88 research outputs found
Note on the Drag experienced by a Circular Cylinder moving in a Viscous Fluid at Small Reynolds Numbers
The Pressure Distributions on the Surface of an Obstacle in a Running Viscous Fluid at Small Reynolds Numbers
Note on the Flow of an Incompressible Viscous Fluid past a Circular Cylinder at Low Reynolds Numbers
Effect of Shear Flow on the Stability of Domains in Two Dimensional Phase-Separating Binary Fluids
We perform a linear stability analysis of extended domains in
phase-separating fluids of equal viscosity, in two dimensions. Using the
coupled Cahn-Hilliard and Stokes equations, we derive analytically the
stability eigenvalues for long wavelength fluctuations. In the quiescent state
we find an unstable varicose mode which corresponds to an instability towards
coarsening. This mode is stabilized when an external shear flow is imposed on
the fluid. The effect of the shear is seen to be qualitatively similar to that
found in experiments.Comment: 13 pages, RevTeX, 8 eps figures included. Submitted to Phys. Rev.
Pearling and Pinching: Propagation of Rayleigh Instabilities
A new category of front propagation problems is proposed in which a spreading
instability evolves through a singular configuration before saturating. We
examine the nature of this front for the viscous Rayleigh instability of a
column of one fluid immersed in another, using the marginal stability criterion
to estimate the front velocity, front width, and the selected wavelength in
terms of the surface tension and viscosity contrast. Experiments are suggested
on systems that may display this phenomenon, including droplets elongated in
extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic
fluids. The related problem of propagation in Rayleigh-like systems that do not
fission is also considered.Comment: Revtex, 7 pages, 4 ps figs, PR
Prediction and control of drop formation modes in microfluidic generation of double emulsions by single-step emulsification
Hypothesis
Predicting formation mode of double emulsion drops in microfluidic emulsification is crucial for controlling the drop size and morphology.
Experiments and modelling
A three-phase Volume of Fluid-Continuum Surface Force (VOF–CSF) model was developed, validated with analytical solutions, and used to investigate drop formation in different regimes. Experimental investigations were done using a glue-free demountable glass capillary device with a true axisymmetric geometry, capable of readjusting the distance between the two inner capillaries during operation.
Findings
A non-dimensional parameter (ζ) for prediction of double emulsion formation mode as a function of the capillary numbers of all fluids and device geometry was developed and its critical values were determined using simulation and experimental data. At logζ > 5.7, drops were formed in dripping mode; the widening jetting occurred at 5 < logζ < 5.7; while the narrowing jetting was observed at logζ < 5. The ζ criterion was correlated with the ratio of the break-up length to drop diameter. The transition from widening to narrowing jetting was achieved by increasing the outer fluid flow rate at the high capillary number of the inner fluid. The drop size was reduced by reducing the distance between the two inner capillaries and the minimum drop size was achieved when the distance between the capillaries was zero
The Two Fluid Drop Snap-off Problem: Experiments and Theory
We address the dynamics of a drop with viscosity breaking up
inside another fluid of viscosity . For , 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 dependence of the shape and
breaking rate.Comment: 4 pages, 3 figure
Simple Viscous Flows: from Boundary Layers to the Renormalization Group
The seemingly simple problem of determining the drag on a body moving through
a very viscous fluid has, for over 150 years, been a source of theoretical
confusion, mathematical paradoxes, and experimental artifacts, primarily
arising from the complex boundary layer structure of the flow near the body and
at infinity. We review the extensive experimental and theoretical literature on
this problem, with special emphasis on the logical relationship between
different approaches. The survey begins with the developments of matched
asymptotic expansions, and concludes with a discussion of perturbative
renormalization group techniques, adapted from quantum field theory to
differential equations. The renormalization group calculations lead to a new
prediction for the drag coefficient, one which can both reproduce and surpass
the results of matched asymptotics
Equilibrium configurations of fluids and their stability in higher dimensions
We study equilibrium shapes, stability and possible bifurcation diagrams of
fluids in higher dimensions, held together by either surface tension or
self-gravity. We consider the equilibrium shape and stability problem of
self-gravitating spheroids, establishing the formalism to generalize the
MacLaurin sequence to higher dimensions. We show that such simple models, of
interest on their own, also provide accurate descriptions of their general
relativistic relatives with event horizons. The examples worked out here hint
at some model-independent dynamics, and thus at some universality: smooth
objects seem always to be well described by both ``replicas'' (either
self-gravity or surface tension). As an example, we exhibit an instability
afflicting self-gravitating (Newtonian) fluid cylinders. This instability is
the exact analogue, within Newtonian gravity, of the Gregory-Laflamme
instability in general relativity. Another example considered is a
self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We
recover the features of the black ring in general relativity.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical
and Quantum Gravity. v2: Minor corrections and references adde
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