Session OJ: Surface Tension Effects III*

Splash or not : Water entry of solid bodies

The impact of a solid sphere on an air-water interface is studied experimentally. Above a threshold velocity, a large cavity is created during the collision process. We have studied exhaustively the dependence of the threshold velocity on the sphere characteristics (size, roughness, surface properties, ...), but also on the gas properties (e.g., density). Experiments suggest that the criterion for air entrainement is defined in terms of a critical capillary number, $Ca=\eta_{air} V/\gamma$, with $\gamma$ the liquid-vapor surface tension and $\eta_{air}$ the air viscosity. A simple model is proposed which allows to capture this behavior.   

Tuning of a splash on elastic membranes

We study the splash of liquid droplets on elastic substrates. In particular we focus on the case where the substrate is a thin polymeric film. We identify the transition between splashing and no-splashing as a function of the applied tension of the membrane and droplet radius. A simple model accounting for the additional energy stored in the deformable elastic sheet is developed and compared with experiment.   

The Dynamics of Sinking

Jumping water striders trust that the interface will be strong enough to catch them when they land. We study the dynamic response of the interface to the impact of a small body and probe the limits of its dynamic strength. Numerical and asymptotic arguments allow us to understand how an object light enough to be supported in equilibrium by surface tension can sink if it strikes the interface too quickly. We quantitatively determine the relation of this critical impact speed to the object's mass. Jumping water striders are shown to typically lie close to this threshold suggesting that it is the threat of sinking that limits their jumping height.   

Bouncing of a hydrophobic solid object upon impact with water surface

It is well known that a water drop impacting with a highly hydrophobic solid surface bounces. Here we show that a tiny hydrophobic solid object may bounce off liquid surface upon impact with the water pool. The impact behavior of such tiny solid with liquid is determined by surface tension, viscosity and density of the liquid, and size, density, hydrophobicity and impact velocity of the solid object. We show that depending on the impact conditions, the solid object may sink, oscillate on the surface, or bounce off. The regime map for such impact behavior is constructed using dimensionless numbers such as the Reynolds and Weber numbers. The implication of this phenomenon with the biological motility exhibited by insects that walk and jump on water is discussed.   

Interface mechanics determining biological cell shapes

To form a functional tissue, biological cells often adhere to each other establishing connections between membranes by means of cadherin molecules. The cells achieve a well-defined relative orientation as well as a faithfully prescribed shape. An excellent example is the cell cluster making up each ommatidium element in the drosophila eye. The similarity of the shape of these cells to connected soap bubbles has been remarked upon [1]. We show that, in order to explain the observed shapes of wild-type and mutant ommatidia, the soap film model has to be expanded into a realistic description of biological membranes and their mechanical properties including changes in interfacial tension due to the presence of cadherins. Surface Evolver simulations demonstrate that realistic modeling of the shape of cell clusters can be obtained using surface energy terms only, emphasizing the importance of interfacial phenomena in cell mechanics and cell morphology. \newline [1] T. Hayashi \& R. W. Carthew, Nature {\bf 431}, 647 (2004)   

Transition flow rate in viscous withdrawal.

We present the results of a numerical study of viscous selective withdrawal. In this system, two immiscible layers of different viscosities are laid in a container. A straw through which fluid is withdrawn is then introduced in the upper fluid. Above a certain transition flow rate, Q, the lower layer also becomes entrained. We determine numerically the dependence of Q on the straw height and viscosity ratio. The transition flow rate corresponds to the point where viscous entrainment from the upper fluid overcomes the resistance of surface tension. Knowing the lengthscales relevant to the flow and interface shape, one can estimate the transition flow rate. Our results were favorably compared with previously published experimental data.   

Capillary origami

The wet fur of a dog coming out of a pond assembles into bunches: this is the most common effect of capillary forces on elasticity structures (the hairs). From a practical point of view, the deformation of flexible elements by surface tension forces dramatically damages mechanical microsystems or lung airways, but also allows the self-organization of nanotube carpets into well defined clump patterns. But capillary forces may generate even more complex structures when flexible sheets are brought to contact with a liquid interface. Here we present experiments where surface tension folds up an elastic sheet around a deposited water droplet, and discuss the different possible shapes obtained. These self-folding origami may be used in microsy stems design as a convenient and robust way to fold two-dimensional planar patterns into 3-dimensional structures, since surface tension effects are enhanced at small scales.   

Bouncing of a Hydrophobic Bead on Water

We present the results of an experimental study of hydrophobic solids impacting the free surface of water. Despite the beads being more dense than water, a variety of behaviors was observed, including sinking, floating and bouncing free of the surface. Beads of several materials and sizes were coated with super-hydrophobic Lycopodium spores and dropped onto the free surface of water at a range of impact velocities. Particular attention was given to elucidating the dependence of the system on the governing parameters, namely both the Weber number and the Bond number, and rebounds were shown to occur only over a limited range of these parameters.