Hysteresis, entrapment, and contact angle

Cumulative volume curves generated by intruding mercury into porous samples are not followed as the pressure is lowered and mercury extrudes out of the pores. In all cases the depressurization curve lies above the pressurization curve and the hysteresis loop does not close even when the pressure is returned to zero, indicating that some mercury is entrapped in the pores. Usually after the sample has been subjected to a first pressurization-depressurization cycle, no additional entrapment occurs during subsequent cycles. In some cases, however, a third or even fourth cycle is required before entrapment ceases. 

The pressure-volume (P-fO work associated with an initial intrusion-extrusion cycle can be calculated from the areas above curves A and C to the maximum intruded volume, indicated by the horizontal dotted line in Fig. 12.1. (The work associated with any graphical area can be calculated with reference to equations (11.8) and (11.9).) This P-V work, I dlTj, can be expressed as 

Even in the absence of mercury entrapment, second or subsequent intrusion-extrusion cycles, curves B and C of Fig. 12.1, continue to show hysteresis with the P-V work, dW2, through a cycle given by 

As illustrated in Fig. 12.1 the P-V work through a second cycle is always less than that through a first cycle since the areas between curves B and C is less than that between A and C. Then, 

The difference between the cyclic integrals jdW and f d 1 2 is the work associated with entrapment of mercury and can be evaluated from the area between curves A and B. 

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Equation (12.19) predicts that changes in U, the pore potential, will effect the quantity of entrapped mercury and/or the difference in contact angle between intrusion and extrusion. Hence, changes in the pore potential will alter the size of the hysteresis loop. 

It is evident from Fig. 12.3 that, as the copper sulfate concentration in the sample is increased, the hysteresis increases, that is the difference between P and increases while, at the same time, the extrusion contact angle decreases. Similarly, the work of entrapment, IF, increases as the salt concentration is raised, as evidenced by the quantities of mercury entrapped in the sample. It can be seen in Fig. 12.3 that the intrusion curves for both treated and untreated samples are virtually identical, indicating that impregnation does not significantly alter the radius of the pore opening. However, in all cases the volume of mercury intruded decreased with increasing salt concentration, an indication that precipi-... 

Three types of experiments were performed at room temperature (21 1 C). They included mobilization of entrapped ganglia contained within the cubic array as in Figure 1, measurement of contact angle hysteresis behavior using both flat plates and spheres, and a determination of surface roughness for spheres and plates. In all studies, air formed the entrapped or bubble phase and one of two liquids, a mineral oil (Oil) or ethylene glycol (ETC), with properties as listed in Table 1, were used as continuous phases. 

Discussion of modelling is confined to network A. It was found that a decrease In contact angle will generate hysteresis, but not entrapment. In any system, and has not been considered further. Mechanism I did not predict... 

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