Rod-climbing rheometry revisited

More, Rishabh V.; Patterson, Reid; Pashkovski, Eugene; McKinley, Gareth H.

doi:10.1039/d3sm00181d

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…The rate-dependent shear relaxation time τ s ( γ ) defined in (2.3) can also be used (if desired) to define a rate-dependent Deborah number De = τ s ( γ )Ω, which incorporates shear thinning in the relaxation time. In addition, the normal stress difference ratio ψ = −Ψ 2,0 /Ψ 1,0 for the PIB solutions used in this study fall in the range 0.205-0.243 as measured from rod-climbing rheometry (More et al 2023). Here, lim γ →0 Ψ 2 = Ψ 2,0 with Ψ 2 being the second normal stress coefficient.…”

Section: Methodsmentioning

confidence: 89%

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

More,

Patterson,

Pashkovski

et al. 2024

J. Fluid Mech.

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It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate or the flow in a Taylor–Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg ( $Wi$ ) number. However, the combined effects of fluid elasticity, shear thinning and finite inertia (as quantified by the Reynolds number $Re$ ) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone–plate geometries, we experimentally explore the entire $Wi$ – $Re$ phase space for a series of nonlinear viscoelastic fluids (with the dependence on shear rate $\dot{\gamma}$ quantified using a shear-thinning parameter $\beta _P(\dot {\gamma })$ ). We tune $\beta _P(\dot {\gamma })$ by varying the dissolved polymer concentration in solution. This progressively reduces shear thinning but leads to finite inertial effects before the onset of elastic instability, and thus naturally results in elasto-inertial coupling. Time-resolved rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry, and document the combined effects of varying $Wi, Re$ and $\beta _P(\dot {\gamma })$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel & McKinley (Phys. Rev. Lett., vol. 77, no. 12, 1996, p. 2459) for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, and thus bridges the gap between purely elastic and elasto-inertial curved streamline instabilities.

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Section: Methodsmentioning

confidence: 89%

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

More,

Patterson,

Pashkovski

et al. 2024

J. Fluid Mech.

Self Cite

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Laun's rule for predicting the first normal stress coefficient in complex fluids: A comprehensive investigation using fractional calculus

Das,

Rathinaraj,

Palade

et al. 2024

Physics of Fluids

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Laun's rule [H. M. Laun, “Prediction of elastic strains of polymer melts in shear and elongation,” J. Rheol. 30, 459–501 (1986).] is commonly used for evaluating the rate-dependent first normal stress coefficient from the frequency dependence of the complex modulus. We investigate the mathematical conditions underlying the validity of Laun's relationship by employing the time-strain–separable Wagner constitutive formulation to develop an integral expression for the first normal stress coefficient of a complex fluid in steady shear flow. We utilize the fractional Maxwell liquid model to describe the linear relaxation dynamics compactly and accurately and incorporate material nonlinearities using a generalized damping function of Soskey–Winter form. We evaluate this integral representation of the first normal stress coefficient numerically and compare the predictions with Laun's empirical expression. For materials with a broad relaxation spectrum and sufficiently strong strain softening, Laun's relationship enables measurements of linear viscoelastic data to predict the general functional form of the first normal stress coefficient but often with a noticeable quantitative offset. Its predictive power can be enhanced by augmenting the original expression with an adjustable power-law index that is based on the linear viscoelastic characteristics of the specific material being considered. We develop an analytical expression enabling the calculation of the optimal power-law index from the frequency dependence of the viscoelastic spectrum and the strain-softening characteristics of the material. To illustrate this new framework, we analyze published data for an entangled polymer melt and for a semiflexible polymer solution; in both cases our new approach shows significantly improved prediction of the experimentally measured first normal stress coefficient.

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Protorheology

Hossain,

Ewoldt

2024

Journal of Rheology

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We all instinctively poke, bounce, scoop, and observe materials to understand rheological properties quickly. Yet, these observations are rarely analyzed quantitatively. To address this, here we introduce the paradigm of protorheology: approximate quantitative inference from simple observations. Several case studies demonstrate how protorheology is an inclusive entry to rheology for a broad range of practitioners and strengthens the confidence and interpretation of accurate laboratory measurements. We survey a range of creative tests according to which rheological phenomenon is revealed. Some new working equations are derived, and all working equations are summarized for convenient reference and comparison across different methods. This establishes a framework to enable increased use of photos, videos, and quantitative inference and to support the increasing interest in digital image analysis, inverse methods, and high-throughput characterization being applied to rheological properties.

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Rod-climbing rheometry revisited

Abstract: The rod-climbing or “Weissenberg” effect, in which the free surface of a complex fluid climbs a thin rotating rod, is a popular and convincing experiment demonstrating the existence of elasticity...

Cited by 3 publications

References 28 publications

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

Laun's rule for predicting the first normal stress coefficient in complex fluids: A comprehensive investigation using fractional calculus

Protorheology

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