Instability traveling

Fig 18 Influence of burning rate and composition of finite-amplitude traveling wave instability solid line stable regime, dotted line unstable regime for 5- x 40-inch motor... 

The third mechanism for nucleation is the fragmentation of active cavitation bubbles [16]. A shape unstable bubble is fragmented into several daughter bubbles which are new nuclei for cavitation bubbles. Shape instability of a bubble is mostly induced by an asymmetric acoustic environment such as the presence of a neighboring bubble, solid object, liquid surface, or a traveling ultrasound, or an asymmetric liquid container etc. [25-27] Under some condition, a bubble jets many tiny bubbles which are new nuclei [6, 28]. This mechanism is important after acoustic cavitation is fully started. 

G.H. Evans and R. Greif. A Study of Traveling Wave Instabilities in a Horizontal Channel Flow with Applications to Chemical Vapor Deposition. Int. J. Heat Mass Transf, 32(5) 895-911,1989. 

In a simplified treatment for longer waves, Benjamin derived an amplification factor a, defined as the amplification experienced by the wave of maximum instability in traveling a distance of 10 cm. If neutral stability exists, a = 1, and if a > 1, wavy flow can be expected. For a vertical wall,... 

The MASC (for "multicomponent adsorption simulation calculations") computer program, which identifies the regions of stability and instability within the sorption fronts, the distance which the front must travel through the bed for the potentially stable regions to attain their ultimate steady-state... 

The use of the electron microscope for studying colloidal systems is limited by the fact that electrons can only travel unhindered in high vacuum, so that any system having a significant vapour pressure must be thoroughly dried before it can be observed. Such pretreatment may result in a misrepresentation of the sample under consideration. Instability of the sample to electron beams could also result in misrepresentation. 

In stud dng stability of flows, it is convenient to pose the problem either as a temporal or as a spatial instability problem. While it is numerically expedient to take a temporal approach, many practical flows are known to follow spatial route. For example in lab experiments for external wall-bounded flows, it is noted that the disturbances grow in space as they travel downstream. This was established unambiguously through the experiments of Schubauer Skramstad (1947) for flat plate boundary layer and is an excellent example of spatial instability problems. However, there are many flows where the instability grows both in space and time. These type of problems to identify whether the flow suffers temporal and/ or spatial instability arise in linear stability analysis. Flow instability studied following descriptions of two independent routes, is an artificial way of treating general instability problems. 

The phenomenon of unstable combustion results from a self-amplifying interaction between combustion processes and the. acoustic oscillations of the gas within the rocket motor. The unexpected appearance of combustion instability in any rocket generally terminates its mission thru motor case rupture from overpressure, disruption of guidance systems by severe vibration, or thrust malalignment. Both axial mode and transverse mode instabilities are observed (Ref 45). In the case of the transverse mode the characteristic wave time is usually that required to travel radially around the proplnt cavity whereas the characteristic time for the axial mode is the time for the wave to travel from end to end in the combustion chamber. Double-base proplnts predominantly are prone to transverse wave instabilities and infrequently to those in the axial mode, while composite proplnts appear to go unstable mostly in the axial mode. In the case of transverse instability chamber pressures have been known o double whereas in axial mode instabilities artificially induced by pulsing the chamber pressure at lOOOpsi, the pressure excursion may reach 300—400psi. A review of recent theoretical combustion modeling for combustion instability has been made by Price (Ref 47)... 

Linde, H. et al.. Interfacial wave motions due to Marangoni instability. I. Traveling periodic wave trains in square and annular containers, J. Colloid Interface Sci., 188, 16-26, 1997. 

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