2,628 research outputs found
Self-similar breakup of polymeric threads as described by the Oldroyd-B model
When a drop of fluid containing long, flexible polymers breaks up, it forms
threads of almost constant thickness, whose size decreases exponentially in
time. Using an Oldroyd-B fluid as a model, we show that the thread profile,
rescaled by the thread thickness, converges to a similarity solution. Using the
correspondence between viscoelastic fluids and non-linear elasticity, we derive
similarity equations for the full three-dimensional axisymmetric flow field in
the limit that the viscosity of the solvent fluid can be neglected. A
conservation law balancing pressure and elastic energy permits to calculate the
thread thickness exactly. The explicit form of the velocity and stress fields
can be deduced from a solution of the similarity equations. Results are
validated by detailed comparison with numerical simulations
Cusp-shaped Elastic Creases and Furrows
The surfaces of growing biological tissues, swelling gels, and compressed
rubbers do not remain smooth, but frequently exhibit highly localized inward
folds. We reveal the morphology of this surface folding in a novel experimental
setup, which permits to deform the surface of a soft gel in a controlled
fashion. The interface first forms a sharp furrow, whose tip size decreases
rapidly with deformation. Above a critical deformation, the furrow bifurcates
to an inward folded crease of vanishing tip size. We show experimentally and
numerically that both creases and furrows exhibit a universal cusp-shape, whose
width scales like at a distance from the tip. We provide a
similarity theory that captures the singular profiles before and after the
self-folding bifurcation, and derive the length of the fold from large
deformation elasticity.Comment: 5 pages, 4 figure
Flight craft Patent
Designing spacecraft for flight into space, atmospheric reentry, and landing at selected site
Anomalous dimensions of the Smoluchowski coagulation equation
The coagulation (or aggregation) equation was introduced by Smoluchowski in
1916 to describe the clumping together of colloidal particles through
diffusion, but has been used in many different contexts as diverse as physical
chemistry, chemical engineering, atmospheric physics, planetary science, and
economics. The effectiveness of clumping is described by a kernel ,
which depends on the sizes of the colliding particles . We consider
kernels , but any homogeneous function can be treated using
our methods. For sufficiently effective clumping , the
coagulation equation produces an infinitely large cluster in finite time (a
process known as the gel transition). Using a combination of analytical methods
and numerics, we calculate the anomalous scaling dimensions of the main cluster
growth, calling into question results much used in the literature. Apart from
the solution branch which originates from the exactly solvable case , we find a new branch of solutions near , which violates
scaling relations widely believed to hold universal
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
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