Analytical solution for a Couette flow of a Giesekus fluid in a concentric annulus

Daprà, Irene; Scarpi, Gianbattista

doi:10.1016/j.jnnfm.2015.07.003

Cited by 8 publications

(8 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These measurements shown in Figure a,b revealed the shear-thinning nature and viscoelastic behavior of the polymeric fluid, both of which can be captured by the Giesekus model. The constitutive equation for a Giesekus fluid with negligible solvent viscosity is given by eq . Here, u is the velocity vector and T is the extra-stress tensor. There are three parameters in the Giesekus model: λ is the stress relaxation time, α is the dimensionless mobility parameter, and μ 0 is the polymer contribution to the zero-shear viscosity of polymeric solution.…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…There are three parameters in the Giesekus model: λ is the stress relaxation time, α is the dimensionless mobility parameter, and μ 0 is the polymer contribution to the zero-shear viscosity of polymeric solution. Dapra and Scarpi 31 have shown that the purely azimuthal Taylor−Couette flow of a Giesekus fluid can be solved analytically to get the normal stress differences and the velocity profile. The analytical expressions for u θ , N 1 , and N 2 were directly taken from this article.…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.1c01861. Analytical expression available in the literature for velocity and stress components of a Giesekus fluid in Taylor–Couette geometry; measured value of θ max corresponding to different speeds of rod rotation; sensitivity analysis of θ dp on a free surface profile and climbing height; and comparison of the viscosity curve calculated using the Giesekus model with the experimental values (PDF) Rod-climbing effect with the bare rod and the oil-coated rod at 200 and 600 rpm (MP4) …”

mentioning

confidence: 99%

“…Analytical expression available in the literature for velocity and stress components of a Giesekus fluid in Taylor–Couette geometry; measured value of θ max corresponding to different speeds of rod rotation; sensitivity analysis of θ dp on a free surface profile and climbing height; and comparison of the viscosity curve calculated using the Giesekus model with the experimental values (PDF)…”

mentioning

confidence: 99%

See 3 more Smart Citations

Contact Line Pinning and Depinning Can Modulate the Rod-Climbing Effect

et al. 2021

View full text Add to dashboard Cite

Our experiments on the rod-climbing effect with an oil-coated rod revealed two key differences in the rod-climbing phenomena compared to a bare rod. First, an enhancement in the magnitude of climbing height for any particular value of the rod rotational speed and second, a decrease in the threshold rod rotational speed required for the appearance of the rod-climbing effect were observed. Observed phenomena are explained by considering the contact line behavior at the rod−fluid interface. Transient evolution of the meniscus at the rod−fluid interface revealed that the three-phase contact line was pinned for a bare rod and depinned for an oil-coated rod. We modeled the subject fluid as a Giesekus fluid to predict the climbing height. The differences in the contact line behavior were incorporated via the contact angle at the rod−fluid interface as a boundary condition. Agreement was found between the observed and predicted climbing height, establishing that contact line behavior may modulate the rod-climbing effect.

show abstract

Section: Theoretical Formulationmentioning

confidence: 99%

Section: Theoretical Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Contact Line Pinning and Depinning Can Modulate the Rod-Climbing Effect

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Furthermore, we note that the zz-component is identically zero. Daprà and Scarpi 50 analytically solved the Giesekus model for steady cylindrical Couette flow and investigated the spatial behavior of the nontrivial stress components in the gap. In their work, the value of ↵ was restricted to ↵ < 0.5, as the Giesekus model does not have a real physical solution outside this range for high Weissenberg numbers.…”

Section: B Start-up Of Cylindrical Couette Flowmentioning

confidence: 99%

A thermodynamic study of shear banding in polymer solutions

Hooshyar

Germann

2016

Physics of Fluids

View full text Add to dashboard Cite

Although shear banding is a ubiquitous phenomenon observed in soft materials, the mechanisms that give rise to shear-band formation are not always the same. In this work, we develop a new two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics. The model is based on the hypothesis that the direct coupling between polymer stress and concentration is the driving mechanism of steady shear-band formation. To obtain smooth banded profiles in the two-fluid framework, a new stress-di↵usive term is added to the time evolution equation for the conformation tensor. The advantage of the new model is that the di↵erential velocity is treated as a state variable. This allows a straightforward implementation of the additional boundary conditions arising from the derivative di↵usive terms with respect to this new state variable. To capture the overshoot of the shear stress during the start of a simple shear flow, we utilize a nonlinear Giesekus relaxation. Moreover, we include an additional relaxation term that resembles the term used in the Rouse linear entangled polymer model to account for convective constraint release and chain stretch to generate the upturn of the flow curve at large shear rates. Numerical calculations performed for cylindrical Couette flow confirm the independency of the solution from the deformation history and initial conditions. Furthermore, we find that stress-induced migration is the responsible di↵usive term for steady-state shear banding. Because of its simplicity, the new model is an ideal candidate for the use in the simulation of more complex flows.

show abstract

Heat transfer for a Giesekus fluid in a rotating concentric annulus

Lorenzini

Daprà

2017

Applied Thermal Engineering

View full text Add to dashboard Cite

Analytical solution for a Couette flow of a Giesekus fluid in a concentric annulus

Cited by 8 publications

References 16 publications

Contact Line Pinning and Depinning Can Modulate the Rod-Climbing Effect

Contact Line Pinning and Depinning Can Modulate the Rod-Climbing Effect

A thermodynamic study of shear banding in polymer solutions

Heat transfer for a Giesekus fluid in a rotating concentric annulus

Contact Info

Product

Resources

About