Stability hydrodynamic

The subject of hydrodynamic stability theory is concerned with the response of a fluid system to random disturbances. The word hydrodynamic is used in two ways here. First, we may be concerned with a stationary system in which flow is the result of an instability. An example is a stationary layer of fluid that is heated from below. When the rate of heating reaches a critical point, there is a spontaneous transition in which the layer begins to undergo a steady convection motion. The role of hydrodynamic stability theory for this type of problem is to predict the conditions when this transition occurs. The second class of problems is concerned with the possible transition of one flow to a second, more complicated flow, caused by perturbations to the initial flow field. In the case of pressure-driven flow between two plane boundaries (Chap. 3), experimental observation shows that there is a critical flow rate beyond which the steady laminar flow that we studied in Chap. 3 undergoes a transition that ultimately leads to a turbulent velocity field. Hydrodynamic stability theory is then concerned with determining the critical conditions for this transition. 

The designation linear to describe the theoretical study of the fate of small initial disturbances is due to the fact that the dynamics of such small disturbances can be described by means of a linear approximation of the Navier-Stokes, continuity, and other transport equations. Because the governing equations are linear, analytic theory is often possible but this requires that the unperturbed state or flow, whose stability we wish to study, be known analytically. Furthermore, this base solution must be quite simple for even the linear approximation of the equations to be analytically tractable. In practice this reduces significantly the number of problems in which complete analytic results are possible and also explains why hydrodynamic stability theory has been particularly successful in analyzing problems 

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Bubble growth will be hmited by the containing vessel and the bubble hydrodynamic stability. Bubbles in group-B systems can grow to several meters in diameter. Bubbles in group-A materials with high fines may reach a maximum stable bubble size of only several cm. 

SBWR power density is a low 42 kW/liter. BWRs are typically -50 kWAiter and about half the power density of PWRs. Low power density means more thermal and hydrodynamic stability margins. Vessel embrittlement, which has not been a problem for BWRs, is even less concern for the SBWR. 

P. Drazin and W. Reid, Hydrodynamic Stability, Cambridge University Press, London, 1981. 

Deviation variables are analogous to perturbation variables used in chemical kinetics or in fluid mechanics (linear hydrodynamic stability). We can consider deviation variable as a measure of how far it is from steady state. 

The method of hydrodynamic stability involves bringing two solutions of different concentrations into contact in a capillary tube, forming a stable and measurable concentration gradient. The diffusion coefficient is a function of the... 

Hydrodynamic stability (free boundary method) Diffusion coefficient determination 5... 

M Southard, L Dias, K Himmelstein, V Stella. Experimental determinations of diffusion coefficients in dilute aqueous solution using the method of hydrodynamic stability. Pharm Res 8 1489-1491, 1991. 

This principle is very general, relating neither to the linearity nor to the symmetry of the transport laws. On the other hand, it is difficult to attribute a physical meaning to dxP- The authors later attempted to derive a local potential from this property, and they applied this concept to the study of the chemical and hydrodynamical stability (e.g., the Benard convection). The results of this approach were published in Glansdorff and Prigogine s book Thermodynamic Theory of Structure, Stability and Fluctuations (LS.IO, 10a), published in 1971. 

TNC. 10. P. Glansdorff and I. Prigogine, Generalized entropy production and hydrodynamic stability, Phys.Lett. 7, 243-244 (1963). 

J. B. Joshi, N. S. Deshpande, M. Dinkar, and D. V. Phanikumar, Hydrodynamic Stability of Multiphase Reactors... 

Detonation, Nonlinear Theory of Unstable One-Dimensional. J.J. Erpenbeck describes in PhysFluids 10(2), 274-89(1969) CA 66, 8180-R(1967) a method for calcg the behavior of 1-dimensional detonations whose steady solns are hydrodynamic ally unstable. This method is based on a perturbation technique that treats the nonlinear terms in the hydro-dynamic equations as perturbations to the linear equations of hydrodynamic-stability theory. Detailed calcns are presented for several ideal-gas unimol-reaction cases for which the predicted oscillations agree reasonably well with those obtd by numerical integration of the hydrodynamic equations, as reported by W. Fickett W.W. Wood, PhysFluids 9(5), 903-16(1966) CA 65,... 

Figure 29.14 demonshates a schematic of connection of HSGD-containing unit to a hemodialysis machine. Here hydrodynamic stability of the column with uncoated dehganding sorbent is achieved via local citrate injection followed by removal of excessive citrate, and concentration of Ca is restored in the connected dialyser. 

The hydrodynamic stability of such films is controlled by the capillary pressure, film... 

Rosensweig, R. E. (1979). Fluidization Hydrodynamic Stabilization with a Magnetic Field. Science, 204,57. 

Chemical considerations lead to two effects that influence the stability of reactive extrusion - the gel effect and the ceiling temperature. Gel effects increase the conversion by an autocatalytic behavior. If the gel effect occurs completely in the screws it stabilizes the process, but if it occurs near or in the die it may have a destabilizing effect. The occurrence of a ceiling temperature slows down the reaction and so has a direct, negative influence on hydrodynamic stability. 

Jackson. R., The Mechanics of Fluidized Beds, Trans. Instn. Chem. Engrs. 41, 13 (1963). Jackson, R., Hydrodynamic Stability of Fluid-Particle Systems, Chap. 2 in Fluidization, 2nd Ed. (Davidson, J. F., Clift, R., and Harrison, D., eds). Academic Press, New York, 1985. 

Theoretical analysis of sheeting in the drainage of thin liquid films has been conducted in [359]. Sheeting dynamics and hole formation (i.e. black spot formation) was described by non-linear hydrodynamic stability analysis based on the equilibrium oscillatory structural component of disjoining pressure. The effect of stepwise thinning, accompanied by formation of holes , was described qualitatively. It is rather arguable whether the term holes for a black spot is appropriate since in 1980 holes in NBF were described as lack of molecules. The use the same term for two different formations is at least confusing. Besides, to have a hole in a CBF is almost as to have a hole in the sea water . 

Individual structural elements of the foam, such as films and borders, can be under hydrostatic equilibrium and can correspond to a true metastable state. Therefore, when there is no diffusion expansion of bubbles in a monodisperse foam, its state can be regarded as metastable in the whole disperse system. Krotov [5-7] has performed a detailed analysis of the real hydrodynamic stability of polyhedral foam by solving two problems determination of... 

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