26 research outputs found
Hydrodynamics of Monolayer Domains at the Air-Water Interface
Molecules at the air-water interface often form inhomogeneous layers in which
domains of different densities are separated by sharp interfaces. Complex
interfacial pattern formation may occur through the competition of short- and
long-range forces acting within the monolayer. The overdamped hydrodynamics of
such interfacial motion is treated here in a general manner that accounts for
dissipation both within the monolayer and in the subfluid. Previous results on
the linear stability of interfaces are recovered and extended, and a
formulation applicable to the nonlinear regime is developed. A simplified
dynamical law valid when dissipation in the monolayer itself is negligible is
also proposed. Throughout the analysis, special attention is paid to the
dependence of the dynamical behavior on a characteristic length scale set by
the ratio of the viscosities in the monolayer and in the subphase.Comment: 12 pages, RevTeX, 4 ps figures, accepted in Physics of Fluids
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
Instability of the origami of a ferrofluid drop in a magnetic field
Capillary origami is the wrapping of an usual fluid drop by a planar elastic
membrane due to the interplay between capillary and elastic forces. Here, we
use a drop of magnetic fluid whose shape is known to strongly depend on an
applied magnetic field. We study the quasi-static and dynamical behaviors of
such a magnetic capillary origami. We report the observation of an overturning
instability that the origami undergoes at a critical magnetic field. This
instability is triggered by an interplay between magnetic and gravitational
energies in agreement with the theory presented here. Additional effects of
elasticity and capillarity on this instability are also discussed.Comment: in press in PRL (2011
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
The effects of polydispersity on the initial susceptibilities of ferrofluids
The effects of particle-size polydispersity on the initial susceptibilities of concentrated ferrofluids are analyzed using a combination of theory and computer simulation. The study is focused on a model ferrofluid with a prescribed magnetic-core diameter distribution, a fixed non-magnetic surface layer (corresponding to a demagnetized layer and adsorbed surfactant) and a combination of dipolar and hard-core interactions. The non-trivial effects of polydispersity are identified by comparing the initial susceptibilities of monodisperse and polydisperse ferrofluids with the same Langevin susceptibility. The theory is based on a correction to the second-order modified mean-field theory arising from a formal Mayer-type cluster expansion; this correction is dependent on a parameter similar to the normal dipolar coupling constant, except that it contains a complicated double average over the particle-size distribution, which means that the initial susceptibility should depend significantly on polydispersity. Specifically, the theory predicts that the initial susceptibility is enhanced significantly by polydispersity. This prediction is tested rigorously against results from Monte Carlo simulations and is found to be robust. The qualitative agreement between theory and simulation is already satisfactory, but the quantitative agreement could be improved by a systematic extension of the cluster expansion. The overall conclusion is that polydispersity should be accounted for carefully in magnetogranulometric analyses of real ferrofluids. © 2014 IOP Publishing Ltd
Unified mathematical Model of the Kinetics of Nanoparticle Phase Condensation in Magnetic Fields
In this paper, we aim to present a unified mathematical modeling and description of the kinetics of magnetic nanoparticles phase condensation (conducting to the appearance of bulk elongated aggregates) under homogeneous permanent or alternating magnetic field. For such case, the aggregate growth rate usually takes the form dV/dt = G(V)∆(t), with V and t being the aggregate's volume and time, respectively, ∆(t)—the supersaturation of the nanoparticle suspension, and with the function G(V) depending on the precise configuration of the applied field. The Liouville equation for the aggregate size distribution function is solved by the method of characteristics. The solution is obtained in parametric form for an arbitrary function G(V), providing a general framework for any type of the applied magnetic field. In the particular case of low-frequency rotating magnetic field (G(V)~V2/3), an explicit expression of the distribution function is obtained, while the dimensionless average aggregate volume 〈V〉 is found by the method of moments allowing a complete decoupling of the system of equations for the statistical moments 〈Vn〉 of the distribution function. Numerical examples are provided for the cases of permanent and low- or medium-frequency rotating fields. It is shown that in all cases, the average volume 〈V〉 only slightly depends on the relative width of the initial size distribution. Nevertheless, at any times, t > 0, the size distribution shows a significant spreading around the average value 〈V〉, which increases progressively with time and achieves a final plateau at long times. This model can be helpful for several biomedical or environmental applications of magnetic nanoparticles in which the nanoparticle suspension undergoes a field-induced phase condensation. © 2020 John Wiley & Sons, Ltd.PK acknowledges the French “Agence Nationale de la Recherche,” Project Future Investments UCA JEDI, No. ANR‐15‐IDEX‐01 (projects ImmunoMag and MagFilter) and the private company Axlepios Biomedicals for financial support. JQC acknowledges the financial support of UCA JEDI and Axlepios Biomedicals through the PhD fellowship. AZ thanks the Russian Science Foundation, project 20‐12‐00031, for the financial support
The Shapes of Flux Domains in the Intermediate State of Type-I Superconductors
In the intermediate state of a thin type-I superconductor magnetic flux
penetrates in a disordered set of highly branched and fingered macroscopic
domains. To understand these shapes, we study in detail a recently proposed
"current-loop" (CL) model that models the intermediate state as a collection of
tense current ribbons flowing along the superconducting-normal interfaces and
subject to the constraint of global flux conservation. The validity of this
model is tested through a detailed reanalysis of Landau's original conformal
mapping treatment of the laminar state, in which the superconductor-normal
interfaces are flared within the slab, and of a closely-related straight-lamina
model. A simplified dynamical model is described that elucidates the nature of
possible shape instabilities of flux stripes and stripe arrays, and numerical
studies of the highly nonlinear regime of those instabilities demonstrate
patterns like those seen experimentally. Of particular interest is the buckling
instability commonly seen in the intermediate state. The free-boundary approach
further allows for a calculation of the elastic properties of the laminar
state, which closely resembles that of smectic liquid crystals. We suggest
several new experiments to explore of flux domain shape instabilities,
including an Eckhaus instability induced by changing the out-of-plane magnetic
field, and an analog of the Helfrich-Hurault instability of smectics induced by
an in-plane field.Comment: 23 pages, 22 bitmapped postscript figures, RevTex 3.0, submitted to
Phys. Rev. B. Higher resolution figures may be obtained by contacting the
author
Ferromagnetic Liquid Thin Films Under Applied Field
Theoretical calculations, computer simulations and experiments indicate the
possible existence of a ferromagnetic liquid state, although definitive
experimental evidence is lacking. Should such a state exist, demagnetization
effects would force a nontrivial magnetization texture. Since liquid droplets
are deformable, the droplet shape is coupled with the magnetization texture. In
a thin-film geometry in zero applied field, the droplet has a circular shape
and a rotating magnetization texture with a point vortex at the center. We
calculate the elongation and magnetization texture of such ferromagnetic thin
film liquid droplet confined between two parallel plates under a weak applied
magnetic field. The vortex stretches into a domain wall and exchange forces
break the reflection symmetry. This behavior contrasts qualitatively and
quantitatively with the elongation of paramagnetic thin films.Comment: 10 pages, 4 figures, Submitted to Phys. Rev.
Phase Coexistence of a Stockmayer Fluid in an Applied Field
We examine two aspects of Stockmayer fluids which consists of point dipoles
that additionally interact via an attractive Lennard-Jones potential. We
perform Monte Carlo simulations to examine the effect of an applied field on
the liquid-gas phase coexistence and show that a magnetic fluid phase does
exist in the absence of an applied field. As part of the search for the
magnetic fluid phase, we perform Gibbs ensemble simulations to determine phase
coexistence curves at large dipole moments, . The critical temperature is
found to depend linearly on for intermediate values of beyond the
initial nonlinear behavior near and less than the where no
liquid-gas phase coexistence has been found. For phase coexistence in an
applied field, the critical temperatures as a function of the applied field for
two different are mapped onto a single curve. The critical densities
hardly change as a function of applied field. We also verify that in an applied
field the liquid droplets within the two phase coexistence region become
elongated in the direction of the field.Comment: 23 pages, ReVTeX, 7 figure