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Jens Eggers

Publications and source records attributed to Jens Eggers.

53 records · Page 3Linked to original sources
arXiv2004

A brief history of drop formation

Surface-tension-related phenomena have fascinated researchers for a long time, and the mathematical description pioneered by Young and Laplace opened the door to their systematic study. The time scale on which surface-tension-driven motion takes place is usually quite short, making experimental investigation quite demanding. Accordingly, most theoretical and experimental work has focused on static phenomena, and in particular the measurement of surface tension, by physicists like Eötvös, Lenard, and Bohr. Here we will review some of the work that has eventually lead to a closer scrutiny of time-dependent flows, highly non-linear in nature. Often this motion is self-similar in nature, such that it can in fact be mapped onto a pseudo-stationary problem, amenable to mathematical analysis.

physics.flu-dyn↗
arXiv2003

Toward a description of contact line motion at higher capillary numbers

The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has already been done for a variety of models, but always assuming the limit of vanishing speed. This excludes phenomena of the greatest current interest, in particular the stability of contact lines. Here we extend perturbation theory to arbitrary order and compute finite speed corrections to existing results. We also investigate the impact of the microscopic physics on the large-scale shape of the interface.

physics.flu-dyn↗
arXiv2003

Hydrodynamic theory of de-wetting

A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, de-wetting case, a critical speed exists above which a stationary contact line is no longer sustainable and a liquid film is being deposited on the solid. Demonstrating this behavior to be a hydrodynamic instability close to the contact line, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid.

physics.flu-dyn↗
arXiv2002

Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle

It is common to relate the dynamic contact angle $θ_d$ to the relative speed between the substrate and the contact line; theory suggests $θ_d^3 \propto U$. In fact, available physical models show that the dynamic angle involves speed logarithmically and in a model dependent manner. Experimental data consistent with this interpretation is cited.

physics.flu-dyn↗
arXiv2002

Dynamics of nanojets

We study the breakup of a liquid jet a few nanometers in diameter, based on a stochastic differential equation derived recently by Moseler and Landman [Science {\bf 289}, 1165 (2000)]. In agreement with their simulations, we confirm that noise qualitatively changes the characteristics of breakup, leading to symmetric profiles. Using the path integral description, we find a self-similar profile that describes the most probable breakup mode. As illustrated by a simple physical argument, noise is the driving force behind pinching, speeding up the breakup to make surface tension irrelevant.

physics.flu-dyn↗
arXiv2001

Theory of Drop Formation

We consider the motion of an axisymmetric column of Navier-Stokes fluid with a free surface. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which constitute a unique continuation of the Navier-Stokes equation through the singular point. We calculate the asymptotic solutions of the Navier-Stokes equation, both before and after the singularity. The solutions have scaling form, characterized by universal exponents as well as universal scaling functions, which we compute without adjustable parameters.

physics.flu-dyn↗
arXiv2001

Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation

We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.

physics.flu-dyn↗
arXiv2000

Air entrainment through free-surface cusps

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow space inside the cusp destroys its stationary shape when the walls of the cusp come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations.

physics.flu-dyn↗
arXiv1999

Spinning jets

A fluid jet with a finite angular velocity is subject to centripetal forces in addition to surface tension forces. At fixed angular momentum, centripetal forces become large when the radius of the jet goes to zero. We study the possible importance of this observation for the pinching of a jet within a slender jet model. A linear stability analysis shows the model to break down at low viscosities. Numerical simulations indicate that angular momentum is expelled from the pinch region so fast that it becomes asymptotically irrelevant in the limit of the neck radius going to zero.

physics.flu-dyn↗
arXiv1999

Sand as Maxwell's demon

We consider a dilute gas of granular material inside a box, kept in a stationary state by shaking. A wall separates the box into two identical compartments, save for a small hole at some finite height $h$. As the gas is cooled, a second order phase transition occurs, in which the particles preferentially occupy one side of the box. We develop a quantitative theory of this clustering phenomenon and find good agreement with numerical simulations.

cond-mat.stat-mech↗
arXiv1999

Coalescence of Liquid Drops

When two drops of radius $R$ touch, surface tension drives an initially singular motion which joins them into a bigger drop with smaller surface area. This motion is always viscously dominated at early times. We focus on the early-time behavior of the radius $\rmn$ of the small bridge between the two drops. The flow is driven by a highly curved meniscus of length $2π\rmn$ and width $Δ\ll\rmn$ around the bridge, from which we conclude that the leading-order problem is asymptotically equivalent to its two-dimensional counterpart. An exact two-dimensional solution for the case of inviscid surroundings [Hopper, J. Fluid Mech. ${\bf 213}$, 349 (1990)] shows that $Δ\propto \rmn^3$ and $\rmn \sim (tγ/πη)\ln [tγ/(ηR)]$; and thus the same is true in three dimensions. The case of coalescence with an external viscous fluid is also studied in detail both analytically and numerically. A significantly different structure is found in which the outer fluid forms a toroidal bubble of radius $Δ\propto \rmn^{3/2}$ at the meniscus and $\rmn \sim (tγ/4πη) \ln [tγ/(ηR)]$. This basic difference is due to the presence of the outer fluid viscosity, however small. With lengths scaled by $R$ a full description of the asymptotic flow for $\rmn(t)\ll1$ involves matching of lengthscales of order $\rmn^2, \rmn^{3/2}$, \rmn$, 1 and probably $\rmn^{7/4}$.

physics.flu-dyn↗
arXiv1999

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $λη$ breaking up inside another fluid of viscosity $η$. For $λ=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $λ$ dependence of the shape and breaking rate.

physics.flu-dyn↗
arXiv1999

Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the profile corresponds to experiments and simulations with fluids at low viscosity. The singularity has similarity form, which we compute analytically. The result agrees well with numerical simulations of the model equations.

chao-dyn↗
arXiv1998

A Continuum Description of Vibrated Sand

The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent impact of the grains on the plate. A linear stability theory reveals that the waves are excited non-resonantly, in contrast to the usual Faraday waves in liquids. Together with the experimentally observed continuum scaling, the model suggests a close connection between the neutral curve and the dispersion relation of the waves, which agrees quite well with experiments. For strong hysteresis we find localized oscillon solutions.

patt-sol↗
arXiv1997

Velocity Probability Distribution Function in the Crossover and the Viscous Range

We derive a multifractal model for the velocity probability density distribution function (PDF), which is valid from the inertial range to the viscous range. The model gives a continuous evolution of velocity PDFs from large to small scales. It also predicts the asymptotic form of the PDF of velocity gradients. More importantly, the model captures the crossover range behavior and thus allows us to address the transition observed in the Helium turbulence experiment[Tabeling et. al., Phys. Rev. E53, 1613 (1996)] quantitatively. We compare both the PDFs and the structure functions predicted by this model with the experiments from the inertial range to the smallest scale resolved by the experiment. The model also predicts that the flatness measured in the crossover region can decrease with the Reynolds number.

chao-dyn↗