Flow ◽  
Slot Channel ◽  
Symmetric State ◽  
The Cross

Abstract In this paper we experimentally studied the instabilities of pre-stretched viscoelastic fluid in cross-slot devices. We first investigate the instability of the flow in a standard cross-slot at different Weissenberg numbers without pre-stretch. It is found the viscoelastic flow is transformed from the steady symmetric state to the instabilities states including the steady asymmetric state and the non-periodically oscillated asymmetric state. This is due to the extension of the polymer in the viscoelastic fluid at the stagnation point stretched by the extensional flow in the cross-slot. We then modified the cross-slot channel in which the viscoelastic fluid is pre-stretched before entering the crossroad region. Due to the pre-stretch, elastic energy is pre-stored in the polymer, and the energy required to fully extend the polymer is also different with those extending from equilibrium state. As a result, the flow remains in the steady asymmetric state in all tested Weissenberg number condition.

The wake instability in viscoelastic flow past confined circular cylinders

1993 ◽  
Vol 344 (1671) ◽  
pp. 265-304 ◽  
Keyword(s):  
Velocity Field ◽  
Flow Visualization ◽  
Cellular Structure ◽  
Flow Instability ◽  
Rectangular Channel ◽  
Extensional Flow ◽  
Viscoelastic Flow ◽  
Circular Cylinders ◽  
Flow Transition ◽  
Wake Instability

Laser Doppler velocimetry (LDV) and video flow visualization are used to investigate the creeping motion of a highly elastic, constant-viscosity fluid flowing past a cylinder mounted centrally in a rectangular channel. A sequence of viscoelastic flow transitions are documented as the volumetric flow rate past the cylinder is increased and elastic effects in the fluid become increasingly important. Velocity profiles clearly show that elasticity has almost no effect on the kinematics upstream of the cylinder, but that the streamlines in the wake of the cylinder are gradually shifted further downstream . Finite element calculations with a nonlinear constitutive model closely reproduce the evolution of the steady two-dimensional velocity field. However, at a well defined set of flow conditions the steady planar stagnation ow in the downstream wake is experimentally observed to become unstable to a steady, three-dimensional cellular structure. The Reynolds number at the onset of the flow instability is less than 0.05 and inertia plays little role in the flow transition, LDV measurements in the wake close to the cylinder reveal large spatially periodic fluctuations of the streamwise velocity that extend along the length of the cylinder and more than five cylinder radii downstream of the cylinder. Fourier analysis shows that the characteristic spatial wavelength of these flow perturbations scales closely with the cylinder radius R . Flow visualization combined with LDV measurements also indicates that the perturbations in the velocity field are confined to the narrow region of strongly extensional flow near the downstream stagnation point. A second flow transition is observed at higher flow rates that leads to steady translation of the cellular structure along the length of the cylinder and time-dependent velocity oscillations in the wake. Measurements of the flow instability are presented for a range of cylinder sizes, and a stability diagram is constructed which shows that the onset point of the wake instability depends on both the extensional deformation of the fluid in the stagnation flow and the shearing flow between the cylinder and the channel.

scholarly journals Single-molecule sequence detection via microfluidic planar extensional flow at a stagnation point

Lab on a Chip ◽  
2010 ◽  
Vol 10 (12) ◽  
pp. 1543 ◽  
Author(s):  
Rebecca Dylla-Spears ◽  
Jacqueline E. Townsend ◽  
Linda Jen-Jacobson ◽  
Lydia L. Sohn ◽  
Susan J. Muller
Keyword(s):  
Stagnation Point ◽  
Single Molecule ◽  
Extensional Flow ◽  
Sequence Detection ◽  
Planar Extensional Flow

Non-Newtonian slender drops in a nonlinear extensional flow

2019 ◽  
Vol 877 ◽  
pp. 561-581 ◽  
Author(s):  
Moshe Favelukis
Keyword(s):  
Stability Analysis ◽  
Power Law ◽  
Analytical Solutions ◽  
Viscosity Ratio ◽  
Extensional Flow ◽  
Shear Thinning ◽  
Newtonian Liquid ◽  
Creeping Flow ◽  
Stationary States ◽  
Power Law Index

In this theoretical report we explore the deformation and stability of a power-law non-Newtonian slender drop embedded in a Newtonian liquid undergoing a nonlinear extensional creeping flow. The dimensionless parameters describing this problem are: the capillary number $(Ca\gg 1)$, the viscosity ratio $(\unicode[STIX]{x1D706}\ll 1)$, the power-law index $(n)$ and the nonlinear intensity of the flow $(|E|\ll 1)$. Asymptotic analytical solutions were obtained near the centre and close to the end of the drop suggesting that only Newtonian and shear thinning drops $(n\leqslant 1)$ with pointed ends are possible. We described the shape of the drop as a series expansion about the centre of the drop, and performed a stability analysis in order to distinguish between stable and unstable stationary states and to establish the breakup point. Our findings suggest: (i) shear thinning drops are less elongated than Newtonian drops, (ii) as non-Newtonian effects increase or as $n$ decreases, breakup becomes more difficult, and (iii) as the flow becomes more nonlinear, breakup is facilitated.

scholarly journals Inertioelastic Flow Instability at a Stagnation Point

2017 ◽  
Vol 7 (4) ◽  
Author(s):  
Noa Burshtein ◽  
Konstantinos Zografos ◽  
Amy Q. Shen ◽  
Robert J. Poole ◽  
Simon J. Haward
Keyword(s):  
Stagnation Point ◽  
Flow Instability

Stagnation-point extensional flow behaviour of M1

1990 ◽  
Vol 35 (2-3) ◽  
pp. 231-250 ◽  
Author(s):  
A.J. Müller ◽  
J.A. Odell ◽  
J.P. Tatham
Keyword(s):  
Stagnation Point ◽  
Extensional Flow ◽  
Flow Behaviour

The Shear and Elongational Flow of Polymer Melts Containing Anisometric Filler Particles; Part I

1984 ◽  
Vol 57 (3) ◽  
pp. 507-522 ◽  
Author(s):  
L. A. Utracki
Keyword(s):  
Yield Stress ◽  
Flow Instability ◽  
Extensional Flow ◽  
Plug Flow ◽  
Dynamic Test ◽  
Melt Processing ◽  
Solid Base ◽  
Transient Effects ◽  
High Concentration ◽  
Simple Method

Abstract There is a dichotomy in the information on flow of anisometric particles. Most of the fundamental studies only consider dilute suspensions in Newtonian liquids, although some authors venture into a semiconcentrated (two-body collision) region and others into pseudoplastic liquids. These publications provide a solid base for understanding the behavior of the high-concentration systems of industrial importance, but without the desirable quantification. The description of these systems is experimental or, at best, qualitative, via simplified constitutive models. At high concentration of anisometric particles, one must consider: yield stress, plug flow, shear segregation, and a change of relaxation spectrum. There is no simple method to correlate the steady-state and dynamic test data. The magnitude of the stress overshoot in transient tests increases with concentration and deformation rate. While the normal stress increases with concentration, the die swell decreases. The yield stress in elongation is larger than that in shear, and the maximum strain at break initially increases with addition of filler, goes through a maximum, and falls to very low values at high loading. The orientation of anisometric particles can be accomplished in converging and diverging, i.e., extensional flow. In a simple shear field, the effect depends on the rate, concentration, and matrix viscosity—in general, shearing causes disorientation of aligned particles. All these effects influence melt processing. For extrusion, the plug flow narrows the range of processing variables, increases the solid-conveying zone, and may lead to flow instability. In injection molding, gating, pattern of orientation (modulated by solidification), and the transient effects depend on the specificity of the rheological behavior of the filled pseudoplastic liquids.

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