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. Snap-in and normal adhesion forces of droplets/bubbles on such soft substrates are directly measured along with the visualized droplet/bubble shape profiles. FINDINGS: The droplet/bubble snap-in force, which corresponds to the short-time spreading dynamics, decreases with a decrease in the substrate shear modulus because of the retarded contact line spreading. The droplet maximal adhesion force on a soft substrate can be counterintuitively either smaller or larger than its counterpart on the rigid substrate depending on different dwelling times, i.e., the droplet/bubble-substrate contact time before droplet/bubble-substrate separation. The former is attributed to the retarded contact line spreading, whereas the latter is attributed to the retarded contact line retraction. The substrate softness- and dwelling time-dependent droplet/bubble adhesion reported in this study will benefit various applications related to soft substrates.

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. The threshold droplet speed is found to be mainly determined by the synergistic effects of global and local dynamic pressures of the impacting droplet, and a modified expression for the threshold droplet speed is proposed. For the quasi-static penetration based on the applied hydrostatic pressure, we find that surface wettability and pore pitch do not affect the penetration threshold pressure but do affect the pressure at which the liquid penetration ceases. This is due to the fact that under quasi-static conditions, the droplet liquid spreads out and merges with that at the adjacent pores on the mesh underside, affecting the wetted area and, hence, the capillary pressure resisting penetration.

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. We carry out the linear stability analysis for a film of a constant thickness which shows that axial forcing of the cylinder may result in either stabilization or destabilization of the axisymmetric flow with respect to the unforced one, depending on the choice of the parameter set. The analysis is extended to the weakly nonlinear stage and it reveals that the system bifurcates subcritically from the equilibrium.

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. The linearized system is examined using the Floquet analysis. Pattern formation in the nonlinear regime is computed numerically from the longwave equations for the thickness and the flow rate of the fluid in two and in three spatial dimensions. For certain amplitude and frequency ranges, combined lateral and normal oscillations can give rise to one or more traveling drops, similar to recent experimental findings by Brunet et al. [Phys. Rev. Lett. 99, 144501 (2007)].

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. We find that it is possible to arrest the rupture even if the forcing parameters of each of the two components correspond separately to the domain where rupture takes place. It is shown that the critical forcing amplitude is easily determined via a single-frequency case when the two forcing frequencies are equal. In the case of different forcing amplitudes and frequencies, the variation of the critical forcing amplitude as a function of the frequency ratio exhibits a unique behavior displaying the emergence of spikes. A related case of an amplitude-modulated single-frequency forcing is also addressed here. For a sufficiently small frequency of the amplitude modulation, a significant increase of the pattern amplitude is observed. In the case of commensurate forcing frequencies, the flow is found to be quasiperiodic.

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. The critical amplitude is demonstrated to increase with the Marangoni number when other parameters are fixed. The critical forcing amplitude at a given forcing frequency is shown to be well approximated by a piecewise linear function of the Marangoni number.

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. At higher mass transfer rates and/or large capillary radii, vapor recoil is found to be the dominant factor. Evaporation lowers the equilibrium height, increases the oscillation frequency and lowers the transition threshold to oscillations. For condensation, two regimes are identified: at high mass transfer rates similar trends to those of evaporation are observed, whereas the opposite is found for low mass transfer rates, resulting in an increased equilibrium height, lower oscillation frequencies and a shift of the transition threshold toward monotonic dynamics.

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. We have systematically investigated the pattern formation for a set of substrate temperatures and solute concentrations in an open system. The flow patterns evolve with time, driven by surface-tension fluctuations due to evaporation and the Soret effect, while the air-liquid interface does not deform. A shadow-graph method is used to follow the pattern formation in time. The patterns are mainly composed of polygons and rolls. The mean pattern size first decreases slightly, and then gradually increases during the evolution. Evaporation affects the pattern formation mainly at the early stages and the local evaporation rate tends to become spatially uniform at the film surface. The Soret effect becomes important at the later stages and affects the mixture for a large mean solute concentration where the Soret number is significantly above zero. The strength of convection increases with the initial solute concentration and the substrate temperature. Our findings differ from the theoretical predictions in which evaporation is neglected.