Meniscus receding

However, desorption follows the meniscus receding mechanism, and vaporization occurs only in pores connected to the vapor phase. As a result, pore C remains fiUed until pore B is emptied, and the sequence of evaporation is in fact B and C together followed by A. This mechanism can lead to very steep Type H2 hysteresis loops. Indeed, a common diagnostic feature of many hysteresis loops is that the steep region leading to the lower closure point occurs at nearly the same relative pressure. It is almost independent of the porous adsorbent, but mainly dependent on the adsorptive. In case of nitrogen this happens at a relative pressure p/po 0.4 [21]. 

The process indicated by line KN on Fig. 3.2(b) starts with a lower meniscns level in the hibe (point K) heating causes liquid to vaporize, and the meniscus recedes to the bottom of tire hibe (point N). On Fig. 3.3 the process traces a path from (J, K) to N. With further heating the path continues along the line of constant molar volnme V -... 

Figure 7 reveals that the free surface position and shape are quite sensitive to the competition between viscous normal stress and the curvature-dependent capillary pressure. As the ratio of the former to the latter, i.e. Ca 5 pv/o, rises, the meniscus recedes toward the nip and curves more sharply. The sample results in Figures 5-10 are for cases in which the effects of gravity and liquid inertia are negligible. The computer program used here is constructed to include these effects as it solves equations (6) - (8) comprehensive case studies and complete portraits of velocity, pressure, stress, and vorticity fields will be reported elsewhere (14). 

Because it is the pressure gradient that causes differential strain and cracking, it is evident that fast evaporation and low permeability are detrimental. Cracks usually appear at the end of the constant rate period when the shrinkage stops and the meniscus recedes into the pore. At this point, the radius of the meniscus is minimal and depends on the pore radius tp and contact angle 6 ... 

Atchley and Prosperetti noted that this description is incomplete. Indeed, as the meniscus recedes, not only does the Laplace pressure fall, but so does the partial pressure of the gas within the pocket. If the internal pressure decreases more rapidly than the Laplace pressure, the interface stops progressing to the crevice mouth. On the contrary, the growth will be unstable if the partial pressure in the gas pocket decreases less rapidly than the Laplace pressure, and the growth is "explosive". 

Let us consider a wet gel in which some liquid suddenly evaporates. As outlined earlier, the liquid in the pores stretches to cover the dry region and a tension develops in the liquid. The tension is balanced by compressive stresses on the solid phase of the gel. Since the network is compliant, the compressive forces cause it to contract into the liquid, and the liquid surface remains at the exterior surface of the gel (Fig. 5.18b). In a polymeric gel, it does not take much force to submerge the solid phase, so that initially the capillary tension of the liquid is low and the radius of the meniscus is large. As drying proceeds, the network becomes stiffer because new bonds are forming (e.g., by condensation reactions) and the porosity is decreasing. The meniscus also deepens (i.e., the radius decreases), and the tension in the liquid increases [Eq. (5.39)]. When the radius of the meniscus becomes equal to the pore radius in the gel, the liquid exerts the maximum possible stress [Eq. (5.41)]. This point marks the end of the CRP beyond this the tension in the liquid cannot overcome the further stiffening of the network. The liquid meniscus recedes into the pores, and this marks the start of the FRP (Fig. 5.18c). Thus, the characteristic features of the CRP are... 

The volume shrinkage of the gel during drying induces an increase of its stiffness. At a given time, the solid network is no more compliant and the meniscus recedes in the pores. At this moment, the stress is maximum since the curvature radius corresponds to that of the shrunk pore (assumed cylindrical). Associated to evaporation, the liquid flows from the core of e gel to the surface. This flow is hindered by the solid arms of the gel. A gel is badly permeable because the size of the pores lies mainly within the range 0.2-10 nm indicating that a gel is a mesoporous material. According to the Darcy s law, the liquid flow, /, is related to permeability, D, by the relation ... 

An unsaturated body contains both gas and liquid in its pores. Gels become unsaturated near the end of drying, when shrinkage stops and the meniscus recedes into the pores. The liquid is said to be in the pendular state when... 

Perhaps the best discussions of the experimental aspects of the capillary rise method are still those given by Richards and Carver [20] and Harkins and Brown [21]. For the most accurate work, it is necessary that the liquid wet the wall of the capillary so that there be no uncertainty as to the contact angle. Because of its transparency and because it is wet by most liquids, a glass capillary is most commonly used. The glass must be very clean, and even so it is wise to use a receding meniscus. The capillary must be accurately vertical, of accurately known and uniform radius, and should not deviate from circularity in cross section by more than a few percent. 

Yabu, H. and Shimomura, M. (2005) Preparation of self-organized mesoscale polymer patterns on a solid substrate continuous pattern formation from a receding meniscus. Adv. Func. Mater,... 

FIG. 6.10 Contact angle hysteresis (a) weighing a meniscus in a Wilhelmy plate experiment versus the depth of immersion of the plate (b) both the advancing and receding contact angles are equal (c) 6a > dr. 

Figure 5. Schemdtic of growing needle-shoped, crystdls in copillary tube. One needle outpdces the others ond is first to cross the meniscus bounddry which recedes in opposite direction owing to evop-ordtion...

It should be noted that on the receding cycle the wet plate surface has previously interacted with water molecules for a different period of time depending on the immersion depth of the plate. Therefore, the bottom deeper immersed portions of the plate interact with the water molecules for a longer period than the shallow immersed portions closer to the top of the plate. This causes small but continuous changes in the meniscus shape even after the three-phase contact line starts to move in the advancing and receding processes. 

Figure 26.16 Effect of plasma treatment on dynamic hysteresis, which is the difference in the d5mamic first cycle advancing line and the receding line, (AF/L)d (mN/m) = (F/L)D,a,i — (F/T)D,r,i IS a direct result of the changing shape of the meniscus during a wetting cycle.

Surface tension—the capillary suction created by a receding liquid meniscus can be extremely high. 

Surface Tension These effects are very common and worth a few more comments. Capillary suction created by a receding liquid meniscus can create very high pressures for collapse. The quantitative... 

Furthermore when drying proceeds, the distance between the receding meniscus and the gel surface increases. According to Darcy s law this implies an... 

While determining the liquid height, it is better to measure with a falling (or receding) meniscus, so that the liquid level is initially raised above its equilibrium value by a slight suction above the capillary tube, and then left to equilibrate. On the other hand, two-armed capillary tubes, connected with a cross tube above the liquid level, are also used to ensure that the pressure in both arms of the glass apparatus is the same. An interesting modification of the capillary rise method is to measure the pressure, AP, that is required to force the meniscus down until it is on the same level as the plane surface of liquid outside the capillary tube. This method is useful to compare the surface tension of water and its dilute solutions. 

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