Stability of a thin viscoelastic film falling down an inclined plane

Hu, Tao; Fu, Qing-fei; Yan, Xiu‐Ping; Yang, Lijun; Xie, Luo

doi:10.1103/physrevfluids.6.083902

Cited by 10 publications

(5 citation statements)

References 48 publications

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“…for each "regularized" model given by (16). It is worth noting that if B = 0 (Newtonian case) we obtain q = 2, s = 1 and from equation ( 22) 1 we retrieve the Orr-Sommerfeld equation [32,33,34].…”

Section: Linear Stabilitymentioning

confidence: 99%

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Linear stability of viscoplastic flows down an incline

Calusi,

Farina,

Fusi

et al. 2024

J. Phys.: Conf. Ser.

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The stability analysis of viscoplastic flows down an inclined plane is done by comparing results obtained through theoretical and numerical studies of “regularized” models. The theoretical analysis is performed for Regularized Bingham and Casson-like fluids via the long-wave approximation method. In particular, the Bingham and the Casson flow have different stability characteristics, for Bingham-type materials an increase in yield stress leads to flow destabilization, while Casson-type materials show the opposite behaviour. The numerical study is performed by using the Papanastasiou and the “exact” Bingham model via a spectral method. The comparison between theoretical and numerical results shows excellent agreement. Our findings highlight that “regularized” and “exact” flow and can have stability characteristics, although they are “practically indistinguishable”. We validate our approach with the Regularized Bingham-like model, which is in rather satisfactory agreement with the experimental data.

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Section: Linear Stabilitymentioning

confidence: 99%

“…In fact, the number of studies in the theoretical, numerical, and experimental fields with the aim to properly describe fluids with complex rheological behaviour are increasing, see e.g. [6,7,8,9,12,10,11,13,14,15,16,17,18,19,20,21,22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Linear stability of viscoplastic flows down an incline

Calusi,

Farina,

Fusi

et al. 2024

J. Phys.: Conf. Ser.

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show abstract

“…We consider the basic flow consisting of h(x, t) = h b , with h b = 1, v b = u b (y)i with u b given by ( 21), and, p = p b (y) where, recalling (20), p b (y) = ξ cot θ(1 − y). Then, we perturb the basic flow superimposing small disturbances, in the form of travelling waves, so that h = 1 + ĥ(y)e iα(x−ct) , u = u b + û(y)e iα(x−ct) ,…”

Section: Linear Stability Furthermore Long-wave Approximationmentioning

confidence: 99%

Stability of a Regularized Casson Flow down an Incline: Comparison with the Bingham Case

Calusi

Farína

Fusi

et al. 2022

Fluids

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In this paper, we study the two-dimensional linear stability of a regularized Casson fluid (i.e., a fluid whose constitutive equation is a regularization of the Casson obtained through the introduction of a smoothing parameter) flowing down an incline. The stability analysis has been performed theoretically by using the long-wave approximation method. The critical Reynolds number at which the instability arises depends on the material parameters, on the tilt angle as well as on the prescribed inlet discharge. In particular, the results show that the regularized Casson flow has stability characteristics different from the regularized Bingham. Indeed, for the regularized Casson flow an increase in the yield stress of the fluid induces a stabilizing effect, while for the Bingham case an increase in the yield stress entails flow destabilization.

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“…The viscoelasticity is described by the Oldroyd-B constitutive equation (Oldroyd 1950), which is one of the simplest constitutive equations (Hu et al. 2021; Boyko & Stone 2022; Varchanis et al. 2022) characterizing a viscoelastic fluid with shear-independent viscosity, non-zero first normal stress and zero second normal stress in steady shear (Aggarwal & Sarkar 2008).…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we numerically investigate the deformation, motion and breakup of an attached droplet subject to a Couette flow for a Newtonian droplet in a viscoelastic matrix (N/V system) and a viscoelastic droplet in a Newtonian matrix (V/N system). The viscoelasticity is described by the Oldroyd-B constitutive equation (Oldroyd 1950), which is one of the simplest constitutive equations (Hu et al 2021;Boyko & Stone 2022;Varchanis et al 2022) characterizing a viscoelastic fluid with shear-independent viscosity, non-zero first normal stress and zero second normal stress in steady shear (Aggarwal & Sarkar 2008). The elastic effect is usually characterized by the Weissenberg number (Wi), defined as the ratio of the first normal stress to the viscous stress (Poole 2012), or alternatively by the Deborah number (De) (Aggarwal & Sarkar 2008;Wang et al 2020a), i.e.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic effects on the deformation and breakup of a droplet on a solid wall in Couette flow

Wang

Shi

et al. 2023

J. Fluid Mech.

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The deformation, movement and breakup of a wall-attached droplet subject to Couette flow are systematically investigated using an enhanced lattice Boltzmann colour-gradient model, which accounts for not only the viscoelasticity (described by the Oldroyd-B constitutive equation) of either droplet (V/N) or matrix fluid (N/V) but also the surface wettability. We first focus on the steady-state deformation of a sliding droplet for varying values of capillary number ( $Ca$ ), Weissenberg number ( $Wi$ ) and solvent viscosity ratio ( $\beta$ ). Results show that the relative wetting area $A_r$ in the N/V system is increased by either increasing $Ca$ , or by increasing $Wi$ or decreasing $\beta$ , where the former is attributed to the increased viscous force and the latter to the enhanced elastic effects. In the V/N system, however, $A_r$ is restrained by the droplet elasticity, especially at higher $Wi$ or lower $\beta$ , and the inhibiting effect strengthens with an increase of $Ca$ . Decreasing $\beta$ always reduces droplet deformation when either fluid is viscoelastic. The steady-state droplet motion is quantified by the contact-line capillary number $Ca_{cl}$ , and a force balance is established to successfully predict the variations of $Ca_{cl}/Ca$ with $\beta$ for each two-phase viscosity ratio in both N/V and V/N systems. The droplet breakup is then studied for varying $Wi$ . The critical capillary number of droplet breakup monotonically increases with $Wi$ in the N/V system, while it first increases, then decreases and finally reaches a plateau in the V/N system.

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Stability of a thin viscoelastic film falling down an inclined plane

Cited by 10 publications

References 48 publications

Linear stability of viscoplastic flows down an incline

Linear stability of viscoplastic flows down an incline

Stability of a Regularized Casson Flow down an Incline: Comparison with the Bingham Case

Viscoelastic effects on the deformation and breakup of a droplet on a solid wall in Couette flow

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