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Many technological processes include preparing some special materials adhering to a product surface. For example, this problem is important for the magnetic tape producing, wire adhering, etc. For a surface withdrawn from the molten metal…
The so-called Landau-Levich-Deryaguin problem treats the coating flow dynamics of a thin viscous liquid film entrained by a moving solid surface. In this context, we use a simple experimental set-up consisting of a partially-immersed…
The dynamics of a thin layer of liquid, between a flat solid substrate and an infinitely-thick layer of saturated vapor, is examined. The liquid and vapor are two phases of the same fluid, governed by the diffuse-interface model. The…
Large aperture telescopes are pivotal for exploring the universe, yet even with state-of-the-art manufacturing and launch technology, their size is limited to several meters. As we aim to build larger telescopes - extending tens of meters -…
In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…
We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus…
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization…
Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…
Paints and coatings often feature interfacial defects due to disturbances during the deposition process which, if they persist until solidification, worsen the product quality. In this article, we investigate the stability of a thin liquid…
Thin disk accretion is often modeled in highly dynamical settings using the two-dimensional equations of viscous hydrodynamics, with viscosity representing unresolved turbulence. These equations are supposed to arise after vertical…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a…
We report a theoretical and numerical investigation of the linear and nonlinear dynamics of a thin liquid film of viscosity $\mu$ sandwiched between a solid substrate and an unbounded liquid bath of viscosity $\lambda \mu$. In the limit of…
This review article examines the complex dynamics of thin-film flows of granular suspensions spreading over rigid solid substrates with free air interfaces. Such systems feature an involved coupling of the free-surface dynamics with the…
The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel…
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…
Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model…
We consider the deposition of a film of viscous liquid on a flat plate being withdrawn from a bath, experimentally and theoretically. For any plate speed $U$, there is a range of ``thick'' film solutions whose thickness scales like…
We consider thin fluid films placed on thermally conductive substrates and exposed to time-dependent spatially uniform heat source. The evolution of the films is considered within the long-wave framework in the regime such that both…
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,…