Energy dissipation of a contact line moving on a nanotopographical defect.

Understanding the origin of the dissipative mechanisms that control the dynamics of a contact line is a real challenge. In order to study the energy dissipation at the contact line when a moving meniscus encounters topographical defects, we developed atomic force microscopy (AFM) experiments using nanofibers with nanometer scale defects. These experiments realized with three liquids are performed in two AFM modes: the contact mode (C-AFM) is used to measure the energy associated with the contact angle hysteresis in the limit of a static situation, deduced from advancing and receding dipping experiments on an isolated defect; the frequency-modulation mode (FM-AFM) is performed at different amplitudes and then velocities to measure the energy dissipated as the contact line moves over the same defect. Strong dissipation peaks appear above a threshold amplitude characteristic of the liquid and the defect, which is determined by the width of the hysteresis measured in statics. Furthermore, the dissipation energy of the moving contact line measured in dynamics is equal to the hysteresis capillary energy whatever the amplitude and is therefore independent of the contact line velocity. These results point out that the defect contribution to dissipation energy of a moving contact line on real surfaces is only governed by the pinning-depinning energy with no contribution of viscous effects.

Wetting at the Nanoscale: Molecular Mobility Induced by Contact Line Forces.

In this paper, we study the interaction of a contact line with molecules physically adsorbed on a surface. We developed specific atomic force microscopy (AFM) experiments where a nanoneedle attached at the extremity of the cantilever is dipped in a liquid droplet. The motion of the contact line at the extremity of the meniscus formed depends on the presence of topographical and chemical defects at the surface of the nanoneedle. The analysis of the force measured by AFM based on a capillary model allows one to distinguish the effects of topographical and chemical defects and to monitor minute changes of surface properties. Using six different liquids and five tips, we show that the change of the surface properties of one nanoneedle results either from the adsorption of airborne molecules when the tip is left in the air or from their desorption by the moving contact line when the tip is repeatedly dipped in the liquid. The desorption rate is found to depend only on the number of dipping cycles and is not influenced by the velocity or the liquid properties. A model based on the estimation of capillary and adsorption energies confirms a capillary desorption mechanism in agreement with the experimental results. Finally, we demonstrate that three distinct desorption mechanisms may be at play. Interestingly, using a deliberate contamination with large hydrocarbon molecules, we show that the capillary desorption studied in this paper can be used to clean surfaces.

Air humidity effects on water-drop icing.

The canonical problem of the icing of a water drop lying on a cold substrate is revisited to take into account the effects of atmospheric conditions on the icing front kinetics and on the tip formation. Here, we demonstrate both experimentally and theoretically that the air humidity induces liquid-vapor phase change at the icing droplet interface and that the associated heat transfer has a strong influence on both the icing front kinetics and the iced drop shape. The experimental results obtained in this study, as well as results from literature, compare well to a modified Stefan model accounting for the effects of humidity, showing a good agreement with the experimental data of both the front kinetics and tip angle.

Molecular Desorption by a Moving Contact Line.

The interaction of the contact line with topographical or chemical defects at the nanometer scale sets the macroscopic wetting properties of a liquid on a solid substrate. Based on specific atomic force microscopy (AFM) experiments, we demonstrate that molecules physically sorbed on a surface are removed by a dynamic contact line. The mechanism of molecules desorption is directly determined by the capillary force exerted at the contact line on the molecules. We also emphasize the potential of AFM to clearly decorrelate the effects of topographical and chemical defects and monitor, with a subsecond time resolution, the dynamics of molecules adsorption on a surface.

Long-range hydrodynamic forces in liquid FM-AFM.

We study the effects of hydrodynamic forces in frequency-modulation AFM experiments (FM-AFM) in liquid. We first establish the theoretical equations needed to derive the interaction stiffness k int and the damping ß int due to the hydrodynamic forces from the frequency shift and the excitation amplitude. We develop specific FM-AFM experiments to measure the variation of k int and ß int over a large range of distance in water up to 200 µm. Comparison between theory and experiments point out that the evolution of k int at short and long distance arises from unsteady hydrodynamic forces on the cantilever. On the other hand, ß int is small at long distance and diverges at short probe-surface distance, as predicted by the classical Reynolds sphere model.

Deformation of a Liquid Near an AFM Tip: Molecular Dynamics Approach.

The interaction between an atomic force microscopy (AFM) probe and a thin film of water deposited over a flat substrate is studied using molecular dynamics (MD). The effects of the film thickness and the probe radius on both the deformation height of the liquid interface and the distance of the jump to contact at which the liquid comes in direct contact with the probe are investigated. The dynamics of the surface deformation and the role of interface fluctuations are studied in detail. The systems considered belong to the thin-film regime described in a semianalytical model previously established by Ledesma-Alonso et al. (Langmuir 2013, 29, 7749-7757). MD simulations predict that for shallow films, both the distance at which the jump to contact occurs and the surface maximal deformation height increase steadily with the layer thickness regardless of the probe radius, which is in agreement with the previously proposed theoretical model. The deformation of the surface was shown to be unstable because of the strong effect of thermal fluctuations. For each of the considered systems, the film thickness was such that interface fluctuations induced the jump to contact. The comparison of the deformation obtained in MD with the profiles predicted by the continuous model points out the complementarity between the two approaches. The results of the molecular approach not only are consistent with those of the continuous model but also provide more information on the description of nanoscale phenomena. In particular, MD results point out the importance of fluctuations when it comes to the description of the particular dynamics of nanosystems involving soft interfaces. This shows the need to improve continuous models by complementing them with a molecular approach for a better accuracy.

van der Waals interaction between a moving nano-cylinder and a liquid thin film.

We study the static and dynamic interaction between a horizontal cylindrical nano-probe and a thin liquid film. The effects of the physical and geometrical parameters, with a special focus on the film thickness, the probe speed, and the distance between the probe and the free surface are analyzed. Deformation profiles have been computed numerically from a Reynolds lubrication equation, coupled to a modified Young-Laplace equation, which takes into account the probe/liquid and the liquid/substrate non-retarded van der Waals interactions. We have found that the film thickness and the probe speed have a significant effect on the threshold separation distance below which the jump-to-contact instability is triggered. These results encourage the use of horizontal cylindrical nano-probes to scan thin liquid films, in order to determine either the physical or geometrical properties of the latter, through the measurement of interaction forces.

Magnetoconvection transient dynamics by numerical simulation.

We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 103-106, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on [Formula: see text] and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.

Destabilization of a liquid metal by nonuniform Joule heating.

We study the effect of an impressing AC magnetic field at the bottom of a liquid metal layer of thickness h. In this situation the fluid is set in motion by the buoyancy forces caused by internal heat sources. The heat sources, caused by the Joule effect induced by the AC field, present an exponentially decaying profile, with characteristic length δ. As the magnetic field is horizontal, the Lorentz force has no influence on the dynamics of the system since it contributes only to the magnetic pressure. We propose an analysis of both the transient and fully developed regimes using linear stability analysis (LSA) and direct numerical simulations (DNSs). The transient period is governed by the temporal evolution of the temperature field as well as the development of the convective instability, which can be concomitant and therefore requires adopting a transient LSA algorithm to track these two effects. The DNSs have been performed for various distributions of the heat sources and various total heat input. This corresponds to independently varying δ/h in the range 0.04≤δ/h≤0.45 and a Rayleigh number 1.1×10^{4}≤Ra≤1.2×10^{5}. We observe the relaxation of the temperature up to the steady conductive profile before the transition to the nonlinear regime when Ra is small, whereas for larger Ra, nonlinear effects appear during the relaxation of the temperature profile. The unsteadiness of the temperature field significantly alters the development of the instability because of a much smaller growth rate. Surprisingly, we observe that δ/h has only a limited influence on averaged quantities as well as on the patterns for both the linear and nonlinear regimes. This comes with the fact that the profiles present an apparent reflectional symmetry, despite the asymmetry of the governing equations.

Dynamics of a thin liquid film interacting with an oscillating nano-probe.

The dynamic interaction between a local probe and a viscous liquid film, which provokes the deformation of the latter, has been studied. The pressure difference across the air-liquid interface is calculated with a modified Young-Laplace equation, which takes into account the effects of gravity, surface tension, and liquid film-substrate and probe-liquid attractive interaction potentials. This pressure difference is injected into the lubrication approximation equation, in order to depict the evolution of a viscous thin-film. Additionally, a simple periodic function is added to an average separation distance, in order to define the probe motion. The aforementioned coupled equations, which describe the liquid film dynamics, were analysed and numerically solved. The liquid surface undergoes a periodic motion: the approaching probe provides an input energy to the film, which is stored by the latter by increasing its surface deformation; afterwards, when the probe moves away, an energy dissipation process occurs as the surface attempts to recover its original flat shape. Asymptotic regimes of the film surface oscillation are discerned, for extreme probe oscillation frequencies, and several length, wavenumber and time scales are yielded from our analysis, which is based on the Hankel transform. For a given probe-liquid-substrate system, with well-known physical and geometric parameters, a periodic stationary regime and instantaneous and delayed probe wetting events are discerned from the numerical results, depending on the combination of oscillation parameters. Our results provide an interpretation of the probe-liquid film coupling phenomenon, which occurs whenever an AFM test is performed over a liquid sample.

Modelling the mechanical behaviour of pit membranes in bordered pits with respect to cavitation resistance in angiosperms.

BACKGROUND AND AIMS: Various correlations have been identified between anatomical features of bordered pits in angiosperm xylem and vulnerability to cavitation, suggesting that the mechanical behaviour of the pits may play a role. Theoretical modelling of the membrane behaviour has been undertaken, but it requires input of parameters at the nanoscale level. However, to date, no experimental data have indicated clearly that pit membranes experience strain at high levels during cavitation events. METHODS: Transmission electron microscopy (TEM) was used in order to quantify the pit micromorphology of four tree species that show contrasting differences in vulnerability to cavitation, namely Sorbus aria, Carpinus betulus, Fagus sylvatica and Populus tremula. This allowed anatomical characters to be included in a mechanical model that was based on the Kirchhoff-Love thin plate theory. A mechanistic model was developed that included the geometric features of the pits that could be measured, with the purpose of evaluating the pit membrane strain that results from a pressure difference being applied across the membrane. This approach allowed an assessment to be made of the impact of the geometry of a pit on its mechanical behaviour, and provided an estimate of the impact on air-seeding resistance. KEY RESULTS: The TEM observations showed evidence of residual strains on the pit membranes, thus demonstrating that this membrane may experience a large degree of strain during cavitation. The mechanical modelling revealed the interspecific variability of the strains experienced by the pit membrane, which varied according to the pit geometry and the pressure experienced. The modelling output combined with the TEM observations suggests that cavitation occurs after the pit membrane has been deflected against the pit border. Interspecific variability of the strains experienced was correlated with vulnerability to cavitation. Assuming that air-seeding occurs at a given pit membrane strain, the pressure predicted by the model to achieve this mechanical state corresponds to experimental values of cavitation sensitivity (P50). CONCLUSIONS: The results provide a functional understanding of the importance of pit geometry and pit membrane structure in air-seeding, and thus in vulnerability to cavitation.

Nanoscale deformation of a liquid surface.

We study the interaction between a solid particle and a liquid interface. A semianalytical solution of the nonlinear equation that describes the interface deformation points out the existence of a bifurcation behavior for the apex deformation as a function of the distance. We show that the apex curvature obeys a simple power-law dependency on the deformation. Relationships between physical parameters disclose the threshold distance at which the particle can approach the liquid before capillarity provokes a "jump to contact." A prediction of the interface original position before deformation takes place, as well as the attraction force measured by an approaching probe, are produced. The results of our analysis agree with the force curves obtained from atomic force microscopy experiments over a liquid puddle.

Critical viscoelastic behavior of polydimethylsiloxane networks around the sol-gel threshold.

Seven model polydimethylsiloxane (PDMS) networks were obtained by hydrosilation of a difunctional vinyl-terminated PDMS prepolymer with a SiH-containing cross-linker. Viscoelastic experiments, completed by size exclusion chromatography and static light scattering experiments, were performed in order to study the influence of molecular parameters on the dynamic properties around the sol-gel threshold. The dynamic critical parameter u was determined from experiments close to and above the sol-gel threshold. Our results show that the growth mechanism of PDMS clusters and the viscoelastic behavior are a function of the ratio NN_{e} , where N and N_{e} are, respectively, the numbers of Kuhn monomers between branch points and between entanglements. For NN_{e}<1 , the growth mechanism of clusters is the critical percolation and u=0.69 , and for NN_{e}>1 , the growth mechanim of clusters is the diffusion-limited cluster aggregation and u=0.76 .