Geschwindigkeit der Verdünnung flüssiger Filme

Colloid and Polymer Science - Die Verdünnung eines mit löslichen Tensiden stabilisierten freien flüssigen Filmes wurde mit hydrodynamischen Methoden unter Berücksichtigung der...     

EFFECT OF THICKNESS NON-HOMOGENEITY ON THE KINETIC BEHAVIOUR OF MICROSCOPIC FOAM FILM

The effect of thickness non-homogeneity on the drainage of microscopic horizontal foam films was studied experimentally and theoretically. Quasi-static and asymmetrical distribution of thickness irregularities over the film surface was established in the experiment. This type of dimpling was modelled theoretically and employed to derive a new equation for the film thinning. It differs from the theoretical expressions known from the literature and is in better agreement with the experimentally determined functional dependence of thinning rate on film size.     

Contribution of the surface dipole moment and the contact potential-induced disjoining pressure to the stress balance at a three-phase contact

The contact between three insulators results in a set up of contact potentials related to the adsorbed dipole moment at each surface. The produced electric field applies force (disjoining pressure) on each interface. This disjoining pressure is a long-ranged force (1/distance²) which is proportional to the difference between the dielectric permittivities of the phases on the two sides of the interface and, for small angles, to the square of the contact angle. The contact potential leads to a logarithmic perturbation of the profile of the three-phase contact zone.     

On the mechanical equilibrium in anisotropic heterogeneous systems

The conditions for equilibrium of liquid surfaces dividing two anisotropic bulk phases have been deduced by means of variational analysis.It has been shown that the presence of an anisotropic tensor in the bulk requires a gradient of surface tension in a state of equilibrium.     

Hydrophilic interactions between organic and water molecules as models for monolayers at the gas/water interface

Model clusters of surfactant prototypes with small number of water molecules are calculated at different levels of theory. All approaches used yield correct trends in the variation of the dipole moment upon tail elongation or polar headgroup variation. Models including one, two, or more water molecules are optimized. The most stable structures are those with maximum number of atoms involved in hydrogen bonding. The normal components of the dipole moment prove to be less sensitive to the nature (aliphatic or aromatic) of the hydrophobic tail, in accord with findings from the phenomenological models. Values of the dipole moment approaching the experimental estimates required inclusion of sufficient aqueous environment (>20 water molecules per hydrophilic head) and of lateral intersurfactant interactions into the model.     

Potential theory in the problems of interfraction at small gap widths. A solid sphere and a droplet

A solid sphere approaches a spherical droplet at small gap widths. The radii of the particles are identical. Potential theory is applied and the problem of interaction brought to the solution of an integrodifferential equation for radial velocity at the droplet/ thin layer interface. Asymptotic formulae are reported for interface velocity and drag force for small and large viscosity ratios. The results are compared with the solutions for a solid sphere and flat tangentially mobile interface. Thus, two major effects may be distinguished: opening of the gap and curving of the streamlines inside the droplets. The latter is shown to cause a relative increase in the drag force.     

Rupture of wetting films caused by nanobubbles

It is now widely accepted that nanometer sized bubbles, attached at a hydrophobic silica surface, can cause rupture of aqueous wetting films due to the so-called nucleation mechanism. But the knowledge of the existence of such nanobubbles does not give an answer to how the subprocesses of this rupture mechanism operate. The aim of this paper is to describe the steps of the rupture process in detail: (1) During drainage of the wetting film, the apex of the largest nanobubble comes to a distance from the wetting film surface, where surface forces are acting. (2) An aqueous "foam film" in nanoscale size is formed between the bubble and the wetting film surface; in this foam film different Derjaguin-Landau-Verwey-Overbeek (DLVO) forces are acting than in the surrounding wetting film. In the investigated system, hydrophobized silica/water/air, all DLVO forces in the wetting film are repulsive, whereas in the foam film the van der Waals force becomes attractive. (3) The surface forces over and around the apex of the nanobubble lead to a deformation of the film surfaces, which causes an additional capillary pressure in the foam film. An analysis of the pressure balance in the system shows that this additional capillary pressure can destabilize the foam film and leads to rupture of the foam film. (4) If the newly formed hole in the wetting film has a sufficient diameter, the whole wetting film is destabilized and the solid becomes dewetted. Experimental data of rupture thickness and lifetime of wetting films of pure electrolyte and surfactant solutions show that the stabilization of the foam film by surfactants has a crucial effect on the stability of the wetting film.     

Hydrodynamical interaction of two emulsion droplets at small separations

The fluid's motion inside emulsion droplets is analysed when they mutually approach along their common axis and a thin liquid film is formed outside. A qualitative flow pattern is presented. Two particular cases are treated — a creeping motion and a boundary layer flow inside the droplets. Estimates are made for the tangential velocity at the droplet/film interface, for the drag force and for the energy dissipated in the respective phases.     

Effective zones of hydrodynamical interaction of fluid particles at small separations

A system of two approaching fluid particles at small gap widths is investigated. The concept of an effective zone of interaction is used to analyse the stationary Navier-Stokes equations in the respective phases. Particular cases are distinguished in which it is possible to make significant simplifications in the governing differential equations. A validity criterion for the lubrication theory equations in the thin layer is proposed, which accounts for the tangential mobility of the interfaces.     

Gevrey Hypoellipticity for Maximally Hypoelliptic Fourth Order Partial Differential Operators

Local C∞ and (sharp) Gevrey hypoellipticity are proved for maximally hypoelliptic fourth order partial differential operators of the form P = D|c|<4 aa(x)Xa in R" where the independent real vector fields Xj,j<n - l, satisfy the Hörmander condition that at most k brackets of the Xj spans the tangent space at each point.