Related papers: Linear stability analysis of a vertical liquid fil…
We present a new application of Lagrangian Perturbation Theory (LPT): the stability analysis of fluid flows. As a test case that demonstrates the framework we focus on the plane Couette flow. The incompressible Navier-Stokes equation is…
Above a critical temperature known as the Leidenfrost point (LFP), a heated surface can suspend a liquid droplet above a film of its own vapor. The insulating vapor film can be highly detrimental in metallurgical quenching and thermal…
Roll solutions at the zigzag boundary, typically selected by patterns and defects in numerical simulations, are shown to be nonlinearly stable. This result also serves as an example that linear decay weaker than the classical diffusive…
The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered. The two fluids are bounded by electrodes…
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and…
The spreading of a thin film of suspension on a spinning disk and the accompanying contact line instability is studied through flow visualization experiments. The critical radius for the onset of instability shows an increase with increase…
Using the short-wavelength instability method, we investigate the linear instability of an exact solution describing upward-propagating mountain waves, derived in A. Constantin, \emph{J. Phys. A: Math. Theor.} (2023), under the assumption…
We consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We allow for the presence of fronts and related contact lines, and explore the role which they play in…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
Spin-wave instability is studied analytically in the case of parallel pumping for thin films under external field perpendicular to the film plane. It is examined whether the instability threshold derived from only the Landau-Lifshitz (LL)…
In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the…
We study the stability and breakup behavior of an axisymmetric liquid thread which is surrounded by another viscous fluid layer through a long wave approximation. The two fluids are immiscible and confined in a concentrically placed…
In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate-film thermal conductivity ratio…
We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…
In this investigation we use a simple model of the dynamics of an inviscid vortex sheet given by the Birkhoff-Rott equation to obtain fundamental insights about the potential for stabilization of shear layers using feedback control. As…
We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…
Consider the thin-film equation $h_t + \left(h h_{yyy}\right)_y = 0$ with a zero contact angle at the free boundary, that is, at the triple junction where liquid, gas, and solid meet. Previous results on stability and well-posedness of this…
We consider the dynamics of a thin liquid film in the attractive substrate potential and under the action of a longitudinal or a tilted vibration. Using a multiscale technique we split the film motion into the oscillatory and the averaged…
We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three dimensional setting. In the previous work (Phys. Fluids, {\bf 22}, 052105 (2010)), we considered two dimensional flow,…
We analyse numerically the linear stability of the fully developed flow of a liquid metal in a rectangular duct subject to a transverse magnetic field. The walls of the duct perpendicular to the magnetic field are perfectly conducting…