Fingering Instability of a Gravity-Driven Thin Film Flowing Down a Vertical Tube with Wall Slippage

Inspired by the antiwetting property of pitcher plants, specialists have designed different functional material with slippery surfaces, and a directional slippery surface has been fabricated. This paper considers a gravity-driven liquid film coating the interior surface of a vertical tube, and different slippery lengths in the azimuthal direction and the axial direction are taken into account. The evolution equation of coating flow is derived using the thin film model, and time responses for two dimensional flow are calculated. Linear stability analysis (LSA) is given based on the traveling wave solutions, demonstrating that the axial slippery effect suppresses the flow instability and causes a larger traveling wave speed. Simultaneously, the azimuthal slippery effect plays a destabilizing role for perturbations with small wavenumbers and it is stabilizing for large wavenumbers. Direct simulations of the fingering flow patterns agree well with the linear stability analysis. Our results offer insight into the influence of wall slippage on the flow stability of liquid in petroleum engineering.

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Feedback control of Marangoni convection in a thin film heated from below

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.578 ◽

2019 ◽

Vol 876 ◽

pp. 573-590 ◽

Cited By ~ 2

Author(s):

Anna E. Samoilova ◽

Alexander Nepomnyashchy

Keyword(s):

Thin Film ◽

Stability Analysis ◽

Feedback Control ◽

Linear Stability ◽

Linear Stability Analysis ◽

Control Strategies ◽

Oscillatory Mode ◽

Linear Feedback ◽

Marangoni Instability ◽

Strategy I

We use linear proportional control for the suppression of the Marangoni instability in a thin film heated from below. Our keen interest is focused on the recently revealed oscillatory mode caused by a coupling of two long-wave monotonic instabilities, the Pearson and deformational ones. Shklyaev et al. (Phys. Rev. E, vol. 85, 2012, 016328) showed that the oscillatory mode is critical in the case of a substrate of very low conductivity. To stabilize the no-motion state of the film, we apply two linear feedback control strategies based on the heat flux variation at the substrate. Strategy (I) uses the interfacial deflection from the mean position as the criterion of instability onset. Within strategy (II) the variable that describes the instability is the deviation of the measured temperatures from the desired, conductive values. We perform two types of calculations. The first one is the linear stability analysis of the nonlinear amplitude equations that are derived within the lubrication approximation. The second one is the linear stability analysis that is carried out within the Bénard–Marangoni problem for arbitrary wavelengths. Comparison of different control strategies reveals feedback control by the deviation of the free surface temperature as the most effective way to suppress the Marangoni instability.

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Shear-flow stability within the atmosphere of Venus

Journal of Fluid Mechanics ◽

10.1017/s002211207400019x ◽

1974 ◽

Vol 66 (2) ◽

pp. 267-272 ◽

Cited By ~ 5

Author(s):

R. D. Cess ◽

Harshvardhan

Keyword(s):

Stability Analysis ◽

Radiative Transfer ◽

Shear Flow ◽

Linear Stability ◽

Linear Stability Analysis ◽

Flow Instability ◽

Flow Stability ◽

Shear Flow Instability ◽

Realistic Formulation ◽

Atmosphere Of Venus

Employing a linear stability analysis, Dudis (1973) has recently suggested that shear-flow instability might exist within the upper stratosphere of Venus owing to destabilization by radiative transfer. We have incorporated a more realistic formulation for radiative transfer into his stability analysis and conclude that such an instability is unlikely.

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