175 research outputs found
Viscoelastic effects and anomalous transient levelling exponents in thin films
We study theoretically the profile evolution of a thin viscoelastic film
supported onto a no-slip flat substrate. Due to the nonconstant initial
curvature at the free surface, there is a flow driven by Laplace pressure and
mediated by viscoelasticity. In the framework of lubrication theory, we derive
a thin film equation that contains local viscoelastic stress through the
Maxwell model. Then, considering a sufficiently regular small perturbation of
the free surface, we linearise the equation and derive its general solution. We
analyse and discuss in details the behaviour of this function. We then use it
to study the viscoelastic evolution of a Gaussian initial perturbation through
its transient levelling exponent. For initial widths of the profile that are
smaller than a characteristic length scale involving both the film thickness
and the elastocapillary length, this exponent is shown to reach anomalously
high values at the elastic-to-viscous transition. This prediction should in
particular be observed at sufficiently short times in experiments on thin
polymer films.Comment: 4 figure
Two-phase flow in a chemically active porous medium
We study the problem of the transformation of a given reactant species into
an immiscible product species, as they flow through a chemically active porous
medium. We derive the equation governing the evolution of the volume fraction
of the species -- in a one-dimensional macroscopic description --, identify the
relevant dimensionless numbers, and provide simple models for capillary
pressure and relative permeabilities, which are quantities of crucial
importance when tackling multiphase flows in porous media. We set the domain of
validity of our models and discuss the importance of viscous coupling terms in
the extended Darcy's law. We investigate numerically the steady regime and
demonstrate that the spatial transformation rate of the species along the
reactor is non-monotonous, as testified by the existence of an inflection point
in the volume fraction profiles. We obtain the scaling of the location of this
inflection point with the dimensionless lengths of the problem. Eventually, we
provide key elements for optimization of the reactor.Comment: 13 pages, 10 figure
Wake and wave resistance on viscous thin films
The effect of an external pressure disturbance, being displaced with a
constant speed along the free surface of a viscous thin film, is studied
theoretically in the lubrication approximation in one- and two-dimensional
geometries. In the comoving frame, the imposed pressure field creates a
stationary deformation of the interface - a wake - that spatially vanishes in
the far region. The shape of the wake and the way it vanishes depend on both
the speed and size of the external source and the properties of the film. The
wave resistance, namely the force that has to be externally furnished in order
to maintain the wake, is analysed in details. For finite-size pressure
disturbances, it increases with the speed, up to a certain transition value
above which a monotonic decrease occurs. The role of the horizontal extent of
the pressure field is studied as well, revealing that for a smaller disturbance
the latter transition occurs at higher speed. Eventually, for a Dirac pressure
source, the wave resistance either saturates in a 1D geometry, or diverges in a
2D geometry
- …