arXiv subjects

J. Eggers

Publications and source records attributed to J. Eggers.

23 records · Page 2Linked to original sources

arXiv2004

Droplet detachment and bead formation in visco-elastic fluids

The presence of a very small amount of high molecular weight polymer significantly delays the pinch-off singularity of a drop of water falling from a faucet, and leads to the formation of a long-lived cylindrical filament. In this paper we present experiments, numerical simulations, and theory which examines the pinch-off process in the presence of polymers. The numerical simulations are found to be in excellent agreement with experiment. As a test case, we establish the conditions under which a small bead remains on the filament; we find that this is due to the asymmetry induced by the self-similar pinch-off of the droplet.

cond-mat.soft↗

arXiv2003

The beads-on-string structure of viscoelastic threads

By adding minute concentrations of a high molecular weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times, for which the evolution can be divided into two distinct regimes. This excludes the very late stages of the evolution, for which the polymers have become fully stretched. For times smaller than the polymer relaxation time, over which the beads-on-string structure develops, we give a simplified local description, which still contains the full complexity of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops.

cond-mat.mtrl-sci↗

arXiv2002

Inviscid coalescence of drops

We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than $\ell_ν = ρν^2/σ$, which is $10 nm$ for water. Using a high-precision boundary integral method, we show that the walls of the thin retracting sheet of air between the drops reconnect in finite time to form a toroidal enclosure. After the initial reconnection, retraction starts again, leading to a rapid sequence of enclosures. Averaging over the discrete events, we find the minimum radius of the liquid bridge connecting the two drops to scale like $r_b \propto t^{1/2}$.

physics.flu-dyn↗

arXiv1996

Singularities in cascade models of the Euler equation

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.

chao-dyn↗

arXiv1996

Classical Kolmogorov scaling is inconsistent with local coupling

We consider cascade models of turbulence which are obtained by restricting the Navier-Stokes equation to local interactions. By combining the results of the method of extended self-similarity and a novel subgrid model, we investigate the inertial range fluctuations of the cascade. Significant corrections to the classical scaling exponents are found. The dynamics of our local Navier-Stokes models is described accurately by a simple set of Langevin equations proposed earlier as a model of turbulence [Phys. Rev. E {\bf 50}, 285 (1994)]. This allows for a prediction of the intermittency exponents without adjustable parameters. Excellent agreement with numerical simulations is found.

chao-dyn↗