904 research outputs found
Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration
In this paper we propose several models that describe the dynamics of liquid
films which are covered by a high concentration layer of insoluble surfactant.
First, we briefly review the 'classical' hydrodynamic form of the coupled
evolution equations for the film height and surfactant concentration that are
well established for small concentrations. Then we re-formulate the basic model
as a gradient dynamics based on an underlying free energy functional that
accounts for wettability and capillarity. Based on this re-formulation in the
framework of nonequilibrium thermodynamics, we propose extensions of the basic
hydrodynamic model that account for (i) nonlinear equations of state, (ii)
surfactant-dependent wettability, (iii) surfactant phase transitions, and (iv)
substrate-mediated condensation. In passing, we discuss important differences
to most of the models found in the literature.Comment: 31 pages, 2 figure
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
In this paper we consider a multiscale phase-field model for
capillarity-driven flows in porous media. The presented model constitutes a
reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model,
valid in situations where interest is restricted to dynamical and equilibrium
behavior in an aggregated sense, rather than a precise description of
microscale flow phenomena. The model is based on averaging of the equation of
motion, thereby yielding a significant reduction in the complexity of the
underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its
macroscopic dynamical and equilibrium properties. Numerical results are
presented for the representative 2-dimensional capillary-rise problem
pertaining to two closely spaced vertical plates with both identical and
disparate wetting properties. Comparison with analytical solutions for these
test cases corroborates the accuracy of the presented multiscale model. In
addition, we present results for a capillary-rise problem with a non-trivial
geometry corresponding to a porous medium
On the shock wave spectrum for isentropic gas dynamics with capillarity
AbstractWe consider the stability problem for shock layers in Slemrod's model of an isentropic gas with capillarity. We show that these traveling waves are monotone in the weak capillarity case, and become highly oscillatory as the capillarity strength increases. Using a spectral energy estimate we prove that small-amplitude monotone shocks are spectrally stable. We also show that monotone shocks have no unstable real spectrum regardless of amplitude; this implies that any instabilities of these monotone traveling waves, if they exist, must occur through a Hopf-like bifurcation, where one or more conjugate pairs of eigenvalues cross the imaginary axis. We then conduct a systematic numerical Evans function study, which shows that monotone and mildly oscillatory profiles in an adiabatic gas are spectrally stable for moderate values of shock and capillarity strengths. In particular, we show that the transition from monotone to nonmonotone profiles does not appear to trigger any instabilities
Utilization of the second gradient theory in continuum mechanics to study motions and thermodynamics of liquid-vapor interfaces
Revisited and completed version; 21 pages. ISBN-13: 9780306429057A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In such fluids, conservative motions verify first integrals that lead to Kelvin circulation theorems and potential equations. The dynamical surface tension of liquid-vapor interfaces is deduced from viscous fluid equations. The result provides and explains the Marangoni effect
Continuum mechanics at nanoscale. A tool to study trees' watering and recovery
The cohesion-tension theory expounds the crude sap ascent thanks to the
negative pressure generated by evaporation of water from leaves. Nevertheless,
trees pose multiple challenges and seem to live in unphysical conditions: the
negative pressure increases cavitation; it is possible to obtain a water
equilibrium between connected parts where one is at a positive pressure and the
other one is at negative pressure; no theory is able to satisfactorily account
for the refilling of vessels after embolism events. A theoretical form of our
paper in the Journal of Theoretical Biology is proposed together with new
results: a continuum mechanics model of the disjoining pressure concept refers
to the Derjaguin School of physical chemistry. A comparison between liquid
behaviour both in tight-filled microtubes and in liquid thin-films is offered
when the pressure is negative in liquid bulks and is positive in liquid
thin-films and vapour bulks. In embolized xylem microtubes, when the air-vapour
pocket pressure is greater than the air-vapour bulk pressure, a refilling flow
occurs between the air-vapour domains to empty the air-vapour pockets although
the liquid-bulk pressure remains negative. The model has a limit of validity
taking the maximal size of trees into account. These results drop inkling that
the disjoining pressure is an efficient tool to study biological liquids in
contact with substrates at a nanoscale range.Comment: The paper is a review and overlap of my different papers about the
watering of trees as a mathematical development of my paper in The Journal of
Theoretical Biology. These results are presented together with new
researches: transfer of liquid water and vapour between xylem microtubes, an
explanation of ultrasounds generated in the watering network considered as
sound pipes, numerical calculations of flows in thin liquid films and of
Poiseuille flows in xylem microtubes, an estimation of the velocity for the
ascent of crude sap and of the recovery time of trees during the spring
perio
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