Surface dilation wave

The model depends on the assumption that a nerve impulse is a propagating disturbance in the form of surface dilation wave note that... 

In the particular case of waves originated in overstability or (linear) oscillatory instability, I have shown how two types of surface waves, transverse and longitudinal (or, better, capillary-gravity and dilational, respectively) can be excited by the Marangoni effect and how they are related to each other thus leading to their combined (symbiotic-like) survival and to resonance effects. I have also given comments about the excitation of internal waves in the layer heated above and hence stably stratified and how in turn these waves are, in particular, related to the surface dilational waves. 

Droplet formation occurs primarily through the surface tension and viscosity dominated breakup of these liquid threads due to symmetric (or dilational) waves as described by Rayleigh (6) for inviscid liquids and by Weber (J) for viscous fluids. Figure 3 shows the double pulsed image of the droplet formation process for No. 2 and SRC-II fuel sprays under identical atomizer conditions. These two photographs illustrate typical differences seen between these two fuels. 

Figure 4.27. Absolute value of the surface dilational modulus obtained by the wave technique (closed symbols) and from oscillating bubbles (open symbols). Surfactant, tridecyldimethyl phosphine oxide A, A c = 2 xlQ-S M O. c = 5 x lO M. Drawn curves fit to [4.5.431. Temperature 22°C. (Redrawn from Wantke et al. (loc. cit.).)...

The earliest available hydrodynamic theory of water wave damping by elastic surface films was published by Lamb (1895). He refers to Reynolds (1880) and the experiments by Aitken (see Scott 1979, Giles and Forrester 1970), but prior publication of the detailed theory is not indicated. All but the outline of the theory was omitted from later editions of this book, and it is likely that Lamb assumed that damping was greatest with an inextensible film, and that intermediate elasticities, therefore, had less effect (cited after Scott 1979). This conclusion was shown by Dorrestein (1951) to be incorrect. The paper by Levich (1940) was the first to present in detail the linearised hydrodynamics of waves on a water surface with surface dilational elasticity. The only cases considered in detail concern insoluble films, and represent the clean and incompressible-film-covered surface. A detailed treatment of the hydrodynamic theory of surface waves, including the effect of an elastic surface film, was published by Levich in 1962. In addition, the damping caused by dissolved surface-active material was considered. Further laboratory experiments performed until 1978 were briefly reviewed by Scott (1979). 

Erik s research focused on the interfacial properties of the ocean surface, and, in particular, how the chemistry of the air-sea interface affects the dynamics of short waves, nearsurface flows and interfacial fluxes of heat, mass and momentum. During his short career, he contributed to over 30 scientific publications in this area. His doctoral research, carried out under the tutelage of well-known colloid and surface chemist, Sydney Ross, concerned the propagating characteristics of surface waves in the presence of adsorbed films. That work was eventually published as a series of seminal papers on capillary ripples, and his theoretical treatment of ripple propagation and a corrected dispersion relation for surface waves in the presence of a surface dilational modulus (with J. Adin Mann, Jr.) still stand as the definitive word on the subject. 

Lucassen J and Hansen RS (1966) Damping of waves on monolayer-covered surfaces. I. Systems with negligible surface dilational viscosity. J Colloid Interface Sci 22 32-44... 

Beside the capillary wave techniques, the oscillating bubble method belongs to the first experiments for measuring the surface dilational elasticity (Lunkenheimer Kretzschmar 1975, Wantke et al. 1980, 1993). For soluble adsorption layers it allows of the exchange of matter at a harmonically deformed bubble surface to be determined. 

Fig. 6.10 Comparison of surface dilation elasticities determined from two different wave damping experiments with Triton X-100 solutions at 150 Hz plane waves ( ), cylindrical waves ( ) according to Jiang et al. (1992)...

Lucassen-Reynders and Lucassen (Lucassen 1968, Lucassen-Reynders and Lucassen 1969) have derived the dispersion relation for a liquid surface in the presence of a surface film. They showed that periodic disturbance of such a film-covered surface results in a surface tension that varies from point to point on the surface because of the fluctuations in surface concentration. Consequently, in addition to a transverse stress being developed, a finite tangential surface stress is also present. The solution to this dispersion equation has two roots, one of which corresponds to the capillary waves (transverse motion) and one of which corresponds to longitudinal or dilational waves derived from the transverse stress. The dispersion relation (D( o)) obtained for a film at the interface between two media is... 

Potential methods of measurement for dilatation parameters are the damping of transverse and longitudinal surface waves and the damping of vibrating bubbles. For theory and measuring techniques see Wiistneck and Kretzschmar [47]. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

Keywords Monolayers Surface light scattering Capillary waves Dispersion equation Dilational elastic modulus Dilational loss modulus Scaling exponent... 

Fig. 4 General solution for the dispersion equation on water at 25 °C. The damping coefficient a vs. the real capillary wave frequency o> , for isopleths of constant dynamic dilation elasticity ed (solid radial curves), and dilational viscosity k (dashed circular curves). The plot was generated for a reference subphase at k = 32431 m 1, ad = 71.97 mN m-1, /i = 0mNsm 1, p = 997.0kgm 3, jj = 0.894mPas and g = 9.80ms 2. The limits correspond to I = Pure Liquid Limit, II = Maximum Velocity Limit for a Purely Elastic Surface Film, III = Maximum Damping Coefficient for the same, IV = Minimum Velocity Limit, V = Surface Film with an Infinite Lateral Modulus and VI = Maximum Damping Coefficient for a Perfectly Viscous Surface Film...

Fig. 5 Wave motion at maximum damping and infinite dilational elasticity. A Motion at the maximum damping coefficient where optimal resonant mode coupling implies that a surface fluid element moves at a 45° angle to the direction of wave propagation. B Wave Motion at infinite dilational elasticity, where the same element is only able to move in the transverse direction...

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