Superimposed hysteresis loops

Low-pressure hysteresis is not confined to Type I isotherms, however, and is frequently superimposed on the conventional hysteresis loop of the Type IV isotherm. In the region below the shoulder of the hysteresis loop the desorption branch runs parallel to the adsorption curve, as in Fig. 4.26, and in Fig. 4.2S(fi) and (d). It is usually found that the low-pressure hysteresis does not appear unless the desorption run commences from a relative pressure which is above some threshold value. In the study of butane adsorbed on powdered graphite referred to in Fig. 3.23, for example, the isotherm was reversible so long as the relative pressure was confined to the branch below the shoulder F. 

Thixotropy and Other Time Effects. In addition to the nonideal behavior described, many fluids exhibit time-dependent effects. Some fluids increase in viscosity (rheopexy) or decrease in viscosity (thixotropy) with time when sheared at a constant shear rate. These effects can occur in fluids with or without yield values. Rheopexy is a rare phenomenon, but thixotropic fluids are common. Examples of thixotropic materials are starch pastes, gelatin, mayoimaise, drilling muds, and latex paints. The thixotropic effect is shown in Figure 5, where the curves are for a specimen exposed first to increasing and then to decreasing shear rates. Because of the decrease in viscosity with time as weU as shear rate, the up-and-down flow curves do not superimpose. Instead, they form a hysteresis loop, often called a thixotropic loop. Because flow curves for thixotropic or rheopectic Hquids depend on the shear history of the sample, different curves for the same material can be obtained, depending on the experimental procedure. 

Table 16-4 shows the IUPAC classification of pores by size. Micropores are small enough that a molecule is attracted to both of the opposing walls forming the pore. The potential energy functions for these walls superimpose to create a deep well, and strong adsorption results. Hysteresis is generally not observed. (However, water vapor adsorbed in the micropores of activated carbon shows a large hysteresis loop, and the desorption branch is sometimes used with the Kelvin equation to determine the pore size distribution.) Capillary condensation occurs in mesopores and a hysteresis loop is typically found. Macropores form important paths for molecules to diffuse into a par-... 

The thixotropic fluids have an apparent viscosity, dependent not only on the shear rate but also on the shear time. Therefore the flow curve of thixotropic fluids, opposite to the all types of aforementioned fluids, which curves for increasing and decreasing shear rate were superimposed (giving one curve), form a hysteresis loop (Fig. 5.5). As results from these curves the apparent viscosity of tixotropic fluids is decreasing with time (Fig. 5. 6), because of the progressive structure destruction. 

Concept Check 20.6 It is possible, by various means (e.g., alteration of microstructure and impurity additions), to control the ease with which domain walls move as the magnetic field is changed for ferromagnetic and ferrimagnetic materials. Sketch a schematic B-versus-H hysteresis loop for a ferromagnetic material, and superimpose on this plot the loop alterations that would occur if domain boundary movement were hindered. 

The isothermal hysteresis loops for Sn-Ag eutectic solder at 25°C and 80°C and the thermo-mechanical fatigue cycle between 25°C and 80°C are superimposed on each other in Fig. 24, which represents the first complete cycle for 1 % mechanical strain. The TMF heating-load cycle initially follows the 25 °C curve but then drops smoothly to the 80 °C curve then, during the cooling-unloading cycle, it initially follows the 80 °C curve but eventually returns to the 25 °C cycle curve. Both Sn-Zn and Sn-Pb eutectic solders exhibit similar behavior [7,15]. 

Hysteresis can be minimized by superimposing a high-amplitude, high-frequency signal on the controller output. The process would not respond to it, but the sticking element would. There is sufficient noise in some measurements to create this effect. But the best solution is to close the loop around the hysteresis element, alone, with a proportional controller-this amounts to installing a positioner on the valve. lore will be said about positioners in Chap. 6. 

---