Body-force instabilities

Acceleration of a flame sheet produces effects of the same type as those of body forces. In a noninertial coordinate system that moves with the flame (or in which the flame moves at a constant velocity), an effective body force appears as a consequence of flame acceleration. This may be seen from equation (89) by bringing Rd f/dx to the right-hand side of the equation the effective nondimensional body force per unit volume becomes R(Fj[ — d f/dx ). Thus a flame acceleration in the direction of its motion (a positive rate of increase of — df/dx) is equivalent to a body force directed from the fresh mixture to the burnt gas. A body-force instability is therefore associated with flame acceleration. By the preceding reasoning, the wavelength... 

There are three basic distinct types of phenomena that may be responsible for intrinsic instabilities of premixed flames with one-step chemistry body-force effects, hydrodynamic effects and diffusive-thermal effects. Cellular flames—flames that spontaneously take on a nonplanar shape—often have structures affected most strongly by diffusive-thermal... 

For decelerating flames, flames propagating downward, or burner-stabilized flames with the flow upward, the body-force effects are stabilizing. Because of other mechanisms of instability, to be discussed later, the ease with which stable laminar deflagrations are observed in the laboratory may be attributable largely to the stabilizing influence of buoyancy. Normal... 

As described above, instability of the interface between the electrolyte and molten metal is a significant problem that is one root cause of the energy inefficiency of Hall cells. Expressed simply, the interface is deformed by the electromagnetic body forces arising from the interaction between currents in the cell and the magnetic field. The currents are themselves affected by the interface position because it determines the distance between the top surface of the aluminum and the bottom of the anode. There is therefore the possibility that interface deformation leads to further interface deformation. Other mechanisms for generating waves at the interface may be significant, for example, the Kelvin-Helmholtz... 

In their studies of interface instability, most of the investigators listed above have employed a Fourier analysis of the coupling between the fluid motion and the electromagnetic body force. Davidson [81] and, in simpler form, Davidson and Lindsay [82] have pursued an alternative approach whereby a global energy balance... 

Gradients in surface tension can also lead to an instability, with subsequent cellular-type flows. These unstable flows are similar in character to the unstable convection that results when a density gradient is parallel to, but opposite, a body force, such as gravity. In this case the fluid is in unstable equilibrium with the heavier fluid on top of the lighter fluid. When a. critical... 

In the preceding section, we have examined a variety of steady thermocapillary and diffusocapillary flows. Not all such flows are stable and in fact surface tension variations at an interface can be sufficient to cause an instability. We consider here the cellular patterns that arise with liquid layers where one boundary is a free surface along which there is a variation in surface tension. It is well known that an unstable buoyancy driven cellular convective motion can result when a density gradient is parallel to but opposite in direction to a body force, such as gravity. An example of this type of instability was discussed in Section 5.5 in connection with density gradient centrifugation. 

The studies on adhesion are mostly concerned on predictions and measurements of adhesion forces, but this section is written from a different standpoint. The author intends to present a dynamic analysis of adhesion which has been recently published [7], with the emphasis on the mechanism of energy dissipation. When two solids are brought into contact, or inversely separated apart by applied forces, the process will never go smoothly enough—the surfaces will always jump into and out of contact, no matter how slowly the forces are applied. We will show later that this is originated from the inherent mechanical instability of the system in which two solid bodies of certain stiffness interact through a distance dependent on potential energy. 

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