Effect of surfactant on the linear stability of a shear-imposed fluid flowing down a compliant substrate

Samanta, Arghya

doi:10.1017/jfm.2021.451

Cited by 10 publications

(10 citation statements)

References 61 publications

(182 reference statements)

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“…(Online version in colour.) unstable streamwise finite wavenumber α is found, where the inertialess instability created due to the wall mode happens as speculated in the study of two-dimensional disturbances [24]. If the spanwise wavenumber is increased, the unstable domain corresponding to wall mode reduces successively, and this fact is followed by the consecutive promotion of the onset of instability for the wall mode.…”

Section: Modal Instability Analysismentioning

confidence: 62%

“…As long as C K decreases, the unstable zone created due to the surface mode increases, and eventually intersects the α-axis (Re = 0) at C K = 2. This fact stipulates the occurrence of inertialess instability in the finite wavelength zone, as revealed in the studies of two-dimensional disturbances [23,24]. However, the onset of instability for the three-dimensional surface instability no longer remains in the long-wave zone as long as the spring stiffness amplifies, as opposed to the result of two-dimensional disturbances [23,24].…”

Section: (B) Effect Of Wall Parameters On the Three-dimensional Primary Instabilitymentioning

confidence: 91%

“…. Indeed, the above elimination procedure in the boundary conditions enables us to formulate a linear eigenvalue problem [12] instead of the quadratic eigenvalue problem [23,24].…”

Section: Linear Perturbation Equationsmentioning

confidence: 99%

“…U and S specify unstable and stable zones. Circle data are taken from Samanta [24]. (Online version in colour.)…”

Section: Modal Instability Analysismentioning

confidence: 99%

“…As discussed by them, the flow configuration will be unstable by the surface mode despite the zero Reynolds number if wall spring stiffness is less than a critical value. The above flow model was further expanded by Samanta [24] when an imposed shear stress is applied at the surfactant-covered fluid surface. As discussed by Samanta, the surface mode can be stabilized by the surface surfactant despite the wall spring stiffness keeping a smaller value than the critical value.…”

Section: Introductionmentioning

confidence: 99%

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Modal analysis of a viscous fluid falling over a compliantwall

Samanta

2021

Proc. R. Soc. A.

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We study the modal instability of a three-dimensional Newtonian viscous fluid falling over a compliant wall under the framework of coupled evolution equations for normal velocity and normal vorticity, respectively. The Chebyshev spectral collocation numerical technique is applied in exploring unstable modes for the three-dimensional disturbances. The unstable zones pertaining to surface mode, wall mode and shear mode reduce as long as the spanwise wavenumber amplifies and corroborates the stabilizing influence of spanwise wavenumber. However, the onset of instability for the wall mode decays as long as the capillary number amplifies and ensures the destabilizing influence of the capillary number. Furthermore, the critical Reynolds number corresponding to surface mode found in the long-wave zone shifts towards the finite wavelength zone with increasing spanwise wavenumber and confirms the extinction of long-wave instability. But the inertialess instability created due to the wall mode disappears with increasing spanwise wavenumber. Moreover, the shear mode emerges in the high Reynolds number zone and is stabilized in the presence of spanwise wavenumber. In addition, the analytical derivation of Squire’s theorem is provided in appendix B for the flow over a compliant wall.

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Section: Modal Instability Analysismentioning

confidence: 62%

Section: (B) Effect Of Wall Parameters On the Three-dimensional Primary Instabilitymentioning

confidence: 91%

“…. Indeed, the above elimination procedure in the boundary conditions enables us to formulate a linear eigenvalue problem [12] instead of the quadratic eigenvalue problem [23,24].…”

Section: Linear Perturbation Equationsmentioning

confidence: 99%

“…U and S specify unstable and stable zones. Circle data are taken from Samanta [24]. (Online version in colour.)…”

Section: Modal Instability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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