Reciprocating flow behavior

There is a reciprocal relation between morphology and flow behavior. Plochocki [1978, 1983] defined the particular rheological composition , (PRC), most frequently observed in polyolefin blends. At PRC the q = T)(( )) function reaches a local maximum or minimum. The existence of the maximum is related to a change of the dispersed phase, e.g., from spherical to fibrillar or from dispersed to co-continuous, while that of the minimum is related to a reciprocal change and/or to variation of the specific volume. 

Fluidity is the reciprocal of the viscosity. A melt with a large fluidity will flow readily, whereas a melt with a large viscosity has a large resistance to flow. While fluidity is often used in dealing with ordinary liquids, virtually all literature dealing with glass forming melts discusses flow behavior in terms of the viscosity. 

The Weissenberg number compares the elastic forces to the viscous effects. It is usually used in steady flows. One can have a flow with a small Wi number and a large De number, and vice versa. Sometimes the characteristic time of the flow in the deflnition of the Deborah number has been taken to be the reciprocal of a characteristic shear rate of the flow in these cases, the Deborah number and the Weissenberg number have the same definition. Pipkin s diagram (see Fig. 3.9 in Tanner 2000) classifies shearing flow behavior in terms of De and Wi, and provides a useful guide for the choice of constitutive equations. 

Flow Behavior of Reciprocating Positive Displacement Machines... 

Many users consider rotaiy compressors, such as the Rootes -type blower, as turbomachines because their behavior in terms of the rotor dynamics is very close to centrifugal and axial flow machineiy. Unhke the reciprocating machines, the rotary machines do not have a veiy high vibration problem but, like the reciprocating machines, they are positive displacement machines. 

An overview of the superplastic behavior of aluminum alloys to demonstrate the grain-size effect is depicted in Fig. 1, in which the quantitative relation between the logarithm of the optimum strain rate for superplastic flow and the grain size (plotted as the logarithm of reciprocal grain size) is clearly shown [4]. The slope of the curve in Fig. 1 is noted to be about 3. 

Until 1984, all of the stopped-flow and temperature-jump kinetic studies of alpha cyclodextrin inclusion-complex formation were explainable in terms of a single-step, binding mechanism. According to this mechanism, the observed rate constant, kobs, (for stopped-flow) and the reciprocal relaxation time, 1/t, (for temperature-jump) should show a linear dependence on the edpha cyclodextrin concentration. Sano and coworkers, however, in the case of the iodide-alpha cyclodextrin interaction, and Hersey and Robinson,in the case of various azo dye-alpha cyclodextrin interactions (see Fig. 7), found that certain guest species exhibit a limiting value of kobs and 1/t at high concentrations of alpha cyclodextrin. This behavior can most simply be explained in terms of a mechanism of the type,... 

Another operational limit in the CFB system involves gas suppliers. Three types of gas suppliers, i.e., a reciprocating compressor, a blower with throttle valve, and a compressor, are commonly used in the CFB system. For blower operation, as the gas flow rate decreases, the pressure head of the blower increases. For compressor operation, the pressure head of the compressor can be maintained constant with variable gas flow rates. The interactive behavior between a CFB system and a blower can be illustrated in Fig. 10.9, where dashed curves refer to the blower characteristics and solid curves refer to the riser pressure drop. At point A, the pressure drop across the riser matches the pressure head provided by a blower thus, a stable operation can be established. Since the pressure drop across the riser in fast fluidization increases with a decrease in the gas flow rate at a given solids circulation rate, a reduction in the gas flow rate causes the pressure drop to move upward on the curve in the figure to point B with an increase in the pressure drop of Spr. In the case shown in Fig. 10.9(a), with the same reduction in the gas flow rate, i.e., SQ, the increase in the pressure drop, Spr, from point A to point B is greater than that which can be provided by... 

Chauveteau and co-workers 24, 48) examined the flow of PEO and HPAA through the extensional flow produced in severe constrictions. They concluded that a coil-stretch transition was responsible for the dilatant behavior observed, and that the critical shear rate required was of the order of 10 times the reciprocal of the Rouse relaxation time. Perhaps the most extensive studies have been those of Haas and co-workers (25, 26, 49). They have explored the critical dilatant behavior on flow through porous media and pursued the hypothesis that the phenomenon is primarily due to a coil-stretch transition beyond a critical deformation rate. They attempted a semiquantitative description based upon the dependence of the lowest order relaxation time of the random coil upon polymer type, molecular weight, solvent quality, and ionic environment. 

Before discussing the influence of combining powders of various morphologies, it is helpful to consider the general behavior of monodispersed particulate pastes. The ease with which a paste can be extruded is determined by the factors described in the Introduction, but for any paste system, characteristic curves can be drawn of the parameters oq, Tq, a, m, n) against the binder content. It is often convenient to plot the inverse or reciprocal of the parameter, as this yields plots which clearly show the distinctive features of paste flow. 

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