42 research outputs found
The Explicit-Implicit-Null method:Removing the numerical instability of PDEs
International audienceno abstrac
Singularities of relativistic membranes
AbstractPointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R</jats:p
Fluid interfaces with very sharp tips in viscous flow
When a fluid interface is subjected to a strong viscous flow, it tends to develop near-conical ends with pointed tips so sharp that their radius of curvature is undetectable. In microfluidic applications, tips can be made to eject fine jets, from which micrometer-sized drops can be produced. Here we show theoretically that the opening angle of the conical interface varies on a logarithmic scale as a function of the distance from the tip, owing to nonlocal coupling between the tip and the external flow. Using this insight we are able to show that the tip curvature grows like the exponential of the square of the strength of the external flow and to calculate the universal shape of the interface near the tip. Our experiments confirm the scaling of the tip curvature as well as of the interface’s universal shape. Our analytical technique, based on an integral over the surface, may also have far wider applications, for example treating problems with electric fields, such as electrosprays
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
Coalescence Dynamics
The merging of two fluid drops is one of the fundamental topologi- cal transitions occurring in free surface flow. Its description has many applications, for example in the chemical industry (emulsions, sprays etc.), in natural flows driving our climate, and for the sintering of mate- rials. After reconnection of two drops, strongly localized surface tension forces drive a singular flow, characterized by a connecting liquid bridge that grows according to scaling laws. We review theory, experiment, and simulation of the coalescence of two spherical drops for different parameters, and in the presence of an outer fluid. We then general- ize to other geometries, such as drops spreading on a substrate and in Hele-Shaw flow, and discuss other types of mass transport, apart from viscous flow. Our focus is on times immediately after reconnection, and on the limit of initially undeformed drops at rest relative to one another
How many ways a cell can move:the modes of self-propulsion of an active drop
Numerous physical models have been proposed to explain how cell motility
emerges from internal activity, mostly focused on how crawling motion arises
from internal processes. Here we offer a classification of self-propulsion
mechanisms based on general physical principles, showing that crawling is not
the only way for cells to move on a substrate. We consider a thin drop of
active matter on a planar substrate and fully characterize its autonomous
motion for all three possible sources of driving: (i) the stresses induced in
the bulk by active components, which allow in particular tractionless motion,
(ii) the self-propulsion of active components at the substrate, which gives
rise to crawling motion, and (iii) a net capillary force, possibly
self-generated, and coupled to internal activity. We determine travelling-wave
solutions to the lubrication equations as a function of a dimensionless
activity parameter for each mode of motion. Numerical simulations are used to
characterize the drop motion over a wide range of activity magnitudes, and
explicit analytical solutions in excellent agreement with the simulations are
derived in the weak-activity regime.Comment: to appear in Soft Matter (2020