Piston theory

Fig. 2.1 Schematic drawing of the so-called piston theory showing the partitioning into DOPC liposomes of (A) propranolol in high-pH medium, (B) diclofenac in low-pH medium, (C) propranolol in low-pH medium, and (D) diclofenac in high-pH medium. (Reprinted from Fig. 3 of ref. 43 with permission from Kluwer Academic/Plenum Publishers.)...

At first glance the results seem to contradict the piston theory of Avdeef (see Chapter 2). However, closer inspection of the equations reveals large differences in the intercepts, indicating large differences in the basic lipophilicity or, as the authors called it, the liposome-philicity of the different species. This, then, indicates differences in the depth of partitioning into the bilayer. 

TLCD are restricted to frequencies, say below 0.5 Hz in practical applications. Only by the invention ofthe passive gas spring this serious limitation is b5q)assed and TLCGD frequencies say up to 5Hz are possible in practical implementations. For proper application of the piston theory, the frequency is actually limited by the (relative) maximum fluid speed, u = which must stay... 

Consequently almost doubling maximum liquid strokes the parametric excitation remains insignificant, while the control becomes more robust, Figure 8b. With a simulated maximum relative fluid speed of 1.7 m/s < 12 m/s, the liquid surface is expected to stay intact, and no problems with respect to the piston theory are expected. 

Set the initial Vz (i) to 1 and turn off the updating. This gives piston flow. The calculated result for avgC for a first-order reaction is 0.3677 versus 0.3679 in theory. The result for a second-order reaction is 0.4998 versus 0.5 in theory. 

Sadi Carnot in the 1820s used caloric theory in developing theories for the heat engine to explain the engine already developed by Watt. Heat engines perform mechanical work by expanding and contracting a piston at two different temperatures. 

The thermodynamical proof of the Stefan-Boltzmann law rests on the existence of radiation pressure. We imagine an enclosure shut off by a movable piston with a reflecting surface. The radiation field exerts a pressure on the piston its magnitude is a function of u, the energy density of the radiation in the enclosure. In fact, both Maxwell s theory and the quantum (corpuscular) theory of light give the formula... 

The above statements of the nature of the photoacoustic effect are drawn primarily from the conclusions of the theory developed by Rosencwaig and Gersho (R-G) (9), based on a onedimensional thermal piston model. Since this is the starting point for extending the theory of photoacoustic spectroscopy (PAS) to include photoacoustic circular dichroism (PACD), a brief survey of the salient factors and important parameters of that treatment follows. 

Dual-head reciprocating pumps offer lower solvent pulsation at the expense of mechanical complexity. Here two pistons fill and pump 180° out of phase and in theory provide pulseless flow. Dual-head pumps are more expensive and have either two check valves (series heads) or four check valves (parallel heads). Both designs generally provide for some type of pressure or flow feedback control to further compensate for minor flow variations during switching from one head to the next. A detailed discussion of the mechanics of these and other pumping systems is provided elsewhere (13). 

The above referenced experiments (adiabatic) occur in flow geometries much more complicated than the simple (isothermal) planar Riemann (shock structure) problems discussed above. Furthermore, the interesting results on shock splitting given in [27], [41-44] all involved piston and not Riemann initial value problems. Hence a direct comparison with the local shock structure theory given here may be difficult. Nonetheless for completeness we record some obvious consistencies and discrepancies between the experimental results and traveling wave theory. 

In 1960, Gatlin and Slobod (130), by utilizing concepts developed by Wilson et al. (131), proposed their "piston-like" displacement theory which explained that the oil and water flowing simultaneously in front of the miscible alcohol piston would adjust their saturations to form stabilized banks whose saturations could be calculated from the relative permeability and viscosity of the fluids. They carried out a number of experiments which initially appeared to agree quite well with this straightforward theory. 

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