Interface motion when characteristics

Discussion. We can now propose a coarse description of the paraffinic medium in a lamellar lyotropic mesophase (potassium laurate-water). Fast translational diffusion, with D 10"6 at 90 °C, occurs while the chain conformation changes. The characteristic times of the chain deformations are distributed up to 3.10"6 sec at 90 °C. Presence of the soap-water interface and of neighboring molecules limits the number of conformations accessible to the chains. These findings confirm the concept of the paraffinic medium as an anisotropic liquid. One must also compare the frequencies of the slowest deformation mode (106 Hz) and of the local diffusive jump (109 Hz). When one molecule wants to slip by the side of another, the way has to be free. If the swinging motions of the molecules, or their slowest deformation modes, were uncorrelated, the molecules would have to wait about 10"6 sec between two diffusive jumps. The rapid diffusion could then be understood if the slow motions were collective motions in the lamellae. In this respect, the slow motions could depend on the macroscopic structure (lamellar or cylindrical, for example)... 

Dynamic fluorescence anisotropy is based on rotational reorientation of the excited dipole of a probe molecule, and its correlation time(s) should depend on local environments around the molecule. For a dye molecule in an isotropic medium, three-dimensional rotational reorientation of the excited dipole takes place freely [10]. At a water/oil interface, on the other hand, the out-of-plane motion of a probe molecule should be frozen when the dye is adsorbed on a sharp water/oil interface (i.e., two-dimensional in respect to the molecular size of a probe), while such a motion will be allowed for a relatively thick water/oil interface (i.e., three-dimensional) [11,12]. Thus, by observing rotational freedom of a dye molecule (i.e., excited dipole), one can discuss the thickness of a water/oil interface the correlation time(s) provides information about the chemi-cal/physical characteristics of the interface, including the dynamical behavioiu of the interfacial structure. Dynamic fluorescence anisotropy measurements are thus expected... 

Capillary Ripples Surface or interfacial waves caused by perturbations of an interface. When the perturbations are caused by mechanical means (e.g., barrier motion), the transverse waves are known as capillary ripples or Laplace waves, and the longitudinal waves are known as Marangoni waves. The characteristics of these waves depend on the surface tension and the surface elasticity. This property forms the basis for the capillary wave method of determining surface or interfacial tension. 

Thermal conductivity at the nanoscale may significantly deviate from the bulk material value from various reasons, of classical and quantum origin [1], First, size effects are influential if the structure dimension is comparable (or smaller) to the phonon characteristic length. This may result in a ballistic motion and the failure of the Fourier s law, even when phonons are treated as particles. Moreover, if the phases of the phonon waves are fixed, for example when interfaces in the structure are flat, wave effects sustain, leading to phonon interference and diffraction effects. 

In summary, when the ridge slides, the friction force increases with its size I because all the viscous dissipation is concentrated at the S/L interface. The ridge slows down as time progresses, and the law R a describing the rate of growth of the hole is characteristic of a sliding mode of motion. 

Two-dimensional motion can be rationally treated in the familiar lubrication approximation , assuming the characteristic scale in the vertical direction (normal to the solid surface) to be much smaller than that in the horizontal (parallel) direction. When the interface is weakly inclined and curved, the density is weakly dependent on the coordinate x directed along the solid surface. The velocities v,u corresponding to weak disequilibrium of the phase field considered above will be consistently scaled if one assumes 9- = 0(1), dx = 0 VS), u = 0(<5 / ), v = O(S ). It is further necessary for consistent scaling of the hydrodynamic equations that the constant part of the chemical potential p, associated with interfacial curvature, disjoining potential, and external forces and weakly dependent on x, be of 0((5), while the dynamic part varying in the vertical direction and responsible for motion across isoclensity levels, be of O(J ). We can assume therefore that p H- V is independent of z. 

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