Convection hydrodynamic stability

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. 

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. 

One might have hoped that, following the modifications to the stability analyses for liquids with free surfaces, quantitative comparisons between experiment and theory could have been made, but such is not the case. Further refinement in both theory and experiment is still required. Nevertheless it is indeed encouraging that all of the experimentally observed qualitative effects regarding convective stability appear to be in agreement with the predictions of hydrodynamic stability theory. 

Accordingly, a hypothesis was formulated, which seeks the theoretical rationale of appearance of the specific flow structures inside the liquid layer. It is known, that under certain circumstances, the surface tension variations may lead to the flow instability and to the induction of convection cells [e.g., 5, 6]. Our preliminary theoretical analysis of the hydrodynamic stability of the system [7] indicated that it is possible, that for the Reynolds numbers exceeding the critical value, convection cells inside the hypophase can be formed. This should lead to the significant increase of the mass transfer rate. 

Methods from heat transfer. The modeling of Benard convection cells in hydrodynamic stability is relevant to our purposes, since it leads to a modal equation identical to Equation 12-9 (Yih, 1969). It turns out interestingly that Equation 12-9 itself can be solved by separation of variables once more. For example, the choice... 

HYDRODYNAMIC AND HYDROMAGNETIC STABILITY. S. Chandrasekhar. Lucid examination of the Rayleigh-Benard problem clear coverage of the theory of instabilities causing convection. 704pp. 5b x 8b. 64071-X Pa. 12.95... 

The stability of open flames attached to flame holders (burners) is also complicated by the hydrodynamics associated with the divergent gas stream from the burner nozzle, heat losses to the burner, and convection of the surrounding air. The stability of such flames relative to their burners and the related phenomena of flash back and blow-off are outside the scope of this book. 

---