Surfaces instabilities

In pressure-swirl atomization, the complex atomization process may be conveniently subdivided into two main stages, as suggested by Lefebvre.12661 In the first stage, surface instabilities are generated as a result of the combined effects of hydrodynamic and aerodynamic forces. In the second stage, surface protuberances are... 

Detailed electronic energy-band calculations have revealed the existence of appropriate surface states near the Fermi energy, indicative of an electronically driven surface instability. Angle-resolved photoemission studies, however, showed that the Fermi surface is very curved and the nesting is far from perfect. Recently Wang and Weber have calculated the surface phonon dispersion curve of the unreconstructed clean W(100) surface based on the first principles energy-band calculations of Mattheis and Hamann. ... 

In general, when the system is subject to stirring by mechanical means or by density or temperature variations during absorption, Ri is difficult to calculate from fundamental principles, and each system has to be considered separately. Among the complicating factors is spontaneous surface instability which may reduce Ri by as much as five times and, before discussing the relation of Ri to the external hydrodynamics, we shall outline the conditions under which spontaneous surface turbulence may occur during mass transfer. 

A third type of surface disturbance is like that envisioned by Bous-sinesq (B6). Fluttering surface instabilities of a very local nature may be observed. A small area of the drop surface can dilate and recede in a periodic fashion much like that observed on the front of large air bubbles rising through liquids. Interference from other types of oscillations quickly compel a change in frequency and location of these surface instabilities. 

In Fig. 7, we display Sc versus c. The gel surface is unstable in the region 8 <8C against the surface disturbances, because they decrease the free energy. Surprisingly, even in the isotropic case <5=1, the surface instability occurs at negative... 

Very interestingly, a similar surface instability was predicted by Grinfeld on uniaxially compressed solids in contact with their melt [94]. The theory has been revived by Nozieres in a general context [95] and has been applied to quantum solids [96]. The theories are limited to linear stability analysis at present. 

The stability of flow in open channels has been investigated theoretically from a more macroscopic or hydraulic point of view by several workers (Cl7, D9, DIO, Dll, 14, J4, K16, V2). Most of these stability criteria are expressed in the form of a numerical value for the critical Froude number. Unfortunately, most of these treatments refer to flow in channels of very small slope, and, under these circumstances, surface instability usually commences in the turbulent regime. Hence, the results, which are based mainly on the Ch<5zy or Manning coefficient for turbulent flow, are not directly applicable in the case of thin film flow on steep surfaces, where the instability of laminar flow is usually in question. The values of the critical Froude numbers vary from 0.58 to 2.2, depending on the resistance coefficient used. Dressier and Pohle (Dll) have used a general resistance coefficient, and Benjamin (B5) showed that the results of such analyses are not basically incompatible with those of the more exact investigations based on the differential rather than the integral ( hydraulic ) equations of motion. The hydraulic treatment of the stability of laminar flow by Ishihara et al. (12) has been mentioned already. 

In addition, patterns created by surface instabilities can be used to pattern polymer films with a lateral resolution down to 100 nm [7]. Here, I summarize various possible approaches that show how instabilities that may take place during the manufacture of thin films can be harnessed to replicate surface patterns in a controlled fashion. Two different approaches are reviewed, together with possible applications (a) patterns that are formed by the demixing of a multi-component blend and (b) pattern formation by capillary instabilities. 

The theoretical framework, within which the existence of surface instabilities created by capillary waves can be predicted is the linear stability analysis [23, 24]. This model assumes a spectrum of capillary waves with wave vectors q and time constant r (Fig. 1.8a). 

FIGURE 1.8. (a) Schematic representation of the device used to study capillary surface instabilities. A polymer-air bilayer of thicknesses /ip and /ia, respectively, is formed by two planar silicon wafer held at a separation d by spacers. A capillary instability with wavelength k = 27t/q is observed upon applying a voltage U or a temperature difference AT. (b) Dispersion relation (prediction of Eq. (1.6)). While all modes are damped (r < 0) in the absence of an interfacial pressure pei, the application of an interfacial force gradient leads to the amplification of a range of k-values, with /.m the maximally amplified mode. 

Electric fields A patterned top electrode generates a laterally inhomogeneous electric field [30], The replication of the electrode pattern is due to two effects. Since the time constant for the amplification of the surface instability scales with the fourth power of the plate spacing (Eq. (1.8)), the film becomes unstable first at locations where the electrode topography protrudes downward towards the polymer film. In a secondary process, the... 

A second approach makes use of capillary surface instabilities that occur in the presence of a destabilizing surface force. Since such a instability mirrors the details of the destabilizing force field, it can be employed as a sensitive tool to study and explore forces that act at the... 

R. P. G. Rutgers and M. R. Mackley, The Effect of Channel Geometry and Wall Boundary Conditions on the Formation of Extrusion Surface Instabilities for LLDPE, J. Non-Newt. Fluid Mech., 98, 185 (2001). 

Surface Instability and the Internal Decay of Metals Stress-Corrosion Cracking... 

Surface Instability and Internal Decay of Metals Hydrogen Embrittlement... 

It should be noted that glass, which is often used as a substrate in inkjet printing experiments, is an insulator. Similarly, although thermo-capillary surface instabilities have been seen to develop in the spreading and evaporation of volatile drops on conductive substrates (silicon and brass), no surface oscillations were observed for those droplets placed on glass. ... 

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