3,818 research outputs found
Statics and dynamics of fluids in nanotubes
The purpose of this article is to study the statics and dynamics of nanotubes
by using the methods of continuum mechanics. The nanotube can be filled with
only a liquid or a vapour phase according to the physicochemical
characteristics of the wall and to the disjoining pressure associated with the
liquid and vapour mother bulks of the fluid, regardless of the nature of the
external mother bulk. In dynamics, flows through nanotubes can be much more
important than classical Poiseuille flows. When the external mother bulk is of
vapour, the flow can be a million times larger than the classical flows when
slippage on wall does not exist.Comment: 20 page
A mechanical model for liquid nanolayers
Liquids in contact with solids are submitted to intermolecular forces making
liquids heterogeneous and stress tensors are not any more spherical as in
homogeneous bulks. The aim of this article is to show that a square-gradient
functional representing liquid-vapor interface free energy corrected with a
liquid density functional at solid surfaces is a well adapted model to study
structures of very thin nanofilms near solid walls. This result makes it
possible to study the motions of liquids in nanolayers and to generalize the
approximation of lubrication in long wave hypothesis.Comment: 10 page
Motions in liquid-vapour interfaces by using a continuous mechanical model
By using a limit analysis for the motion equations of viscous fluid endowed
with internal capillarity, we are able to propose a dynamical expression for
the surface tension of moving liquid-vapour interfaces without any
phenomenological assumption. The proposed relation extends the static case,
yields the Laplace formula in cases of mass transfer across interfacial layers
and allows to take the second coefficient of viscosity of compressible fluids
into account. We generalize the Maxwell rule in dynamics and directly explain
the Marangoni effect.Comment: 15 page
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
Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle
The equation of motions and the conditions on surfaces and edges between
fluids and solids in presence of non-constant surface energies, as in the case
of surfactants attached to the fluid particles at the interfaces, are revisited
under the principle of virtual work. We point out that adequate behaviors of
surface concentrations may drastically modify the surface tension which
naturally appears in the Laplace and the Young-Dupr\'e equations. Thus, the
principle of virtual work points out a strong difference between the two
revisited concepts of surface energy and surface tension.Comment: 20 page
Multi-gradient fluids
An internal energy function of the mass density, the volumetric entropy and
their gradients at n-order generates the representation of multi-gradient
fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the
equation of motion which generalizes the case of perfect compressible fluids.
First integrals of flows are extended cases of perfect compressible fluids. The
equation of motion and the equation of energy are written for dissipative
cases, and are compatible with the second law of thermodynamics.Comment: Ricerche di matematica, Springer Verlag, In pres
The watering of tall trees - Embolization and recovery
We can propound a thermo-mechanical understanding of the ascent of sap to the
top of tall trees thanks to a comparison between experiments associated with
the cohesion-tension theory and the disjoining pressure concept for liquid
thin-films. When a segment of xylem is tight-filled with crude sap, the liquid
pressure can be negative although the pressure in embolized vessels remains
positive. Examples are given that illustrate how embolized vessels can be
refilled and why the ascent of sap is possible even in the tallest trees
avoiding the problem due to cavitation. However, the maximum height of trees is
limited by the stability domain of liquid thin-films.Comment: Extended introduction and additive comments removed from the Journal
of Theoretical Biology.22 page
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