We experimentally study the mechanical pressure exerted by a set of respectively passive isotropic and self-propelled polar disks onto two different flexible unidimensional membranes. In the case of the isotropic disks, the mechanical pressure, inferred from the shape of the membrane, is identical for both membranes and follows the equilibrium equation of state for hard disks. On the contrary, for the self-propelled disks, the mechanical pressure strongly depends on the membrane in use, and is thus not a state variable. When self propelled disks are present on both sides of the membrane, we observe an instability of the membrane akin to the one predicted theoretically for Active Brownian Particles against a soft wall. In that case, the integrated mechanical pressure difference across the membrane can not be computed from the sole knowledge of the packing fractions on both sides; a further evidence of the absence of equation of state.

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.

We study the interaction between an AFM probe and a liquid film deposited over a flat substrate. We investigate the effects of the physical and geometrical parameters, with a special focus on the film thickness E, the probe radius R, and the distance D between the probe and the free surface. Deformation profiles have been calculated from the numerical simulations of the Young-Laplace equation by taking into account the probe/liquid and the liquid/substrate interactions, characterized by the Hamaker constants, Hpl and Hls. We demonstrate that the deformation of a shallow film is determined by a particular characteristic length λF = (2πγE(4)/Hls)(1/2), resulting from the balance between the capillary force (γ is the surface tension) and the van der Waals liquid/substrate attraction. For the case of a bulk liquid, the extent of the interface deformation is simply controlled by the capillary length λC = (γ/Δρg)(1/2). These trends point out two asymptotic regimes, which in turn are bounded by two characteristic film thicknesses Eg = (Hls/2πΔρg)(1/4) and Eγ = (R(2)Hls/2πγ)(1/4). For E > Eg, the bulk behavior is recovered, and for E < Eγ, we show the existence of a particular shallow film regime in which a localized tip effect is observed. This tip effect is characterized by the small magnitude of the deformation and an important restriction of its radial extent λF localized below the probe. In addition, we have found that the film thickness has a significant effect on the threshold separation distance Dmin below which the irreversible jump-to-contact process occurs: Dmin is probe radius-dependent for the bulk whereas it is film-thickness-dependent for shallow films. These results have an important impact on the optimal AFM scanning conditions.

The interaction between a nanoprobe and a liquid surface is studied. The surface deformation depends on physical and geometric parameters, which are depicted by employing three dimensionless parameters: Bond number B_{o}, modified Hamaker number H_{a}, and dimensionless separation distance D. The evolution of the deformation is described by a strongly nonlinear partial differential equation, which is solved by means of numerical methods. The dynamic analysis of the liquid profile points out the existence of a critical distance D_{min}, below which the irreversible wetting process of the nanoprobe happens. For D ≥ D_{min}, the numerical results show the existence of two deformation profiles, one stable and another unstable from the energetic point of view. Different deformation length-scales, characterizing the stable liquid equilibrium interface, define the near- and the far-field deformation zones, where self-similar profiles are found. Finally, our results allow us to provide simple relationships between the parameters, which leads to determine the optimal conditions when performing atomic force microscope measurements over liquids.

We examine the shape of droplets atop deformable thin elastomeric films prepared with an anisotropic tension. As the droplets generate a deformation in the taut film through capillary forces, they assume a shape that is elongated along the high tension direction. By measuring the contact line profile, the tension in the membrane can be completely determined. Minimal theoretical arguments lead to predictions for the droplet shape and membrane deformation that are in excellent agreement with the data. On the whole, the results demonstrate that droplets can be used as probes to map out the stress field in a membrane. DOI: 10.1103/PhysRevLett.118.198002 The physics of liquid droplets in contact with soft or deformable solids, elastocapillarity, is an active subject of research. Between capillary origami and wrinkling instabilities of thin films [1][2][3][4][5][6][7][8][9], the bending, coiling, and winding of slender structures [10][11][12][13][14][15][16], and elasticitymediated propulsion of droplets [17][18][19], there is no shortage of complexity, self-assembly, or beautiful examples of pattern formation in the field. In addition, some recent results have forced us to question familiar concepts of solid-liquid interactions. For instance, studies on the partial wetting of liquid drops on soft solids show that Young's law is applicable on length scales much larger than the bulk elastocapillary length γ=E, where γ is the liquid-air surface tension and E is the Young's modulus of the solid. However, on smaller length scales, the contact line reveals a wetting ridge set by a Neumann construction involving surface stresses [20][21][22][23][24][25][26].Partial wetting on deformable substrates may also be studied by employing a highly compliant geometry, such as a droplet on a thin freestanding film [27][28][29][30][31]. These studies have considered clamped films which are held taut and support a uniform and isotropic tension. As shown in Fig. 1(a), the Laplace pressure of the droplet creates a bulge in the film below it, in the shape of a spherical cap, which is of the same order in size as the droplet itself. The deformations generated may be orders of magnitude larger than the bulk elastocapillary length, because stretching of the membrane is the relevant mode of elasticity [28][29][30][31]. The contact line profile is determined by a Neumann construction, which incorporates both mechanical and interfacial tensions. This profile is characterized by the angles subtended by the liquid (θ d ) and bulge (θ b ) to the surrounding film [ Fig. 1(a)], which remains completely flat, i.e., the film's angle relative to the horizontal θ m ¼ 0. From the Neumann construction, these angles are set by two parameters: the Young's angle θ Y of the same solid supported on a rigid substrate and the ratio T in =γ, where T in is the total mechanical and interfacial tension acting inside the contact region of the membrane or drop system [31]. In the limit of infinite tension, the bulge vanishes and Young's law is recovered.In this stud...

The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one-and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationary deformation of the interface -a wake -that spatially vanishes in the far region. The shape of the wake and the way it vanishes depend on both the speed and size of the external source and the properties of the film. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analyzed in detail. For finite-size pressure disturbances, it increases with the speed, up to a certain transition value above which a monotonic decrease occurs. The role of the horizontal extent of the pressure field is studied as well, revealing that for a smaller disturbance the latter transition occurs at a higher speed. Eventually, for a Dirac pressure source, the wave resistance either saturates for a 1D geometry, or diverges for a 2D geometry.

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.

An experimental investigation was conducted to study the dynamical behaviour of a model valve in a pulsatile flow. The valve is modelled as a pair of curved, rectangular, flexible leaflets that open and close under a time-periodic flow. Using image analysis, the range of flow parameters for which a valve (of a particular geometry and material properties of the leaflets) works correctly were identified. A correct performance was considered to be when the valve opened in one direction but blocked the flow in the reversed direction. A model is proposed to predict the performance of the valves. Furthermore, an analysis of fluid strains is conducted for valves that operate correctly to identify the influence of the valve’s design on fluid stresses. The main purpose of this investigation is to gain insight for the design of future prosthetic heart valves.