Variational approach for Stokes flow through a two-dimensional non-uniform channel.

A variational approach is proposed to study the Stokes flow in a two-dimensional non-uniform channel. By using the stationarity of the Lagrangian, the Euler-Lagrange equations are established which leads to a simple set of ordinary differential equations to provide an estimate for the average pressure drop explicitly in terms of the channel shape function. The results for the pressure drop show an excellent agreement with the second-order extended lubrication theory.

Soft wetting: Substrate softness- and time-dependent droplet/bubble adhesion.

Hypothesis: The droplet/bubble adhesion characteristics depend on the length of the droplet/bubble three-phase contact line. Since the deformation caused by the liquid-gas interfacial tension on the soft substrate, referred as to the wetting ridge, retards contact line spreading and retraction, we conjecture that the droplet/bubble adhesion characteristics depend also on the substrate softness.

Experiments: Soft substrates with various shear moduli are prepared and characterized by the spreading and receding dynamics of water droplets and underwater bubbles.

Dynamic and Quasi-static Droplet Penetration through Meshes.

We investigate experimentally the effects of pore size, surface wettability, and penetration mode on the characteristics of liquid penetration through meshes. Utilizing the impact of droplets and the hydrostatic pressure, we study water penetration through superhydrophobic, hydrophobic, superhydrophilic, and hydrophilic meshes with different uniform radii and pitch values of the pores. In the case of dynamic penetration enabled by the droplet impact, our results show that surface wettability has a negligible effect on either the threshold speed of the droplet penetration or the penetrating liquid mass.

Stability analysis of a thin liquid film on an axially oscillating cylindrical surface in the high-frequency limit.

We consider an axisymmetric liquid film on a horizontal cylindrical surface subjected to axial harmonic oscillation in the high-frequency limit. We derive and analyze the nonlinear evolution equation describing the nonlinear dynamics of this physical system in terms of the averaged film thickness. The method used for the derivation of the evolution equation is based on long-wave theory and the separation of the relevant fields into fast and slow components.

Nonlinear pattern formation in thin liquid films under external vibrations.

We study a thin liquid film with a free surface on a planar horizontal substrate. The substrate is subjected to oscillatory accelerations in the normal and/or in the horizontal direction(s). The description is based on the longwave approximation including inertia effects, which are important due to the large velocities imparted by external vibrations.

Nonlinear dynamics of a thin liquid film on an axially oscillating cylindrical surface subjected to double-frequency forcing.

The nonlinear dynamics of a thin axisymmetric liquid film on a horizontal cylindrical substrate subjected to an axial double-frequency forcing that consists of two components of different amplitudes and frequencies and a possible phase shift is considered in this paper. A nonlinear evolution equation governing the spatiotemporal dynamics of the film interface has been derived in the long-wave limit. Similar to the case of a single-frequency forcing considered in our earlier work, there exists a critical forcing amplitude below which the film undergoes a long-time capillary rupture typical for a static cylinder, whereas above it the film remains continuous.

Nonlinear dynamics of a thin nonisothermal liquid film on an axially oscillating cylindrical surface.

The nonlinear dynamics of a nonisothermal thin liquid film on a horizontal cylindrical surface subjected to axial harmonic vibration is investigated in this paper. It is found that the capillary instability of an axisymmetric film on a still cylinder can be saturated via the Marangoni effect by heating the film at the gas side, similar to the saturation of the Rayleigh-Taylor instability in the planar case. If the capillary instability is not saturated by the Marangoni effect, the combined capillary-Marangoni instability can be saturated by the harmonic axial forcing provided that the forcing amplitude exceeds a certain critical value depending on the rest of parameters.

Capillary rise of a meniscus with phase change.

The Lucas-Washburn equation, describing the motion of a liquid body in a capillary tube, is extended to account for the effect of phase change - evaporation or condensation. The system is found to always possess a stable equilibrium state when the temperature jump across the interface is confined to a certain range. We show that phase change affects the equilibrium height of the meniscus, the transition threshold from monotonic to oscillatory dynamics, and the frequency of oscillations, when present.

Dynamics of thin liquid films falling on vertical cylindrical surfaces subjected to ultrasound forcing.

Axial ultrasound forcing applied to a vertical cylinder is shown to affect a gravity-driven flow of a thin liquid film on its outer surface. In the case of larger forcing amplitudes, we find that the film flow can be completely stopped.

Marangoni convection in binary mixtures.

Marangoni instabilities in binary mixtures in the presence of the Soret effect and evaporation are different from those in pure liquids. In contrast to a large amount of experimental work on Marangoni convection in pure liquids, such experiments in binary mixtures are not available in the literature, to our knowledge. Using binary mixtures of NaCl/water in an open system, evaporation of water molecules at the liquid-vapor interface is inevitable.