Instability system

Emulsions are thermodynamically instable systems. The work AW which is necessary for dispersion is determined by the inier/uce tension y and the interface magnification of the disperse phase AA ... 

Fig. 5.3. A degenerate state may mean an instable system "superpolarizfjble ), which adapts itself very easily to an external (even very small) perturbation. The figure shows how the hydrogen atom in a degenerate state changes when a proton approaches it. (a) the atom in a non-perturbed stationary state 2px (b) The proton interacts with the hydrt en atom, but the 2px orbital does not reflect this. It is true that the orbital 2px describes the total energy vecy well (because the interaction is weak), but it describes the electron charge distribution in the hydrogen atom interacting with the proton very badly, (c) Contrary to this, the function = (2s) + + 2py), satisfies the Schrddinger equation fo" the unperturbed hydrt en atom as well as the function...

SPl INSTABLE SYSTEM, energy decrease with respect to the... 

This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

A similar Marongoni instability can be provoked in a single component system by a temperature gradient [31] as illustrated in Fig. XIII-2. The wavelength of the instability is approximately... 

Prigogine I and Lefever R 1968 Symmetry breaking instabilities in dissipative systems J. Chem. Phys. 48 1695-700... 

In addition to flame fronts, which have been extensively studied experimentally, front instabilities have been investigated for the isothennal cubic autocatalytic iodate arsenous acid system [70] as well as for polymerization... 

W, g potential functions, k 1, has been discussed in various papers (see, for example, [6, 11, 9, 16, 3]). It has been pointed out that, for step-sizes /j > e = 1/ /k, the midpoint method can become unstable due to resonances [9, 16], i.e., for specific values of k. However, generic instabilities arise if the step-size k is chosen such that is not small [3, 6, 18], For systems with a rotational symmetry this has been shown rigorously in [6j. This effect is generic for highly oscillatory Hamiltonian systems, as argued for in [3] in terms of decoupling transformations and proved for a linear time varying system without symmetry. 

An instability of the impulse MTS method for At slightly less than half the period of a normal mode is confirmed by an analytical study of a linear model problem [7]. For another analysis, see [2]. A special case of this model problem, which gives a more transparent description of the phenomenon, is as follows Consider a two-degree-of-freedom system with Hamiltonian p + 5P2 + + 4( 2 This models a system of two springs con-... 

The first system is characterized by a partial miscibility of the liquid phases, the second one is instable with incongruent melting points at -54... 

The reverse of the association or formation reactions would represent the dissociation or instability constant for the systems, i.e., —log Kj, = log TsTjjjstji,. 

To achieve sufficient vapor pressure for El and Cl, a nonvolatile liquid will have to be heated strongly, but this heating may lead to its thermal degradation. If thermal instability is a problem, then inlet/ionization systems need to be considered, since these do not require prevolatilization of the sample before mass spectrometric analysis. This problem has led to the development of inlet/ionization systems that can operate at atmospheric pressure and ambient temperatures. Successive developments have led to the introduction of techniques such as fast-atom bombardment (FAB), fast-ion bombardment (FIB), dynamic FAB, thermospray, plasmaspray, electrospray, and APCI. Only the last two techniques are in common use. Further aspects of liquids in their role as solvents for samples are considered below. 

There are a number of sources of instability in premixed combustion systems (23,24). 

System instabilities involve interactions between flows in different parts of a reacting system. Although these instabilities can cause turbulence, they caimot be analy2ed on their own and the whole system should be considered as a unit (11,25). 

Phase Diagram (Zenz and Othmer) Zenz and Othmer (op. cit.) have graphically represented (Fig. 17-2) all gas-solid svstems in which the gas is flowing counter to gravity as a function o pressure drop per unit of height versus velocity. Note that line OAB in Fig. 17-2 is the pressure-drop versus gas-velocity curve for a packed bed and BD the cui ve for a fluid bed. Zenz indicates an instability between D and H because with no sohds flow all the particles will be entrained from the bed however, if sohds are added to replace those entrained, system JJ prevails. The area DHJJ will be discussed further. 

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