Related papers: Oscillatory thermocapillary instability of a film …
Flow structure stability of a steady radial thermocapillary flow from the local heat source in cylindrical geometry has been studied numerically. The up boundary of the liquid was partially covered by the stationary film of an insoluble…
Flow of a thin viscous film down a flat inclined plane becomes unstable to long wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle…
We investigate the role of thermal instability, arising from radiative cooling of an optically thin, dusty plasma, by linear stability analysis. The corresponding isobaric stability condition for condensation mode is found to be modified…
Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be…
The stability of an evaporating thin liquid film on a solid substrate is investigated within lubrication theory. The heat flux due to evaporation induces thermal gradients; the generated Marangoni stresses are accounted for. Assuming the…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
Numerical methods are developed to solve the problem of abnormal changes of current (conductivity) in polymer composite films which may be used as current, pressure or temperature sensors. General nonlinear model includes the heat equation,…
A photoionized gas in thermal equilibrium can display a thermal instability, with 3 or more solutions in the multi-branch region of the S-shape curve giving the temperature versus the radiation-to-gas-pressure ratio. Many studies have been…
We study stationary, periodic solutions to the thermocapillary thin-film model \begin{equation*} \partial_t h + \partial_x \Bigl(h^3(\partial_x^3 h - g\partial_x h) + M\frac{h^2}{(1+h)^2}\partial_xh\Bigr) = 0,\quad t>0,\ x\in \mathbb{R},…
Rotational mixing, the key process in stellar evolution, transports angular momentum and chemical elements in stellar radiative zones. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical…
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the…
Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base…
Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped…
We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)] in the microcanonical…
We revisit here the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Unlike previous work, the turbulent base state velocity profile proposed here requires only a…
We apply a previously developed asymptotic model (J. Fluid. Mech. 915, A133 (2021)) to study instabilities of free surface films of nanometric thickness on thermally conductive substrates in two and three spatial dimensions. While the…