136 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
Symmetric and Asymmetric Coalescence of Drops on a Substrate
The coalescence of viscous drops on a substrate is studied experimentally and
theoretically. We consider cases where the drops can have different contact
angles, leading to a very asymmetric coalescence process. Side view experiments
reveal that the "bridge" connecting the drops evolves with self-similar
dynamics, providing a new perspective on the coalescence of sessile drops. We
show that the universal shape of the bridge is accurately described by
similarity solutions of the one-dimensional lubrication equation. Our theory
predicts a bridge that grows linearly in time and stresses the strong
dependence on the contact angles. Without any adjustable parameters, we find
quantitative agreement with all experimental observations.Comment: 5 pages, 4 figure
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