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When a liquid droplet impacts a vibrated micro-structured surface with asymmetric topology, the liquids perform a horizontal motion during its bouncing. The moving effect is observed when the liquid is in contact with a low surface energy…
A thin liquid film covered with an insoluble surfactant in the vicinity of a first-order phase transition is discussed. Within the lubrication approximation we derive two coupled equations to describe the height profile of the film and the…
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…
In binary mixtures, the lifetimes of surface bubbles can be five orders of magnitude longer than those in pure liquids because of slightly different compositions of the bulk and the surfaces, leading to a thickness-dependent surface tension…
The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and…
The early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The…
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…
This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is…
Fluidisation is the process by which the weight of a bed of particles is supported by a gas flow passing through it from below. When fluidised materials flow down an incline, the dynamics of the motion differ from their non-fluidised…
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, we often use a thin film approximation, which…
We consider two stacked ultra-thin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linear analyses show…
Investigations of free-standing liquid films enjoy an increasing popularity due to their relevance for many fundamental and applied scientific problems. They constitute soap bubbles and foams, serve as membranes for gas transport or as…
Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a…
This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed…
Soft substrates are deformed by liquid-vapor surface tension upon contact with liquid droplets, forming the well-known wetting ridge. This ridge dynamically propagates with the moving contact line and critically influences liquid spreading.…
The effects of thermal coupling between two thin liquid layers, separated by a gas layer, are discussed. The liquid layers undergo long-wavelength instabilities driven by gravitational and thermocapillary stresses. To study the dynamics,…
Surfactants that are deposited at aqueous liquid films have the ability to generate surface tension gradients at the air-water interface, and thereby induce Marangoni flow. Combined with the production and depletion of surfactants at…
The dewetting of thin nanofilms is significantly impacted by thermal fluctuations, liquid-solid slip, and disjoining pressure, which can be described by lubrication equations augmented by appropriately scaled noise terms, known as…
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…
The van der Waals forces across a very thin liquid layer (nanofilm) in contact with a plane solid wall make the liquid nonhomogeneous. The dynamics of such flat liquid nanofilms is studied in isothermal case. The Navier-Stokes equations are…