312 research outputs found
Dissipation in Dynamics of a Moving Contact Line
The dynamics of the deformations of a moving contact line is studied assuming
two different dissipation mechanisms. It is shown that the characteristic
relaxation time for a deformation of wavelength of a contact line
moving with velocity is given as . The velocity
dependence of is shown to drastically depend on the dissipation
mechanism: we find for the case when the dynamics is governed
by microscopic jumps of single molecules at the tip (Blake mechanism), and
when viscous hydrodynamic losses inside the moving
liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated
dominant dissipation mechanism can be experimentally determined using
relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T.
Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].Comment: REVTEX 8 pages, 9 PS figure
A practical density functional for polydisperse polymers
The Flory Huggins equation of state for monodisperse polymers can be turned
into a density functional by adding a square gradient term, with a coefficient
fixed by appeal to RPA (random phase approximation). We present instead a model
nonlocal functional in which each polymer is replaced by a deterministic,
penetrable particle of known shape. This reproduces the RPA and square gradient
theories in the small deviation and/or weak gradient limits, and can readily be
extended to polydisperse chains. The utility of the new functional is shown for
the case of a polydisperse polymer solution at coexistence in a poor solvent.Comment: 9 pages, 3 figure
Undulation Instability of Epithelial Tissues
Treating the epithelium as an incompressible fluid adjacent to a viscoelastic
stroma, we find a novel hydrodynamic instability that leads to the formation of
protrusions of the epithelium into the stroma. This instability is a candidate
for epithelial fingering observed in vivo. It occurs for sufficiently large
viscosity, cell-division rate and thickness of the dividing region in the
epithelium. Our work provides physical insight into a potential mechanism by
which interfaces between epithelia and stromas undulate, and potentially by
which tissue dysplasia leads to cancerous invasion.Comment: 4 pages, 3 figure
Critical holes in undercooled wetting layers
The profile of a critical hole in an undercooled wetting layer is determined
by the saddle-point equation of a standard interface Hamiltonian supported by
convenient boundary conditions. It is shown that this saddle-point equation can
be mapped onto an autonomous dynamical system in a three-dimensional phase
space. The corresponding flux has a polynomial form and in general displays
four fixed points, each with different stability properties. On the basis of
this picture we derive the thermodynamic behaviour of critical holes in three
different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.
Pinning of a solid--liquid--vapour interface by stripes of obstacles
We use a macroscopic Hamiltonian approach to study the pinning of a
solid--liquid--vapour contact line on an array of equidistant stripes of
obstacles perpendicular to the liquid. We propose an estimate of the density of
pinning stripes for which collective pinning of the contact line happens. This
estimate is shown to be in good agreement with Langevin equation simulation of
the macroscopic Hamiltonian. Finally we introduce a 2--dimensional mean field
theory which for small strength of the pinning stripes and for small capillary
length gives an excellent description of the averaged height of the contact
line.Comment: Plain tex, 12 pages, 3 figures available upon reques
Roughening Transition in a Moving Contact Line
The dynamics of the deformations of a moving contact line on a disordered
substrate is formulated, taking into account both local and hydrodynamic
dissipation mechanisms. It is shown that both the coating transition in contact
lines receding at relatively high velocities, and the pinning transition for
slowly moving contact lines, can be understood in a unified framework as
roughening transitions in the contact line. We propose a phase diagram for the
system in which the phase boundaries corresponding to the coating transition
and the pinning transition meet at a junction point, and suggest that for
sufficiently strong disorder a receding contact line will leave a
Landau--Levich film immediately after depinning. This effect may be relevant to
a recent experimental observation in a liquid Helium contact line on a Cesium
substrate [C. Guthmann, R. Gombrowicz, V. Repain, and E. Rolley, Phys. Rev.
Lett. {\bf 80}, 2865 (1998)].Comment: 16 pages, 6 encapsulated figure
Molecular Weight Dependence of Spreading Rates of Ultrathin Polymeric Films
We study experimentally the molecular weight dependence of spreading
rates of molecularly thin precursor films, growing at the bottom of droplets of
polymer liquids. In accord with previous observations, we find that the radial
extension R(t) of the film grows with time as R(t) = (D_{exp} t)^{1/2}. Our
data substantiate the M-dependence of D_{exp}; we show that it follows D_{exp}
\sim M^{-\gamma}, where the exponent \gamma is dependent on the chemical
composition of the solid surface, determining its frictional properties with
respect to the molecular transport. In the specific case of hydrophilic
substrates, the frictional properties can be modified by the change of the
relative humidity (RH). We find that \gamma \approx 1 at low RH and tends to
zero when RH gets progressively increased. We propose simple theoretical
arguments which explain the observed behavior in the limits of low and high RH.Comment: 4 pages, 2 figures, to appear in PR
Deviations from the mean field predictions for the phase behaviour of random copolymers melts
We investigate the phase behaviour of random copolymers melts via large scale
Monte Carlo simulations. We observe macrophase separation into A and B--rich
phases as predicted by mean field theory only for systems with a very large
correlation lambda of blocks along the polymer chains, far away from the
Lifshitz point. For smaller values of lambda, we find that a locally
segregated, disordered microemulsion--like structure gradually forms as the
temperature decreases. As we increase the number of blocks in the polymers, the
region of macrophase separation further shrinks. The results of our Monte Carlo
simulation are in agreement with a Ginzburg criterium, which suggests that mean
field theory becomes worse as the number of blocks in polymers increases.Comment: 6 pages, 4 figures, Late
Fluctuations of a driven membrane in an electrolyte
We develop a model for a driven cell- or artificial membrane in an
electrolyte. The system is kept far from equilibrium by the application of a DC
electric field or by concentration gradients, which causes ions to flow through
specific ion-conducting units (representing pumps, channels or natural pores).
We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain
the membrane equation of motion within Stokes hydrodynamics. At steady state,
the applied field causes an accumulation of charges close to the membrane,
which, similarly to the equilibrium case, can be described with renormalized
membrane tension and bending modulus. However, as opposed to the equilibrium
situation, we find new terms in the membrane equation of motion, which arise
specifically in the out-of-equilibrium case. We show that these terms lead in
certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let
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