Quantifying both viscoelasticity and surface tension: Why sharp tips overestimate cell stiffness.

Quantifying the mechanical properties of cells is important to better understand how mechanics constrain cellular processes. Furthermore, because pathologies are usually paralleled by altered cell mechanical properties, mechanical parameters can be used as a novel way to characterize the pathological state of cells. Key features used in models are cell tension, cell viscoelasticity (representing the average of the cell bulk), or a combination of both. It is unclear which of these features is the most relevant or whether both should be included. To clarify this, we performed microindentation experiments on cells with microindenters of various tip radii, including micrometer-sized microneedles. We obtained different cell-indenter contact radii and measured the corresponding contact stiffness. We derived a model predicting that this contact stiffness should be an affine function of the contact radius and that, at vanishing contact radius, the cell stiffness should be equal to the cell tension multiplied by a constant. When microindenting leukocytes and both adherent and trypsinized adherent cells, the contact stiffness was indeed an affine function of the contact radius. For leukocytes, the deduced surface tension was consistent with that measured using micropipette aspiration. For detached endothelial cells, agreement between microindentation and micropipette aspiration was better when considering these as only viscoelastic when analyzing micropipette aspiration experiments. This work suggests that indenting cells with sharp tips but neglecting the presence of surface tension leads to an effective elastic modulus whose origin is in fact surface tension. Accordingly, using sharp tips when microindenting a cell is a good way to directly measure its surface tension without the need to let the viscoelastic modulus relax.

Self-excitation of Leidenfrost drops and consequences on their stability.

Volatile liquids (water, alcohol, etc.) poured on hot solids levitate above a layer of vapor. Unexpectedly, these so-called Leidenfrost drops often suddenly start to oscillate with star shapes, a phenomenon first reported about 140 y ago. Similar shapes are known to be triggered when a liquid is subjected to an external periodic forcing, but the unforced Leidenfrost case remains unsolved. We show that the levitating drops are excited by an intrinsic periodic forcing arising from a vibration of the vapor cushion. We discuss the frequency of the vibrations and how they can excite surface standing waves possibly amplified under geometric conditions of resonance-an ensemble of observations that provide a plausible scenario for the origin, mode selection, and sporadic nature of the Leidenfrost stars.

On the rebound of soapy drops.

Pure water is known to bounce on super-hydrophobic materials, and we discuss here whether this remains true if the surface tension of water is lowered by either alcohol or surfactants. After determining the threshold in surface tension below which drops stick to the substrate, we show that a decrease of surface tension makes the rebound slower, a consequence of the reduced stiffness of this kind of spring. We also report that water with "slow" surfactants can still bounce despite a static surface tension smaller than the rebound threshold, which is interpreted as an effect of dynamic surface tension. The liquid is substantially deformed at impact, which impoverishes the surfactants at the its surface and thus can trigger repellency for a wetting liquid.

Superhydrophobic frictions.

Contrasting with its sluggish behavior on standard solids, water is extremely mobile on superhydrophobic materials, as shown, for instance, by the continuous acceleration of drops on tilted water-repellent leaves. For much longer substrates, however, drops reach a terminal velocity that results from a balance between weight and friction, allowing us to question the nature of this friction. We report that the relationship between force and terminal velocity is nonlinear. This is interpreted by showing that classical sources of friction are minimized, so that the aerodynamical resistance to motion becomes dominant, which eventually explains the matchless mobility of water. Our results are finally extended to viscous liquids, also known to be unusually quick on these materials.

Thermophobic Leidenfrost.

We report that a volatile liquid deposited on a hot substrate with a gradient of temperature does not only levitate (Leidenfrost effect), but also spontaneously accelerates to the cold. This thermophobic effect is also observed with sublimating solids, and we attribute it to the ability of temperature differences to tilt (slightly) the base of the "object", which induces a horizontal component to the levitating force. This scenario is tested by varying the drop size (with which the acceleration increases) and the substrate temperature (with which the acceleration decreases), showing that the effect can be used to control, guide and possibly trap the elusive Leidenfrost drops.

Viscous bouncing.

Repellent materials are known for their ability to make impacting water recoil and takeoff, which keeps them dry after rain. Here we show that the ability of drops to bounce can be extended by two orders of magnitude, in terms of the liquid viscosity. We measure and model two main characteristics of these viscous rebounds, namely the contact time of the drops and the elasticity of the collision, which allows us to understand how and why viscous liquids can be repelled by hydrophobic solids.

On the shape of giant soap bubbles.

We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical size [Formula: see text], where [Formula: see text] is the mean thickness of the soap film and [Formula: see text] is the capillary length ([Formula: see text] stands for vapor-liquid surface tension, and [Formula: see text] stands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures.

Antifogging abilities of model nanotextures.

Nanometre-scale features with special shapes impart a broad spectrum of unique properties to the surface of insects. These properties are essential for the animal's survival, and include the low light reflectance of moth eyes, the oil repellency of springtail carapaces and the ultra-adhesive nature of palmtree bugs. Antireflective mosquito eyes and cicada wings are also known to exhibit some antifogging and self-cleaning properties. In all cases, the combination of small feature size and optimal shape provides exceptional surface properties. In this work, we investigate the underlying antifogging mechanism in model materials designed to mimic natural systems, and explain the importance of the texture's feature size and shape. While exposure to fog strongly compromises the water-repellency of hydrophobic structures, this failure can be minimized by scaling the texture down to nanosize. This undesired effect even becomes non-measurable if the hydrophobic surface consists of nanocones, which generate antifogging efficiency close to unity and water departure of droplets smaller than 2 µm.

Capillary descent.

A superhydrophobic capillary tube immersed in water and brought in contact with the bath surface will be invaded by air, owing to its aerophilicity. We discuss this phenomenon where the ingredients of classical capillary rise are inverted, which leads to noticeable dynamical features. (1) The main regime of air invasion is linear in time, due to the viscous resistance of water. (2) Menisci in tubes with millimetre-size radii strongly oscillate before reaching their equilibrium depth, a consequence of inertia. On the whole, capillary descent provides a broad variety of dynamics where capillary effects, viscous friction and liquid inertia all play a role.

Water ring-bouncing on repellent singularities.

Texturing a flat superhydrophobic substrate with point-like superhydrophobic macrotextures of the same repellency makes impacting water droplets take off as rings, which leads to shorter bouncing times than on a flat substrate. We investigate the contact time reduction on such elementary macrotextures through experiment and simulations. We understand the observations by decomposing the impacting drop reshaped by the defect into sub-units (or blobs) whose size is fixed by the liquid ring width. We test the blob picture by looking at the reduction of contact time for off-centered impacts and for impacts in grooves that produce liquid ribbons where the blob size is fixed by the width of the channel.

Capillary muscle.

The contraction of a muscle generates a force that decreases when increasing the contraction velocity. This "hyperbolic" force-velocity relationship has been known since the seminal work of A. V. Hill in 1938 [Hill AV (1938) Proc R Soc Lond B Biol Sci 126(843):136-195]. Hill's heuristic equation is still used, and the sliding-filament theory for the sarcomere [Huxley H, Hanson J (1954) Nature 173(4412):973-976; Huxley AF, Niedergerke R (1954) Nature 173(4412):971-973] suggested how its different parameters can be related to the molecular origin of the force generator [Huxley AF (1957) Prog Biophys Biophys Chem 7:255-318; Deshcherevskii VI (1968) Biofizika 13(5):928-935]. Here, we develop a capillary analog of the sarcomere obeying Hill's equation and discuss its analogy with muscles.

Popsicle-Stick Cobra Wave.

The cobra wave is a popular physical phenomenon arising from the explosion of a metastable grillage made of popsicle sticks. The sticks are expelled from the mesh by releasing the elastic energy stored during the weaving of the structure. Here we analyze both experimentally and theoretically the propagation of the wave front depending on the properties of the sticks and the pattern of the mesh. We show that its velocity and its shape are directly related to the recoil imparted to the structure by the expelled sticks. Finally, we show that the cobra wave can only exist for a narrow range of parameters constrained by gravity and rupture of the sticks.

Drop friction on liquid-infused materials.

We discuss in this paper the nature of the friction generated as a drop glides on a textured material infused by another liquid. Different regimes are found, depending on the viscosities of both liquids. While a viscous drop simply obeys a Stokes-type friction, the force opposing a drop moving on a viscous substrate becomes non-linear in velocity. A liquid on an infused material is surrounded by a meniscus, and this specific feature is proposed to be responsible for the special frictions observed on both adhesive and non-adhesive substrates.

Spreading of Bubbles after Contacting the Lower Side of an Aerophilic Slide Immersed in Water.

While the dynamics of complete wetting has been widely studied for liquids, the way a gas spreads on a solid is by far less known. We report here the events following the rise of a millimeter-size air bubble towards a textured material immersed in water and covered by a thin plastron of air. Bubbles contact the material either directly at the end of the rise, or after a few rebounds, which affects the initial shape of the bubble and the resulting dynamics of contact. Then, air spreads on the material, owing to surface tension and later buoyance, which tends to flatten further the bubble. The corresponding dynamics are shown to result from the inertial resistance of water, which explains how spreading bubbles reach centimeter sizes in typically 10 ms.

Elastocapillary Instability in Mitochondrial Fission.

Mitochondria are dynamic cell organelles that constantly undergo fission and fusion events. These dynamical processes, which tightly regulate mitochondrial morphology, are essential for cell physiology. Here we propose an elastocapillary mechanical instability as a mechanism for mitochondrial fission. We experimentally induce mitochondrial fission by rupturing the cell's plasma membrane. We present a stability analysis that successfully explains the observed fission wavelength and the role of mitochondrial morphology in the occurrence of fission events. Our results show that the laws of fluid mechanics can describe mitochondrial morphology and dynamics.

Capillary instability on an elastic helix.

We present the results of a combined experimental and theoretical investigation of the capillary instability of an elastic helical thread bound within a fluid. The influence of the thread's elastic energy on the classic Rayleigh-Plateau instability is elucidated. The most unstable wavelength can be substantially increased by the influence of the helical coil. The relation between our system and the capture thread of the orb-spider is discussed.

Shooting in a foam.

We study the motion of a solid sphere after its fast impact on a bath of liquid foam. We identify two regimes of deceleration. At short times, the velocity is still large and the foam behaves similar to a Newtonian fluid of constant viscosity. Then we measure a velocity threshold below which the sphere starts experiencing the foam's elasticity. We interpret this behavior using a visco-elasto-plastic model for foam rheology. Finally we discuss the possibility of stopping a projectile in the foam, and evaluate the capture efficiency.

The force of impacting rain.

Drop impacts are difficult to characterize due to their transient, non-stationary nature. We discuss the force generated during such impacts, a key quantity for animals, plants, roofs or soil erosion. Although a millimetric drop has a modest weight, it can generate collision forces on the order of thousand times this weight. We measure and discuss this amplification, considering natural parameters such as drop radius and density, impact speed and response time of the substrate. We finally imagine two kinds of devices allowing us to deduce the size of the raindrop from impact forces.

Wave drag on floating bodies.

We measure the deceleration of liquid nitrogen drops floating at the surface of a liquid bath. On water, the friction force is found to be about 10 to 100 times larger than on a solid substrate, which is shown to arise from wave resistance. We investigate the influence of the bath viscosity and show that the dissipation decreases as the viscosity is increased, owing to wave damping. The measured resistance is well predicted by a model imposing a vertical force (i.e., the drop weight) on a finite area, as long as the wake can be considered stationary.

Measuring skill via player dynamics in football dribbling.

Although a myriad of studies have been conducted on player behavior in football, in-depth studies with structured theory are rare due to the difficulty in quantifying individual player skills and team strategies. We propose a physics-based mathematical model that describes football players' movements during dribbling situations, parameterized by the attacker aggressiveness, the defender hesitance and the top speed of both players. These player- and situation-specific parameters are extracted by fitting the model to real player trajectories from Major League Soccer games, and enable the quantification of player dribbling attributes and decisions beyond classical statistics. We show that the model captures the essential dribbling dynamics, and analyze how differences between parameters in varying game situations provide valuable insights into players' behavior. Lastly, we quantitatively study how changes in the player's parameters impact dribbling performance, enabling the model to provide scientific guidance to player training, scouting and game strategy development.