The spontaneous puncture of thick liquid films

We call thick those films for which the disjoining pressure and thermal fluctuations are ineffective. Water films with thickness $h$ in the $1{-}100~\unicode[STIX]{x03BC}\text{m}$ range are thick, but are also known, paradoxically, to nucleate holes spontaneously. We have uncovered a mechanism solving the paradox, relying on the extreme sensitivity of the film to surface tension inhomogeneities. The surface tension of a free liquid film is lowered by an amount $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ over a size $a$ by chemical or thermal contamination. At the same time this spot diffuses (within a time $a^{2}/D$, with $D$ the diffusion coefficient of the pollutant in the substrate), the Marangoni stress $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}/a$ induces an inhomogeneous outward interstitial flow which digs the film within a time $\unicode[STIX]{x1D70F}_{0}\sim \sqrt{\unicode[STIX]{x1D70C}ha^{2}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}}$, with $\unicode[STIX]{x1D70C}$ the density of the liquid. When the Péclet number $Pe=a^{2}/D\unicode[STIX]{x1D70F}_{0}$ is larger than unity, the liquid substrate motion reinforces the surface tension gradient, triggering a self-sustained instability insensitive to diffusional regularisation. Several experimental illustrations of the phenomenon are given, both qualitative and quantitative, including a precise study of the first instants of the unstable dynamics made by controlled perturbations of a Savart sheet at large $Pe$.

The break-up of free films pulled out of a pure liquid bath

In this paper, we derive a lubrication model to describe the non-stationary free liquid film that is created when a vertical frame is pulled out of a liquid reservoir at a given velocity. We here focus on the case of a pure liquid, corresponding to a stress-free boundary condition at the liquid/air interfaces of the film, and thus employ an essentially extensional description of the flow. Taking into account van der Waals interactions between the interfaces, we observe that film rupture is well defined in time as well as in space, which allows us to compute the critical thickness and the film height at the moment of rupture. The theoretical predictions of the model turn out to be in quantitative agreement with experimental measurements of the break-up height of silicone oil films in a wide range of pulling velocities and supporting fibre diameters.

The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate

We consider a viscous drop, loaded with an insoluble surfactant, spreading over an inclined plane that is covered initially with a thin surfactant-free liquid film. Lubrication theory is employed to model the flow using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the late-time multi-region asymptotic structure of the spatially one-dimensional spreading flow. A simplified differential–algebraic equation model is derived for key variables characterising the spreading process, using which the late-time spreading and thinning rates are determined. Focusing on the neighbourhood of the drop’s leading-edge effective contact line, we then examine the stability of this region to small-amplitude disturbances with transverse variation. A dispersion relationship is described using long-wavelength asymptotics and numerical simulations, which reveals physical mechanisms and new scaling properties of the instability.

Films in narrow tubes

We consider the axisymmetric arrangement of an annular liquid film, coating the inner surface of a narrow cylindrical tube, in interaction with an active core fluid. We introduce a low-dimensional model based on the two-phase weighted residual integral boundary layer (WRIBL) formalism (Dietze & Ruyer-Quil, J. Fluid Mech., vol. 722, 2013, pp. 348–393) which is able to capture the long-wave instabilities characterizing such flows. Our model improves upon existing works by fully representing interfacial coupling and accounting for inertia as well as streamwise viscous diffusion in both phases. We apply this model to gravity-free liquid-film/core-fluid arrangements in narrow capillaries with specific attention to the dynamics leading to flooding, i.e. when the liquid film drains into large-amplitude collars that occlude the tube cross-section. We do this against the background of linear stability calculations and nonlinear two-phase direct numerical simulations (DNS). Due to the improvements of our model, we have found a number of novel/salient physical features of these flows. First, we show that it is essential to account for inertia and full interphase coupling to capture the temporal evolution of flooding for fluid combinations that are not dominated by viscosity, e.g. water/air and water/silicone oil. Second, we elucidate a viscous-blocking mechanism which drastically delays flooding in thin films that are too thick to form unduloids. This mechanism involves buckling of the residual film between two liquid collars, generating two very pronounced film troughs where viscous dissipation is drastically increased and growth effectively arrested. Only at very long times does breaking of symmetry in this region (due to small perturbations) initiate a sliding motion of the liquid film similar to observations by Lister et al. (J. Fluid Mech., vol. 552, 2006, pp. 311–343) in thin non-flooding films. This kickstarts the growth of liquid collars anew and ultimately leads to flooding. We show that streamwise viscous diffusion is essential to this mechanism. Low-frequency core-flow oscillations, such as occur in human pulmonary capillaries, are found to set off this sliding-induced flooding mechanism much earlier.

An Exploration of the Effects of Dissolved Ionic Solids on Bubble Merging in Water and Its Impact on the Leidenfrost Transition

Theoretical models and MD simulation studies suggest that dissolved salts tend to alter the surface tension at liquid vapor interfaces and affect the stability of the free liquid film between adjacent bubbles. Recent modeling of the Leidenfrost phenomenon also indicates that bubble merging is a key mechanism affecting the Leidenfrost transition conditions. This investigation summarizes the results of an investigation of the effects of dissolved salts on liquid film stability and bubble merging in the aqueous solution. The interaction of pairs of bubbles injected into solution with different dissolved salt concentrations was studied experimentally to determine the probability of merging from statistics for ensembles of bubble pairs. The results of these experiments indicate that very low dissolved salt concentrations can strongly reduce the tendency of adjacent bubbles to merge, implying that the presence of the dissolved salt in such cases strongly enhances the stability of the free liquid film between adjacent bubbles. The trends are compared to predictions of free liquid film stability by wave instability theory and MD simulations. These trends are also compared to experimental data indicating the effects of dissolved salt on the Leidenfrost transition. These comparisons indicate that the suppression of merging due to the effects of some dissolved salts can significantly alter the Leidenfrost transition conditions. The implications of this in quenching of cast aluminum or steel parts using water of variable hardness are also discussed.