The d'Alembert-lagrange principle for gradient theories and boundary conditions

Motions of continuous media presenting singularities are associated with phenomena involving shocks, interfaces or material surfaces. The equations representing evolutions of these media are irregular through geometrical manifolds. A unique continuous medium is conceptually simpler than several media with surfaces of singularity. To avoid the surfaces of discontinuity in the theory, we transform the model by considering a continuous medium taking intoaccount more complete internal energies expressed in gradient developments associated with the variables of state. Nevertheless, resulting equations of motion are of an higher order than those of the classical models: they lead to non-linear models associated with more complex integration processes on the mathematical level as well as on the numerical point of view. In fact, such models allow a precise study of singular zones when they have a non negligible physical thickness. This is typically the case for capillarity phenomena in fluids or mixtures of fluids in which interfacial zones are transition layers between phases or layers between fluids and solid walls. Within the framework of mechanics for continuous media, we propose to deal with the functional point of view considering globally the equations of the media as well as the boundary conditions associated with these equations. For this aim, we revisit the d'Alembert-Lagrange principle of virtual works which is able to consider the expressions of the works of forces applied to a continuous medium as a linear functional value on a space of test functions in the form of virtual displacements. At the end, we analyze examples corresponding to capillary fluids. This analysis brings us to numerical or asymptotic methods avoiding the difficulties due to singularities in simpler -but with singularities- models.Comment: 17 page

Electrodeposited metal-organic framework films as self-assembled hierarchically superstructured supports for stable omniphobic surface coatings

Superhierarchically rough films are rapidly synthesised on metal substrates via electrochemically triggered self-assembly of meso/macroporous-structured metal-organic framework (MOF) crystals. These coatings are applied to immobilise a functional oil with low surface energy to provide stable coatings repellent to a wide range of hydrophobic as well as hydrophilic fluids. Such omniphobic surfaces are highly interesting for several applications such as anti-fouling, anti-icing, and dropwise condensation, and become easily scalable with the presented bottom-up fabrication approach. As investigated by environmental scanning electron microscopy (ESEM), the presented perfluorinated oil-infused Cu-BTC coating constitutes of a flat liquid-covered surface with protruding edges of octahedral superstructured MOF crystals. Water and non-polar diiodomethane droplets form considerably high contact angles and even low-surface-tension fluids, e.g. acetone, form droplets on the infused coating. The repellent properties towards the test fluids do not change upon extended water spraying in contrast to oil-infused porous copper oxide or native copper surfaces. It is discussed in detail, how the presented electrodeposited MOF films grow and provide a proficient surface morphology to stabilise the functional oil film due to hemiwicking

Symmetry Relations in Viscoplastic Drag Laws

The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of non-linear viscoplastic fluids. This follows from Edelen's non-linear generalization of the Onsager relation for the special case of \emph{strongly dissipative} rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction-velocity response given by a dissipation potential. This leads to a non-linear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to non-linear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces

Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions

We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic magnetic fields and non-trivial pressure profiles supported by a discrete set of ideal interfaces with irrational rotational transforms. Numerical solutions are computed using the Stepped Pressure Equilibrium Code, SPEC, and benchmarks and convergence calculations are presented.Comment: Submitted to Plasma Physics and Controlled Fusion for publication with a cluster of papers associated with workshop: Stability and Nonlinear Dynamics of Plasmas, October 31, 2009 Atlanta, GA on occasion of 65th birthday of R.L. Dewar. V2 is revised for referee

Exotic Electrostatics: Unusual Features of Electrostatic Interactions between Macroions

We present an overview of our understanding of electrostatic interactions between charged macromolecular surfaces mediated by mobile counter- and coions. The dichotomy between the weak and the strong coupling regimes is described in detail and the way they engender repulsive and attractive interactions between nominally equally charged macroions. We also introduce the concept of dressed counterions in the case of many-component Coulomb fluids that are partially weakly and partially strongly coupled to local electrostatic fields leading to non-monotonic interactions between equally charged macroions. The effect of quenched surface charge disorder on the counterion-mediated electrostatic interactions is analyzed within the same conceptual framework and shown to lead to unexpected and extraordinary electrostatic interactions between randomly charged surfaces with equal mean surface charge densities or even between effectively neutral macroion surfaces. As a result, these recent developments challenge some cherished notions of pop culture.Comment: 18 pages, 5 figure

Imbibition dynamics of nano-particulate ink-jet drops on micro-porous media

Ink-jet printing of nano-metallic colloidal fluids on to porous media such as coated papers has become a viable method to produce conductive tracks for low-cost, disposable printed electronic devices. However, the formation of well-defined and functional tracks on an absorbing surface is controlled by the drop imbibition dynamics in addition to the well-studied post-impact drop spreading behavior. This study represents the first investigation of the realtime imbibition of ink-jet deposited nano-Cu colloid drops on to coated paper substrates. In addition, the same ink was deposited on to a non-porous polymer surface as a control substrate. By using high-speed video imaging to capture the deposition of ink-jet drops, the time-scales of drop spreading and imbibition were quantified and compared with model predictions. The influences of the coating pore size on the bulk absorption rate and nano-Cu particle distribution have also been studied

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