The centre-mode instability of viscoelastic plane Poiseuille flow

Khalid, Mohammad; Chaudhary, Indresh; Garg, Piyush; Shankar, V.; Subramanian, Ganesh

doi:10.1017/jfm.2021.60

Cited by 45 publications

(84 citation statements)

References 79 publications

(183 reference statements)

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“…For pPF at sufficiently high β, the trend reverses, and we observe a stable purely elastic eigenmode becoming unstable for Re > 0. While a full Wi − β − Re critical surface is required to draw a definite conclusion regarding the influence of inertia on each mode, we note here that our observations are in line with the recent work on elasto-inertial instabilities (Chaudhary et al 2019;Khalid et al 2021a).…”

Section: Resultssupporting

confidence: 89%

“…In figure 3 we present the neutral stability curves for various values of β, while figure 4 shows the critical Weissenberg number Wi c and the corresponding critical wavenumber k 1,c as functions of β. The neutral stability curves are skewed towards small values of k 1 in a way reminiscent of the elasto-inertial (Chaudhary et al 2019;Khalid et al 2021a) and purely elastic modes (Khalid et al 2021b) discovered recently. Despite these similarities, we were unable to use the re-scaling procedure proposed in those works to collapse all our neutral stability data on a single master curve.…”

Section: Resultsmentioning

confidence: 82%

“…Once coherent states are resolved in direct numerical simulations of free-slip flows, a boundary condition homotopy similar to the one employed here can be used to track those solutions back to the no-slip conditions (Waleffe 2003). Recent work on elasto-inertial parallel shear flows (Garg et al 2018;Chaudhary et al 2019Chaudhary et al , 2021Khalid et al 2021a) associates linear instabilities at high Wi and Re with the very leading eigenvalues studied here. As already mentioned above, the same instability can be traced to the purely elastic case, Re = 0, for sufficiently large values of β and Wi (Khalid et al 2021b).…”

Section: Discussionmentioning

confidence: 99%

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Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

et al. 2021

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We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

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Section: Resultssupporting

confidence: 89%

Section: Resultsmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

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Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

et al. 2021

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“…Zhang et al (2013) proposed a dimensionless parameter characterizing the non-monotonic effect of elasticity on the linear stability, that is, the ratio of the polymer relaxation time to the characteristic instability time scale, applicable to both short-time and long-time horizons. In addition to these wall-mode instabilities reviewed above, a new centre-mode instability in plane Poiseuille flow of Oldroyd-B fluids has been reported recently by Khalid et al (2021). This novel mode only exists for dilute polymer concentrations (with the viscosity ratio β > 0.5) and highly elastic fluids (with the elasticity number E > 0.01).…”

Section: Linear Stability/instability In Viscoelastic Shear Flowsmentioning

confidence: 77%

“…Despite the simplicity of the Oldroyd-B model, it has been reported to be able to reliably reproduce the purely elastic instabilities observed in experiments of viscometric flows (Shaqfeh 1996) and discover the centre-mode linear instability in the stability analysis of viscoelastic pipe flows (Garg et al 2018). This model has been used in many previous works on the stability analyses of viscoelastic flows (Sureshkumar & Beris 1995b;Morozov & van Saarloos 2007;Zhang et al 2013;Morozov & van Saarloos 2019;Khalid et al 2021).…”

Section: Governing Equations and Parametersmentioning

confidence: 99%

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

2021

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Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. (Phys. Rev. Lett., vol. 121, 2018, 024502). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidence of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expansion of the disturbance around linear critical conditions. The perturbed parameter is the Reynolds number with the others being unperturbed. A third-order Ginzburg–Landau equation is derived with its coefficient indicating the bifurcation type of the flow. After exploring a large parameter space, we found that polymer concentration plays an important role: at high polymer concentrations (or small solvent-to-solution viscosity ratio $\beta \lessapprox 0.785$ ), the nonlinearity stabilizes the flow, indicating that the flow will bifurcate supercritically, while at low polymer concentrations ( $\beta \gtrapprox 0.785$ ), the flow bifurcation is subcritical. The results agree qualitatively with experimental observations where critical $\beta \approx 0.855$ . The pipe flow of upper convected Maxwell fluids can be linearly unstable and its bifurcation type is also supercritical. At a fixed value of $\beta$ , the Landau coefficient scales with the inverse of the Weissenberg number ( $Wi$ ) when $Wi$ is sufficiently large. The present analysis provides a theoretical understanding of the recent studies on the supercritical and subcritical routes to the elasto-inertial turbulence in viscoelastic pipe flows.

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Insights into the tiger stripe phenomenon of polypropylene and its blend in injection molding with a rapid heat exchange mold

Luo,

Ou,

Peng

et al. 2024

J of Applied Polymer Sci

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To examine the formation of tiger stripes (TS) phenomenon on the surface of the injection molding parts, a home‐made injection mold with a rapid heat exchange system and in situ measurement of pressure and temperature was designed and manufactured. Based on this special mold, the TS diagrams as a function of mold temperature and injection pressure for isotactic polypropylene (iPP) and its blend with a type of polyolefin elastomer (iPP/POE) were explored for the first time. It is found that there exists a critical mold temperature and a critical injection pressure for the TS appearance or disappearance in both systems. The critical temperatures of TS disappearance for iPP and iPP/POE are ~50 and ~ 120°C, respectively. As evidenced by the correlation between melt pressure drop and TS appearance, the wall slip mechanism is regarded as the main cause of TS formation. Compared with the critical shear stress of wall slip (σw) in totally molten PP, the lower σw value in this study further indicates that the wall slip could be facilitated by the crystallization of iPP during injection. Combined with white light interferometer, micro‐area x‐ray diffraction nanoindentation and scanning electron microscopy, it is demonstrated that the cloudy and glossy region of TS in pure iPP system could be distinguished by surface crystallinity. In the blend system, however, the rubber phase orientation as a dominant factor contributes to the glossiness of TS.

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The centre-mode instability of viscoelastic plane Poiseuille flow

Abstract: Abstract

Cited by 45 publications

References 79 publications

Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

Insights into the tiger stripe phenomenon of polypropylene and its blend in injection molding with a rapid heat exchange mold

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