Path dependent mixing

Path dependent mixing and variable, vapour flash volumes. 

Path Dependent Mixing of Boiling Cryogenic Liquids... 

Since LPGs are mixtures, they suffer from all the evaporation instability and path-dependent mixing behaviours met with LNG. Thus, provision must be made for stratification and its removal by adequate mixing, and the possible occurrence of rollover and vapour explosions. More importantly, there must be adequate emergency venting to release associated BOR spikes and thereby avoid over-stressing the concrete structure of the tank, which may not be designed to withstand the pressures associated with bod-off instabdities. 

Ceramic membrane is the nanoporous membrane which has the comparatively higher permeability and lower separation fector. And in the case of mixed gases, separation mechanism is mainly concerned with the permeate velocity. The velocity properties of gas flow in nanoporous membranes depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collision. The Knudsen number Kn Xydp is characteristic parameter defining different permeate mechanisms. The value of the mean free path depends on the length of the gas molecule and the characteristic pore diameter. The diffusion of inert and adsorbable gases through porous membrane is concerned with the contributions of gas phase diffusion and sur u e diffusion. 

The mixing process is, of course, irreversible, and is accompanied by an irreversible increase in entropy. Mixing with evaporation is particularly difficult to model because, in addition to the thermal mixing and release of thermal overfill, there is the compositional heat of mixing with irreversible entropy production which is sig-nificantiy path dependent. A considerable volume of vapour is produced by the usual positive heat of compositional mixing and by thermal contact between colder and hotter components (no homogeneous nucleate boiling has been observed) before the final equilibrium state of the mixture is achieved. 

However, because the mixing is path-dependent, the volume of vapour produced is a variable path-dependent phenomenon. This path dependence is clearly demonstrated when liquid propane and liquid butane are mixed and the vapour produced has to be recondensed by limited available refrigeration. Briefly, when colder liquid (propane rich) is added to hotter liquid (butane rich), the vapour generated is found experimentally to be twice that produced by the alternative when hot is added to cold [5],... 

The mixing experiments at Southampton demonstrated conclusively that vapour flash volumes are path-dependent, and may be expected to be much larger than those predicted from heats of mixing. It follows that all cryogenic liquid mixing can... 

When a rollover occurs, the mixing is irreversible and therefore path-dependent. The spontaneous penetrative mixing is from bottom to top, and the vapour flash volume can therefore be expected to be larger than that predicted from the heat of mixing and thermal overfill of the two layers. 

In the pure concerted reaction there is no need to invoke the cationic or anionic intermediates in describing the transition state, but it now becomes evident that some deviation from this idealized route may be possible, and then we need a way to comment upon and to measure the extent to which the cationic or anionic character is mixed in in the transition state. This is now widely accomplished with the aid of energy surfaces of the type shown schematically in Fig. 5-19. Depending on the nature of the surface, the reaction path may follow a route far from the diagonal representing the pure concerted reaction, and the primary goal is to identify the location of the transition state on this surface. 

D flows and time-dependent 2D flows, and mixes the fluid by continuously stretching different volumes of the fluid and folding them into one another. In a qualitative sense, the path taken by a given fluid element in the flow depends in a sensitive way on its encounters with a series of weak secondary flows or eddies, present even at low Re in the comers of channels, which transport the element across the flow [167],... 

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