Capillary constant penetration into

Fig. 4 illustrates the time-dependence of the length of top s water column in conical capillary of the dimensions R = 15 pm and lo =310 pm at temperature T = 22°C. Experimental data for the top s column are approximated by the formula (11). The value of A is selected under the requirement to ensure optimum correlation between experimental and theoretical data. It gives Ae =3,810 J. One can see that there is satisfactory correlation between experimental and theoretical dependencies. Moreover, the value Ae has the same order of magnitude as Hamaker constant Ah. But just Ah describes one of the main components of disjoining pressure IT [13]. It confirms the rightness of our physical arguments, described above, to explain the mechanism of two-side liquid penetration into dead-end capillaries. 

The pressure of mercury is kept constant by maintaining the mercury in the reservoir at a constant level. Somewhat more difficult to guarantee is the use of the same capillary. This implies that when a capillary is broken, or behaves erratically (commonly, as a result of penetration of impurities into the bore), a new calibration curve must be constructed. If the highest accuracy is aimed at, the temperature of the electrolytic cell must also be controlled by using a water-jacket or by immersing the cell in a thermostatted bath. 

Fig. 3 shows the results of spontaneous suction of the solution into the capillary having radius r = 5 pm, and of subsequent displacement of the solution under external pressure drop AP. The suction-displacement cycles are repeated 10 times. The distance of solution penetration, x, was nearly the same and is equal to about 9 cm. Curves 1 and 1 correspond to experiments with pure water, and curves 2 and 2 to the first cycle with EOio solution. In both cases the dependencies of f values on time t are linear, in agreement with Eq. (2), when the latter was integrated over the / values after substitution v = d//dr and assuming = constant ... 

The results obtained lead to the conclusion that three mechanisms of penetration of nonionic surfactant solutions into hydrophobic capillaries are possible. The first takes place at a high concentration of surfactant, Q > Q. Spontaneous imbibition advances at a high rate but is limited to some finite length Iq, which depends on Q, r, and Gi. The second mechanism is realized when Co< Q. The rate of penetration in this case is much lower, being controlled by the reduced concentration, Cm = constant, near the meniscus. At still lower concentration of bulk solution Cq, the diffusion mechanism of penetration takes place in thin capillaries. The rate of penetration is determined here by the surface diffusion of surfactant molecules in advance of the meniscus. 

Tandmor and Gogos [2] devised an equation for the penetration distance into a capillary under constant pressure from the Poisieuille equation and a mass balance ... 

The measured normalized wetting rates for various test liquids (for cellulose fibers Fig. 23) can be transformed into the cosine of the contact angle (cos0) and plotted as a function of the liquid surface tension (Fig. 24). The resulting linear relationship cos 0 = 1 — b(y — jc) was established empirically by Zisman and Fox [120] and found to hold for solid with low surface tensions. The critical surface tension 7c corresponds to the surface tension of the liquid that will just spread over/wet completely the solid. The constant C reflects the capillary geometry of the porous solid and may change in a non-predictable manner during the penetration process of different test liquids. It was concluded from the experiments performed [112] that there is no need to determine the constant C in order to obtain solid-surface tensions, because the position of the maximum in the C-7iv cos 0 vs. 7iv plot, which is expected to... 

The kinetics of wicking from a finite (limited) liquid reservoir (a single drop wicking into a fabric) are more complicated than those of wicking from a liquid pool of essentially constant volume. Wicking of a drop can be divided into two phases of different kinetics [52-55]. At first, the drop spreads on the substrate and penetrates the porous substrate underneath. As long as most of the liquid remains on the outer surface of the substrate, the capillary penetration is kinetically similar to that from an infinite reservoir [56]. During the second phase of the capillary... 

The wicking process is kinetically quite different when capillary penetration is accompanied by diffusion of the liquid into the fibers into a finish on fibers. Sorption within fibers decreases the volume of the liquid flowing in the capillary spaces and reduces the interfiber spaces available for capillary penetration because of swelling of the fibers. As a consequence of these complications, the exponent g in Eq. (23) is no longer constant but depends on the drop volume [53,54]. The area covered by the liquid spreading within the fabric does not correlate with the drop absorbency time. When the drop absorbency time is used to evaluate fabric absorbency, an inadequate drop volume can lead to misleading results if cap-... 

Our approach uses the fact that the Washburn equation is an approximate solution for the liquid imbibition into a vertical capillary (refs. 1,4, 7, 8, 9). The equation of motion for a liquid raising in a vertical capillary with constant radius ris eq. 1, where h is the height of penetration at time t, gthe gravity constant, t the dynamic viscosity, f> the gravimetric density and o the surface tension of the liquid. 

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