Capillary imbibition

Let us consider one more physical phenomenon, which can influence upon PT sensitivity and efficiency. There is a process of liquid s penetration inside a capillary, physical nature of that is not obvious up to present time. Let us consider one-side-closed conical capillary immersed in a liquid. If a liquid wets capillary wall, it flows towards cannel s top due to capillary pressure pc. This process is very fast and capillary imbibition stage is going on until the liquid fills the channel up to the depth l , which corresponds the equality pcm = (Pc + Pa), where pa - atmospheric pressure and pcm - the pressure of compressed air blocked in the channel. 

There are two approaches to explain physical mechanism of the phenomenon. The first model is based on the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

The hygroscopicity of a drug and pharmaceutical substances is a potential parameter to be considered in tablet formulation. The moisture uptake rate is quite variable depending on the type of drug and excipients as well as the environmental conditions. So, a concise definition of hygroscopicity is not possible. Powders can absorb moisture by both capillary imbibition and swelling. The instantaneous water absorption prosperties of pharmaceutical excipients correlate with total surface area while the total absorption capacity correlates with powder porosity [22],... 

Three mechanisms can be considered for the migration of an ink vehicle such as oil capillary imbibition, spreading, and bulk diffusion. It takes about 100 ms for a fresh print to travel from one nip of the printing press to the next in a commercial multicolor printing press. In this time the oil vehicle is sufficiently drained from the ink that set off does not occur in the second colour unit. The driving force for capillary imbibition is surface tension ... 

If the oil vehicle has a surface tension of 30 mN/m and a viscosity of 0.5 Pa.s and if the paper is uncompressed newsprint the void fraction, tortuosity and mean effective capillary radius will be approximately 0.6, 5 and 2 pm, respectively. Equation (8) then predicts that in 100 ms capillary imbibition could withdraw 9 pm of vehicle from the surface. 

This is more than adequate to set news inks at commercial levels of ink application. Capillary imbibition is thus the predominant ink setting mechanism since spreading and bulk diffusion are much slower processes. However, two complications arise in this simplistic model. Implicit in the model is the assumption that the capillaries are connected to an inexhaustible supply of liquid. This is not the case, and it would be more reasonable to assume that as the larger capillaries drain the oil from the surface of the paper differential capillary pressures in the interconnected network drain the vehicle into progressively smaller capillaries emptying the larger ones (see Figure 1). These differential pressures can be expressed as ... 

Capillary effects are encountered in many areas of interface and colloid science, with its importance relative to other processes (e.g., fluid dynamics) depending on the exact situation. For example, when two spherical drops of a liquid in an emulsion make contact and coalesce to form a larger drop (Fig. 6.2a), the extent and duration of flow due to the capillary phenomenon is limited and fluid dynamics is of little practical importance. When there is an extensive amount of flow, on the other hand, such as in capillary imbibition, wicking processes, or capillary displacement (Fig. 6.2b) fluid dynamics may become important. 

We should not forget ecological applications. A duck s feathers are not wet-table by water, but if we spill surface active molecules, such as are found in washing-up liquid, into our rivers, the surface tension of the water is reduced. Young s equation shows that cos e is increased and may attain the value unity. At this point, capillary imbibition occurs and water will penetrate duck feathers. Ducks catch cold and die. 

Figure 10.3 (a) Schematic of the geometry used to simulate capillary imbibition of a wetting fluid in smooth and rough capillaries (b) snapshot of MD simulation showing fluid imbibition and the formation ofthln precursor films ahead of the capillary front, (with permissions from ref. )... 

The capillary imbibition of a metal halide melt inside BNNTs, molybdenum disulfide (M0S2) nanotubes, and CNTs was simulated using From the simulation of initial insertion of the Pb ... 

A. N. Enyashin, R. Kreizman, and G. Seifert, Capillary imbibition of PbI2 melt by inoi anic and carbon nanotubes, / Phys. Chem. C, 113,13664 (2009). 

The capillary imbibition behavior of packed bed columns with a range of model hydrophobic soil types prepared by using two routes to hydrophobicity is shown (1) trimethylchlorosilane and (2) model hydrophobic SOM consisting of either individual or equimolar mixture of palmitic acid (PA) and stigmasterol (ST) at quantities equivalent to that in natural nonwetting soils.With increasing proportion of hydrophobic particulate content in the packed bed column, the... 

Figures Capillary imbibition in model hydrophobic particulate beds using (A) silanized quartz (inset, water contact angle from initial slope method) and (B) SOM components (water contact angle from initial slope is provided in brackets).

The capillary imbibition characteristics of single SOM components, PA- or ST-coated particulate beds (Figure 3(B)), were similar to that of the partially hydrophobic model hydrophobic compositions (Figure 3(A)), and the contact... 

Figure 5 The influence of the surfactant concentration on the capillary Imbibition In 100% silane-coated hydrophobic quartz particulate beds (surfactant concentration, corresponding surface tension, y, and contact angle, 9, evaluated from Initial slope are provided In brackets).

Starov, V.M., Zhdanov, S.A.,Velarde, M.G., 2004. Capillary imbibition of surfactant solutions in porous media and thin capillaries partial wetting case. J. CoUoid Interface Sci. 273, 589. 

SPONTANEOUS CAPILLARY IMBIBITION OF SURFACTANT SOLUTIONS INTO HYDROPHOBIC CAPILLARIES... 

In the case of partial wetting, the capillary imbibition in the horizontal direction proceeds according to the following dependency ... 

A characteristic time scale of the equilibration of the surfactant concentration in a cross section of the capillary, x RVD = 0.1 sec, if we use for estimations f 10 pm and D 10 cm /sec. A characteristic time scale of the spontaneous capillary imbibition or rise into hydrophobic capillaries is much bigger than 0.1 sec (see Figure 5.10 and Figure 5.11). This means that the surfactant concentration is constant in any cross section of the capillary and depends only on the position, X (Figure 5.9), that is, C = C(t, jc). We also assume that the adsorption equilibrium in any cross section is also reached. Taking this into account, the equation can be rewritten after both sides are divided by R I2 as ... 

Equation 5.38 shows that the case under consideration is governed by a completely different mechanism as compared with the case of the horizontal imbibition (where remains constant over time). In the case of the spontaneous capillary rise in hydrophobic capillaries, CJt) does not remain constant but must increase as the capillary rise progresses. The comparison of Figure 5.11 and Figure 5.10 shows that the time scale of the spontaneous capillary rise is around 100 times bigger than the corresponding time scale in the case of the capillary imbibition into horizontal capillaries. 

In the following text the problem of the spontaneous capillary rise of surfactant solntions in hydrophobic capillaries is considered in the case when concentration at the capillary inlet is below CMC. In this case, the transport of surfactant molecules is described by Equation 5.15 and Eqnation 5.16, and boundary conditions (5.17) throngh (5.19). The snbstantial difference from the spontaneons capillary imbibition is that now the relation between l(t) and the concentration on the moving meniscus, C, is given by relation (5.37), which shows that is an unknown function of time. Using these equations and boundary conditions, we show in the following text that l(t) dependency on time can be calculated, and it is proportional to the sqnaie root of time at the initial stage of the capillary rise (see Appendix 1 for details). 

The kinetics of the capillary imbibition of aqueous surfactant solutions into hydrophobic capillaries has been investigated earlier in Section 5.2. It has been shown that the rate of imbibition is controlled by the adsorption of the surfactant molecules in front of the moving meniscus on the bare hydrophobic surface of the capillary. This process results in a partial hydrophilization of the surface of the capillary in front of the moving meniscus and provides the possibility for the aqueous surfactant solution to penetrate into the initially hydrophobic capillary. Therefore, no surfactant molecules on the meniscus, no imbibition. In the following text, the imbibition of surfactant solutions into the porous substrates, which are partially wetted by water, is considered. It is shown that the situation in this case is considerably different from the case of hydrophobic porous media. 

This qualitative conclusion is justified in the following text using the theoretical consideration of the capillary imbibition of aqueous surfactant solutions into cylindrical capillaries whose walls are partially wetted by water. 

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