240 research outputs found
Stick-slip instability for viscous fingering in a gel
The growth dynamics of an air finger injected in a visco-elastic gel (a
PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the
standard Saffmann-Taylor instability, we observe - with increasing finger
velocities - the existence of two new regimes: (a) a stick-slip regime for
which the finger tip velocity oscillates between 2 different values, producing
local pinching of the finger at regular intervals, (b) a ``tadpole'' regime
where a fracture-type propagation is observed. A scaling argument is proposed
to interpret the dependence of the stick-slip frequency with the measured
rheological properties of the gel.Comment: 7 pages, 4 figures. Submitted to Europhysics Letter
Scaling Relations of Viscous Fingers in Anisotropic Hele-Shaw Cells
Viscous fingers in a channel with surface tension anisotropy are numerically
studied. Scaling relations between the tip velocity v, the tip radius and the
pressure gradient are investigated for two kinds of boundary conditions of
pressure, when v is sufficiently large. The power-law relations for the
anisotropic viscous fingers are compared with two-dimensional dendritic growth.
The exponents of the power-law relations are theoretically evaluated.Comment: 5 pages, 4 figure
Gravity-driven instability in a spherical Hele-Shaw cell
A pair of concentric spheres separated by a small gap form a spherical
Hele-Shaw cell. In this cell an interfacial instability arises when two
immiscible fluids flow. We derive the equation of motion for the interface
perturbation amplitudes, including both pressure and gravity drivings, using a
mode coupling approach. Linear stability analysis shows that mode growth rates
depend upon interface perimeter and gravitational force. Mode coupling analysis
reveals the formation of fingering structures presenting a tendency toward
finger tip-sharpening.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review
Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell
We report analytical results for the development of the viscous fingering
instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We
derive a generalized version of Darcy's law in such cylindrical background, and
find it recovers the usual Darcy's law for flow in flat, rectangular cells,
with corrections of higher order in b/a. We focus our interest on the influence
of cell's radius of curvature on the instability characteristics. Linear and
slightly nonlinear flow regimes are studied through a mode-coupling analysis.
Our analytical results reveal that linear growth rates and finger competition
are inhibited for increasingly larger radius of curvature. The absence of
tip-splitting events in cylindrical cells is also discussed.Comment: 14 pages, 3 ps figures, Revte
Microscopic Selection of Fluid Fingering Pattern
We study the issue of the selection of viscous fingering patterns in the
limit of small surface tension. Through detailed simulations of anisotropic
fingering, we demonstrate conclusively that no selection independent of the
small-scale cutoff (macroscopic selection) occurs in this system. Rather, the
small-scale cutoff completely controls the pattern, even on short time scales,
in accord with the theory of microscopic solvability. We demonstrate that
ordered patterns are dynamically selected only for not too small surface
tensions. For extremely small surface tensions, the system exhibits chaotic
behavior and no regular pattern is realized.Comment: 6 pages, 5 figure
Control of rotorcraft retreating blade stall using air-jet vortex generators
A series of low-speed wind tunnel tests were carried out on an oscillating airfoil fitted with two rows of air-jet vortex generators (AJVGs). The airfoil used had an RAE 9645 section and the two spanwise arrays of AJVGs were located at x/c=0.12 and 0.62. The devices and their distribution were chosen to assess their ability to modify/control dynamic stall; the goal being to enhance the aerodynamic performance of helicopter rotors on the retreating blade side of the disc. The model was pitched about the quarter chord with a reduced frequency
(k) of 0.1 in a sinusoidal motion defined by a=15o+10sin_ t. The measured data indicate that, for continuous blowing from the front row of AJVGs with a momentum blowing coefficient (C μ) greater than 0.008, modifications to the stalling process are encouraging. In particular, the pitching moment behavior exhibits delayed stall and there is a marked reduction in the normal force hysteresis
Parallel flow in Hele-Shaw cells with ferrofluids
Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow
with relative velocity parallel to the interface between them. The interface is
unstable due to a Kelvin-Helmholtz type of instability in which fluid flow
couples with inertial effects to cause an initial small perturbation to grow.
Large amplitude disturbances form stable solitons. We consider the effects of
applied magnetic fields when one of the two fluids is a ferrofluid. The
dispersion relation governing mode growth is modified so that the magnetic
field can destabilize the interface even in the absence of inertial effects.
However, the magnetic field does not affect the speed of wave propagation for a
given wavenumber. We note that the magnetic field creates an effective
interaction between the solitons.Comment: 12 pages, Revtex, 2 figures, revised version (minor changes
Rotating Hele-Shaw cells with ferrofluids
We investigate the flow of two immiscible, viscous fluids in a rotating
Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic
field is applied. The interplay between centrifugal and magnetic forces in
determining the instability of the fluid-fluid interface is analyzed. The
linear stability analysis of the problem shows that a non-uniform, azimuthal
magnetic field, applied tangential to the cell, tends to stabilize the
interface. We verify that maximum growth rate selection of initial patterns is
influenced by the applied field, which tends to decrease the number of
interface ripples. We contrast these results with the situation in which a
uniform magnetic field is applied normally to the plane defined by the rotating
Hele-Shaw cell.Comment: 12 pages, 3 ps figures, RevTe
Experimental investigation of the initial regime in fingering electrodeposition: dispersion relation and velocity measurements
Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor
instability, was identified in the quasi-two-dimensional electrodeposition of
copper. We present here measurements of the dispersion relation of the growing
front. The instability is accompanied by gravity-driven convection rolls at the
electrodes, which are examined using particle image velocimetry. While at the
anode the theory presented by Chazalviel et al. describes the convection roll,
the flow field at the cathode is more complicated because of the growing
deposit. In particular, the analysis of the orientation of the velocity vectors
reveals some lag of the development of the convection roll compared to the
finger envelope.Comment: 11 pages, 15 figures, REVTEX 4; reference adde
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