Stability of an elastico-viscous liquid film flowing down an inclined plane

Gupta, A. S.; Rai, Lajpat

doi:10.1017/s0305004100041475

Cited by 20 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The instability of this film is driven by surface forces, just a5 the droplet breakup is driven by interfacial forces. Also in this case the instability is enhanced by the elasticity of the fluid for both an Oldroyd-B fluid (Lai, 1967;Gupta and Rai, 1967) and a Coleman and No11 second-order fluid (Gupta, 1967;Gupta and Rai, 1968;Minale and Astarita, 1996).…”

Section: Figure 2 Hysteresis Region For Blends Of Pdms In Pi9mentioning

confidence: 89%

Study of the morphological hysteresis in immiscible polymer blends

1998

View full text Add to dashboard Cite

Section: Figure 2 Hysteresis Region For Blends Of Pdms In Pi9mentioning

confidence: 89%

Study of the morphological hysteresis in immiscible polymer blends

1998

View full text Add to dashboard Cite

“…a Deborah number, De, should satisfy De ⌧ 1) and are best-suited for steady or quasi-steady ('slow') flows [10]. The Oldroyd-B constitutive model is better-suited for unsteady shear flows with substantial viscoelastic e↵ects, and subsequent linear stability studies using this model (or the closely-related Upper-convected Maxwell model) confirmed the destabilizing influence of viscoelasticity and also revealed that an elastic instability may be present if the Deborah number is su ciently large (even when the Reynolds number is zero) [11][12][13][14][15]. Viscoelastic analogues to the Benney [16][17][18] and IBL [19] equations have also been derived and analyzed, and numerical simulations of both the Newtonian and viscoelastic Benney equations indicate that a variety of nonlinear states including travelling waves and chaos may be excited (see [20] and section V).…”

Section: Introductionmentioning

confidence: 93%

Dynamics of gravity-driven viscoelastic films on wavy walls

2019

View full text Add to dashboard Cite

The linear stability and nonlinear dynamics of viscoelastic liquid films flowing down inclined surfaces with sinusoidal topography are investigated. The Oldroyd-B constitutive model is used, and numerical solutions of a long-wave nonlinear evolution equation for the film thickness (introduced by Davalos-Orozco[1]) provide insight into the influence of elasticity and wall topography on the nonlinear film dynamics, while Floquet analysis of the linearized evolution equation is used to study the onset of linear instability. Focusing initially on inertialess films (with zero Reynolds number), linear stability results are organized into three regimes based on the wall wavelength. For su ciently short and su ciently long wall wavelengths, the onset of instability is not tangibly a↵ected by the topography. There is, however, an intermediate range of wavelengths where, as the wall wavelength is increased, the critical Deborah number for the onset of instability first decreases (topography is destabilizing) and then increases su ciently for topography to be stabilizing (relative to the flat wall). Solutions to a perturbation amplitude equation indicate that the character of the instability changes substantially within this intermediate range; topography induces streamwise variations in the base-state velocity at the free surface which couple with perturbations and substantially influence the instability growth rate. Very similar trends are observed for Newtonian films and variations in the critical Reynolds number. Simulations of the full nonlinear evolution equation produce a broad range of nonlinear states including traveling waves, time-periodic waves, and chaos. Perturbations to the film generally saturate at higher amplitudes for cases with larger linear growth rates (e.g. with increasing Deborah number or for a destabilizing wall wavelength), and topography introduces finer temporal scales in the dynamics. The qualitative influences of inclination and inertia on the nonlinear dynamics are shown to be simply related to the influence of elasticity using analytical linear stability results for the flat-wall case.

show abstract

“…For instance, the constitutive equation for Oldroyd's 'liquid B ' (see Oldroyd 1950) is found to yield only stable solutions to the same problem. I n fact, this constitutive equation has been adopted by Wei Lai (1967) and by Gupta & Rai (1967) to examine the stability of flow down an inclined plane.…”

Section: -51mentioning

confidence: 99%

A note on the static stability of an elastico-viscous fluid

Craik

1968

J. Fluid Mech.

View full text Add to dashboard Cite

A recent analysis by Gupta (1967) suggests that a layer of elastico-viscous fluid at rest between parallel plane boundaries may be in unstable equilibrium. This surprising result is attributable to the inadequacy of the constitutive equation adopted by Gupta as the basis for his analysis. An alternative constitutive relation, which takes account of the entire strain-history of the motion, leads to the more reasonable result that the equilibrium is stable whenever the fluid has a ‘fading memory’.

show abstract

Stability of an elastico-viscous liquid film flowing down an inclined plane

Cited by 20 publications

References 7 publications

Study of the morphological hysteresis in immiscible polymer blends

Study of the morphological hysteresis in immiscible polymer blends

Dynamics of gravity-driven viscoelastic films on wavy walls

A note on the static stability of an elastico-viscous fluid

Contact Info

Product

Resources

About