28 research outputs found
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
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
Stability analysis of polarized domains
Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains
with deformable boundaries. Stability analysis of these domains depends on a
family of nontrivial integrals. We present a closed form evaluation of these
integrals as a combination of Legendre functions. This result allows exact and
explicit formulae for stability thresholds and growth rates of individual
modes. We also evaluate asymptotic behavior in several interesting limits.Comment: 12 pages, 3 figures, Late
Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis
The Saffman-Taylor viscous fingering instability occurs when a less viscous
fluid displaces a more viscous one between narrowly spaced parallel plates in a
Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in
which fingers of different lengths compete, spread and split. Our weakly
nonlinear analysis of the instability predicts these phenomena, which are
beyond the scope of linear stability theory. Finger competition arises through
enhanced growth of sub-harmonic perturbations, while spreading and splitting
occur through the growth of harmonic modes. Nonlinear mode-coupling enhances
the growth of these perturbations with appropriate relative phases, as we
demonstrate through a symmetry analysis of the mode coupling equations. We
contrast mode coupling in radial flow with rectangular flow geometry.Comment: 36 pages, 5 figures, Latex, added references, to appear in Physica D
(1998
Dynamics at the serine loop underlie differential affinity of cryptochromes for CLOCK:BMAL1 to control circadian timing.
Mammalian circadian rhythms are generated by a transcription-based feedback loop in which CLOCK:BMAL1 drives transcription of its repressors (PER1/2, CRY1/2), which ultimately interact with CLOCK:BMAL1 to close the feedback loop with ~24 hr periodicity. Here we pinpoint a key difference between CRY1 and CRY2 that underlies their differential strengths as transcriptional repressors. Both cryptochromes bind the BMAL1 transactivation domain similarly to sequester it from coactivators and repress CLOCK:BMAL1 activity. However, we find that CRY1 is recruited with much higher affinity to the PAS domain core of CLOCK:BMAL1, allowing it to serve as a stronger repressor that lengthens circadian period. We discovered a dynamic serine-rich loop adjacent to the secondary pocket in the photolyase homology region (PHR) domain that regulates differential binding of cryptochromes to the PAS domain core of CLOCK:BMAL1. Notably, binding of the co-repressor PER2 remodels the serine loop of CRY2, making it more CRY1-like and enhancing its affinity for CLOCK:BMAL1
The Saffman-Taylor problem on a sphere
The Saffman-Taylor problem addresses the morphological instability of an
interface separating two immiscible, viscous fluids when they move in a narrow
gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend
the classic Saffman-Taylor situation, by considering the flow between two
curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We
derive the mode-coupling differential equation for the interface perturbation
amplitudes and study both linear and nonlinear flow regimes. The effect of the
spherical cell (positive) spatial curvature on the shape of the interfacial
patterns is investigated. We show that stability properties of the fluid-fluid
interface are sensitive to the curvature of the surface. In particular, it is
found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw
flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.