Note on the stability of a visco-elastic liquid film flowing down an inclined plane

Gupta, A. S.; Rai, Lajpat

doi:10.1017/s0022112068002375

Cited by 36 publications

(7 citation statements)

References 5 publications

(1 reference statement)

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“…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: 90%

Study of the morphological hysteresis in immiscible polymer blends

1998

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

confidence: 90%

Study of the morphological hysteresis in immiscible polymer blends

1998

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“…In many practical applications, the film is viscoelastic, and early studies investigated the linear stability of viscoelastic gravity-driven films using second-order fluid models for the stress [7][8][9]. These studies found that elasticity enhanced inertial instability, however second-order models assume that a representative fluid relaxation time is small relative to a characteristic time scale of the flow (i.e.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of gravity-driven viscoelastic films on wavy walls

2019

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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.

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“…(40) and (41) into Eqs. (23) to (26), we obtain the disturbance equations as Substituting from Eqs. (40) and (41)…”

Section: Stability Analysismentioning

confidence: 99%

“…The stability of thin micropolar liquid film flowing down a vertical wall and a vertical cylinder [20,21] has been analyzed and the results show that the micropolar parameter plays an important role in stabilizing the film flow. The viscoelastic fluid, a subclass of microstructure flows, exhibits certain viscoelastic effects on normal and shear stresses and several investigations have been reported on the flow and stability of a falling film of viscoelastic fluids [22][23][24][25][26][27][28][29][30]. For these classes of fluids, (i) the current state of stress is a function of the history of past motion; (ii) the phenomenon of elastic recoil creep and stress relaxation occur; and (iii) the relation between the stress and velocity field is highly nonlinear, even in situations where the history of the strain is highly repetitive.…”

Section: Introductionmentioning

confidence: 99%

Stability of Viscoelastic Fluid Flowing Through Porous Medium Down Non-uniformly Heated Inclined Plane

El-Sayed

Moussa

Hassan

et al. 2013

Heat Trans. Asian Res.

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The stability of a thin layer of viscoelastic fluid flowing through a porous medium down a non-uniformly heated inclined plane with a constant temperature gradient along the plane is considered. The film flow system is influenced by gravity, mean surface tension, thermocapillary forces, viscoelastic forces, porosity, and permeability of porous medium. We seek a solution of the stability problem in a series in small wave numbers, and the obtained results, when the plane is heated in the downstream direction, show that the Marangoni, Galileo, Biot numbers, porosity, and permeability of the porous medium have dual roles in the stability of the flow system, while the viscoelastic parameter and angle of inclination have stabilizing effects, and the Prandtl number has a destabilizing effect. The effects of these physical parameters are also discussed in the case when the plane is cooled in the downstream direction, and we found that their effects are opposite to those of the previous case.

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Note on the stability of a visco-elastic liquid film flowing down an inclined plane

Cited by 36 publications

References 5 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

Stability of Viscoelastic Fluid Flowing Through Porous Medium Down Non-uniformly Heated Inclined Plane

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