A thin-film equation for a viscoelastic fluid, and its application to the Landau–Levich problem

Datt, Charu; Kansal, Minkush; Snoeijer, Jacco H.

doi:10.1016/j.jnnfm.2022.104816

Cited by 9 publications

(17 citation statements)

References 41 publications

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“…Namely, the calculations are based on the second-order fluid: while this lubrication model is equivalent to that obtained with Oldroyd-B fluid when viscoelasticity is introduced perturbatively (Ro & Homsy 1995; Datt et al. 2022), its quantitative validity at strong viscoelasticity remains to be explored, more so when polymers in moving contact-line problems have been observed to be strongly stretched (Smith & Bertola 2010; Shin et al. 2016).…”

Section: Discussionmentioning

confidence: 99%

“…We emphasise here that the second-order fluid thin-film equation is asymptotically equivalent to the Oldroyd-B model for weakly viscoelastic steady flows (see the Appendix in Datt et al. 2022), ensuring the validity of (2.1). Importantly, the viscoelastic term scales as whereas the viscous term scales as .…”

Section: Modified Cox–voinov Lawmentioning

confidence: 97%

“…The lubrication equation for steady contact-line motion with Navier-slip boundary condition has been derived recently for the second-order fluid (Datt et al. 2022). Denoting the interface profile as (see figure 1), the lubrication equation reads where is the Navier-slip length.…”

Section: Modified Cox–voinov Lawmentioning

confidence: 99%

“…The so-called second-order fluid is appropriate for modelling slow and steady flows in the weak viscoelasticity limit (Tanner 2000; Morozov & Spagnolie 2015; De Corato, Greco & Maffettone 2016). This constitutive relation was recently given a long-wave expansion (Datt, Kansal & Snoeijer 2022), yielding a thin-film equation that can be used to describe contact-line motion in the presence of normal stress. The approach resembles somewhat the analysis by Han & Kim (2014), who used corner solutions of the second-order fluid to estimate how normal stress affects the pressure inside the liquid.…”

Section: Introductionmentioning

confidence: 99%

“…However, the thin-film description by Datt et al. (2022) results from a systematic long-wave expansion (naturally involving the gradient of pressure, rather than the pressure), and has the additional benefit of being applicable beyond the no-slip condition to relieve the moving contact-line singularity. We focus on the case of partial wetting using a Navier-slip condition as a microscopic regularisation, so that the slip length appears as the inner scale.…”

Section: Introductionmentioning

confidence: 99%

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Viscoelastic wetting: Cox–Voinov theory with normal stress effects

Kansal,

Bertin,

Datt

et al. 2024

J. Fluid Mech.

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The classical Cox–Voinov theory of contact line motion provides a relation between the macroscopically observable contact angle, and the microscopic wetting angle as a function of contact-line velocity. Here, we investigate how viscoelasticity, specifically the normal stress effect, modifies the wetting dynamics. Using the thin film equation for the second-order fluid, it is found that the normal stress effect is dominant at small scales yet can significantly affect macroscopic motion. We show that the effect can be incorporated in the Cox–Voinov theory through an apparent microscopic angle, which differs from the true microscopic angle. The theory is applied to the classical problems of drop spreading and dip coating, which shows how normal stress facilitates (inhibits) the motion of advancing (receding) contact lines. For rapid advancing motion, the apparent microscopic angle can tend to zero, in which case the dynamics is described by a regime that was already anticipated in Boudaoud (Eur. Phys. J. E, vol. 22, 2007, pp. 107–109).

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Section: Discussionmentioning

confidence: 99%

Section: Modified Cox–voinov Lawmentioning

confidence: 97%

Section: Modified Cox–voinov Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Viscoelastic wetting: Cox–Voinov theory with normal stress effects

Kansal,

Bertin,

Datt

et al. 2024

J. Fluid Mech.

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Deposition of shear‐thinning viscoelastic fluids by an elongated bubble in a circular channel regarding the weakly elastic regime

Chun,

Yang,

Feng

2024

Droplet

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Thin‐film deposition of fluids is ubiquitous in a wide range of engineering and biological applications, such as surface coating, polymer processing, and biomedical device fabrication. While the thin viscous film deposition in Newtonian fluids has been extensively investigated, the deposition dynamics in frequently encountered non‐Newtonian complex fluids remain elusive, with respect to predictive scaling laws for the film thickness. Here, we investigate the deposition of thin films of shear‐thinning viscoelastic fluids by the motion of a long bubble translating in a circular capillary tube. Considering the weakly elastic regime with a shear‐thinning viscosity, we provide a quantitative measurement of the film thickness with systematic experiments. We further harness the recently developed hydrodynamic lubrication theory to quantitatively rationalize our experimental observations considering the effective capillary number and the effective Weissenberg number , which describe the shear‐thinning and the viscoelastic effects on the film formation, respectively. The obtained scaling law agrees reasonably well with the experimentally measured film thickness for all test fluids. Our work may potentially advance the fundamental understanding of the thin‐film deposition in a confined geometry and provide valuable engineering guidance for processes that incorporate thin‐film flows and non‐Newtonian fluids.

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Generalized second-grade fluid flow over a tilted plate with bump topography

Panda

2024

Rheol Acta

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A thin-film equation for a viscoelastic fluid, and its application to the Landau–Levich problem

Cited by 9 publications

References 41 publications

Viscoelastic wetting: Cox–Voinov theory with normal stress effects

Viscoelastic wetting: Cox–Voinov theory with normal stress effects

Deposition of shear‐thinning viscoelastic fluids by an elongated bubble in a circular channel regarding the weakly elastic regime

Generalized second-grade fluid flow over a tilted plate with bump topography

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