Stability of fluid flows coupled by a deformable solid layer

Patne, Ramkarn; Ramon, Guy Z.

doi:10.1017/jfm.2020.774

Cited by 5 publications

(2 citation statements)

References 42 publications

(132 reference statements)

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“…If the number of intersections with the temporal stability curve is an odd number then the formed cusp point is genuine; if the count is even then it is an evanescent cusp point. The existence of a genuine cusp point implies the presence of absolute instability, while that of an evanescent mode signifies a spurious cusp point (Yeo, Khoo & Zhao 1999, 2001; Patne & Shankar 2017; Patne & Ramon 2020).…”

Section: Long-wave Analysismentioning

confidence: 99%

Spatio-temporal dynamics of a two-layer pressure-driven flow subjected to a wall-normal temperature gradient

Patne

Chandarana

2023

J. Fluid Mech.

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The present study investigates the linear spatio-temporal and weakly nonlinear stability of a pressure-driven two-layer channel flow subjected to a wall-normal temperature gradient commonly encountered in industrial applications. The liquid–liquid interface tension is assumed to be a linearly decreasing function of temperature. The study employs both numerical (pseudo-spectral method) and long-wave approaches. The general linear stability analysis (GLSA) predicts shear-flow and thermocapillary modes that arise due to the imposed pressure and temperature gradients, respectively. The previous stability analyses of the same problem predicted a negligible effect of the pressure-driven flow on the linear stability of the system. However, the GLSA reveals stabilising and destabilising effects of the pressure-driven flow depending on the viscosity ratio ( $\mu _r$ ), thermal conductivity ratio ( $\kappa _r$ ), interface position ( $H$ ) and the sign of the imposed temperature gradient ( $\beta _1$ ). The analysis predicts a range of $H$ for given $\mu _r$ and $\kappa _r$ , which can not be stabilised by the thermocapillarity. The numerically predicted long-wave instability is then captured using the long-wave asymptotic approach. The arguments based on the physical mechanism further successfully explain the role of $\mu _r$ , $\kappa _r$ , $H$ , the sign of $\beta _1$ and the interaction between the velocity and temperature perturbations in stabilising/destabilising the flow. The spatio-temporal analysis reveals the dominance of the spanwise mode in causing the absolutely unstable flow. The weakly nonlinear analysis reveals a subcritical pitchfork bifurcation without shear flow. However, with the shear flow, the streamwise mode undergoes a supercritical Hopf bifurcation.

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Section: Long-wave Analysismentioning

confidence: 99%

Spatio-temporal dynamics of a two-layer pressure-driven flow subjected to a wall-normal temperature gradient

Patne

Chandarana

2023

J. Fluid Mech.

Self Cite

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“…Such hydrodynamic instabilities may result in interfacial deformation when the shear exerted by the flow exceeds the surface tension, which may cause crumpling of the forming film. Fluid shear, due to relative motion of the phases in a roll-to-roll process, may also result in an instability leading to a deformed film [89]. Elastic crumpling of the formed film may occur when the film experiences gradients in temperature and therefore expands in a non-uniform way, resulting in a crumpled morphology.…”

Section: Interfacial Polymerizationmentioning

confidence: 99%