Hydrodynamic bistability

Remark. Instability and bistability are defined as properties of the macroscopic equation. The effect of the fluctuations is merely to make the system decide to go to one or the other macroscopically stable point. Similarly the Taylor instability and the Benard cells are consequences of the macroscopic hydrodynamic equations. ) Fluctuations merely make the choice between different, equally possible macrostates, and, in these examples, determine the location of the vortices or of the cells in space. (In practice they are often overruled by extraneous influences, such as the presence of a boundary.) Statements that fluctuations shift or destroy the bistability are obscure, because on the mesoscopic level there is no sharp separation between stable and unstable systems. Some authors call a mesostate (i.e., a probability distribution P) bistable when P has two maxima, however flat. This does not correspond to any observable fact, however, unless the maxima are well-separated peaks, which can each be related to separate macrostates, as in (1.1). 

The applicability of the reaction-rate formula in the intermediate-friction regime to the interpretation of conformational changes of bi-naphtyl in solution has been discussed.47 The intramolecular motion is governed by a bistable potential depending on a single variable, which is identified with the dihedral angle between the naphthalene moieties in binaphtyl. The influence of hydrodynamic interactions and coupling with the other coordinates of the molecules also are evoked. 

So far as the mechanism of bistability is concerned in non-reacting system including membrane process, there is general agreement that it is related to the interplay of the hydrodynamics flux and electrostatic flux, which act in opposite directions [32]. 

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