Capillary curve

Example The capillary curve for one vertical plate is given by d y dx ... 

If we consider the electric boundary layer to consist of orientated molecules of constant moment perpendicular to the surface, this would give a constant value of 8 and a parabolic electro-capillary curve. Hence the outward force the molecules exert will be inversely proportional to the square of the area they occupy and thus inversely proportional to the fourth power of their distance apart a result in agreement with the known properties of doublets. 

The cr, V, or electro-capillary, curve for dilute sulphuric acid of a strength used by Lippmann is almost exactly parabolic and... 

It thus appears that the surface concentration calculated with the aid of Gibbs equation is equal on the one hand to minus the surface charge found by Lippmann s equation from the slope of the electro-capillary curve and on the other hand to minus the number of grm. equivalents of mercurous ions taken up by an expanding mercury surface or thrown off a contracting one in the course of the N emst ionic transfer. 

Fig. 12.14 Effect of the method of measurement on the value of D/Do for HDPE. Curve 1, frozen extrudates Curve 2, extrudates annealed at 160°C in hot silicon oil Curve 3, photographs of extrudates emerging from capillary Curve 4, photographs of extrudates in hot silicon oil. [Reprinted by permission from J. L. White and J. F. Roman, Extrudate Swell During the Melt Spinning of Fibers-Influence of Rheological Properties and Take-up Force, J. Appl. Polym. Sci., 20, 1005 (1976).]...

Electrocapillary curve — Figure. Electro capillary curves of a mercury electrode in aqueous solutions of different electrolytes (modified from [i] with permission)... 

As shown in the Figure, electro capillary curves are affected by - specific adsorption of ions (here, anions) at the electrode surface. Additionally, they are influenced by the - space charge region of the electrical double layer. Thus, electrocapillary curves as well as capacitance curves provide useful information on the electrical double-layer structure of electrode surfaces. 

Measurement of the electrocapillary curve consists of changing the potential stepwise and determining the pressure required to return the mercury meniscus to the same location in the fine capillary. A plot of this pressure as a function of potential is nothing but the electro-capillary curve, within a constant, as seen from Eq. 53H. The best way to determine the magnitude of this constant is by calibration with a known system. This requires, of course, one accurate determination of y by an independent method. Very careful experiments were performed by Gouy around the turn of the century, and these results are used even now as the primary standard for electrocapillary measurements. 

For polarized Interfaces, capacitances can be readily measured directly with great precision. For mercury, capacitance-applied potential curves constitute the basic information for double layer analyses, outweighing that from electro-capillary curves. 

The section of the surface of a liquid in contact with a solid plate dipping into it vertically is called the capillary curve, and an equation for it can be obtained.1... 

Generally, in liquid air system, the capillary curve resembles the shape given in Fig. 20. Usually, the pressure values are well defined only in interval [s r,l]c[0,l], where is the residual saturation, because in the exsorption... 

The result of such experiments are shown in Fig. 13. At first the rates of evaporation from pure capillary (curve 1) and from those pretreated with CA... 

FIG. 13 Kinetics of evaporation L t) of water from native quartz capillary (curve 1) and from the capillary pretreated with CA solution in ethanol (curve 2) at pjp = 0.48, r = 7.6 pm. 

In the next experiment, CA was deposited on the capillary surface locally. For this purpose, only a part of the capillary was filled with CA solution in ethanol and the boundary was marked on the external capillary surface. Ethanol was then evaporated from the capillary, the empty side of which was previously sealed. Thus, only a part of the capillary surface was pretreated with CA. Next, the capillary was filled with pure water and evaporation was observed from the nontreated part of the capillary. As seen from Fig. 14, the rate of evaporation from the pretreated capillaries (curves 1-3) was equal to that from the control capillary not treated with CA (curve 4), unless the meniscus approached the region covered with CA. At this moment the evaporation rate sharply slowed due to transfer of CA molecules from the capillary surface onto the meniscus. Fig. 14 shows that the evaporation decreases sharply when the distance from the entrance of the capillary to the meniscus was L = z, where z is the coordinate of the boundary of the pretreated part. 

FIG. 14 Kinetics of water evaporation L t) from quartz capillaries, r = 9 pm, at pjp = 0.54 with locally deposited adsorption CA layers (curves 1-3) and from a nontreated capillary (curve 4). The distance z between capillary entrance and the position of deposited CA layer was equal to 0.8 (curve 1), 4.23 (curve 2), and 6,14 mm (curve 3). 

FIGURE 2.9 Generalized representation of an electro-capillary curve. 

The effect of Triton X-100 on the current-voltage curve of the iron (III)-diethylenetriaminepentaacetic acid complex has been explained as follows [226] at low levels of surfactant the mercury is only partly covered by surfactant and the reversible reduction proceeds at the uncovered portions of the undisturbed surface and at the covered areas a penetration-controlled reaction occurs. As the Triton concentration is increased so the penetration-controlled reaction contribution increases. When the coverage is complete only the second wave is observed on the polarogram. The shift in the half-wave potential with increasing surfactant concentration is probably due to increased adsorbed layer thickness and is shown along with the polarograms and electrocapillary capillary curves in the absence and presence of Triton X-100 in Fig. 11.35. 

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