123 research outputs found
Note on the Drag experienced by a Circular Cylinder moving in a Viscous Fluid at Small Reynolds Numbers
The Influence of Vortices upon the Drag experienced by an Elliptic Cylinder moving through an Inviscid Liquid
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
The shrinking instability of toroidal liquid droplets in the Stokes flow regime
We analyze the stability and dynamics of toroidal liquid droplets. In
addition to the Rayleigh instabilities akin to those of a cylindrical droplet
there is a shrinking instability that is unique to the topology of the torus
and dominates in the limit that the aspect ratio is near one (fat tori). We
first find an analytic expression for the pressure distribution inside the
droplet. We then determine the velocity field in the bulk fluid, in the Stokes
flow regime, by solving the biharmonic equation for the stream function. The
flow pattern in the external fluid is analyzed qualitatively by exploiting
symmetries. This elucidates the detailed nature of the shrinking mode and the
swelling of the cross-section following from incompressibility. Finally the
shrinking rate of fat toroidal droplets is derived by energy conservation.Comment: 6 pages, 7 figure
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
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