Stability analysis of viscoelastic film flows over an inclined substrate with rectangular trenches

Marousis, A.; Pettas, D.; Karapetsas, George; Dimakopoulos, Yannis; Tsamopoulos, John

doi:10.1017/jfm.2021.163

Cited by 5 publications

(2 citation statements)

References 73 publications

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“…On the other hand, at large Reynolds numbers, a stability analysis of the flow may allow us to find other stable solutions of the flow where the flow period could differ from that of the geometry. For instance, recently, Marousis et al (2021) have performed the stability analysis of viscoelastic film flows over an inclined substrate with rectangular trenches. In this flow, with periodic positioning of the rectangular trenches, the authors have used the Floquet-Bloch theory to be able to examine the disturbances with wavelengths larger than that of the trenches.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

“…For instance, recently, Marousis et al. (2021) have performed the stability analysis of viscoelastic film flows over an inclined substrate with rectangular trenches. In this flow, with periodic positioning of the rectangular trenches, the authors have used the Floquet–Bloch theory to be able to examine the disturbances with wavelengths larger than that of the trenches.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

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Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Rahmani

Taghavi

2022

J. Fluid Mech.

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Plane Poiseuille flow of a Bingham fluid in a channel armed with a superhydrophobic (SH) lower wall is analysed via a semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents a groovy structure with air trapped inside its cavities. Therefore, the fluid adjacent to the wall undergoes stick–slip conditions. The model is developed based on introducing infinitesimal wall-induced perturbations into the motion equations, followed by Fourier series expansions, and solving the resulting equations as a boundary value problem. The Navier slip law accounts for the slip at the liquid/air interface (assuming the Cassie state). The presented analysis is fairly comprehensive, covering the creeping and inertial regimes for thick channels (via the semi-analytical and DNS solutions). The main dimensionless numbers are the Reynolds ( $Re$ ), Bingham ( $Bi$ ) and slip ( $b$ ) numbers, as well as the groove periodicity length ( $\ell$ ) and the slip area fraction ( $\varphi$ ). By increasing $Bi$ , the perturbation and slip velocity fields grow. As $Re$ increases, the perturbation and slip velocity fields become asymmetric. For certain flow parameters, an unyielded plug zone may appear on the SH wall liquid/air interface, while its formation is accelerated by inertial effects. The results classify the regimes of creeping and inertial flows via predicting the onset of the unyielded plug zone formation at the SH wall.

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Section: Summary and Concluding Remarksmentioning

confidence: 99%

Section: Summary and Concluding Remarksmentioning

confidence: 99%