Local contact angle

Thus D(r) is given by the slope of the V versus P plot. The same distribution function can be calculated from an analysis of vapor adsorption data showing hysteresis due to capillary condensation (see Section XVII-16). Joyner and co-woikers [38] found that the two methods gave very similar results in the case of charcoal, as illustrated in Fig. XVI-2. See Refs. 36 and 39 for more recent such comparisons. There can be some question as to what the local contact angle is [31,40] an error here would shift the distribution curve. 

P., Dynamics of wetting local contact angles, J. Fluid. Mecdi. 212 (1990) 55-63. 

The central element responsible for this sequence is the dewetted fluid collected the rim, characterised mainly by its width w. Thus, w may be considered as the cmcial parameter determining the final 3D morphology. The volume V of this rim is exclusively determined by polymer from the dewetted area, i.e. by the dewetted distance and the thickness h of the film, w has to be related to the separation distance of the non-wettable patches and the local contact angle , taking into account that ... 

Finally, given that pressure on the boundary is directly related to the local contact angle [20], we again use experimental data for the contact angle versus voltage characteristics of the EWOD device [22] to compute the electrode voltages needed to achieve the boundary pressures a. In general, there will be some uncertainty about the device parameters. 

Henceforth, spherical cavities will be considered in the analysis (Fig. 2). The angular location of the top of the cavity is denoted by Bq (Fig. 2). Let the angular location of the liquid-air interface inside a cavity be denoted by On (Fig. 2) and let (p be the local contact angle of the interface with the wall. The interface is assumed to be spherical. The volume V> of the air inside the cavity is given by... 

The physically relevant solution of equation (18) is = 9, i.e. the local contact angle inside the cavity must equal the equiUbrium contact angle of the flat material [32, 33]. Once ip is known, equations (16) and (17) can be used to solve for the equilibrium values of py and %. 

Table 1 lists the equilibrium values of 0h at different values of Co (i e. at different values of 9q) for = 0.1739 and 0e = 70°. Once % is known, equation (16) or (17) can be used to obtain the equilibrium value of. The first two columns of Table 1 specify the size of the spherical cavity. An interface will remain pinned at the top edge of the spherical cavity if 180° 0e 0o (see [31] for details). Thus, whenever this condition is satisfied the Cassie-Baxter state is possible in the cavities because the local contact angle condition is satisfied at the top edge of the spherical cavities. The corresponding value of Ou is equal to Oq. These values for 0 = 0o are listed in Table 1. For 0q > (= 70°), the local contact angle condition cannot...

To explore the entire energy landscape, Ecav could be plotted as a function of and f. The extrema on this landscape will be the equilibrium solutions, discussed above, of which some will be the stable solutions. In this work, we will select a probable path in this landscape. The values of Ecav will be plotted for this path. To this end, assume that the liquid-air interface is first in the Cassie-Baxter state. As the liquid-air interface moves toward the other equilibrium states, the value of 9u will increase until it reaches the next available equilibrium state given in Table 1. At each intermediate state, between the equilibrium states, it will be assumed that the interface is spherical, the gas pressure is such that it is in accordance with the ideal gas law (equation (16)) and that the interface is in mechanical equilibrium (equation (17)). Thus, equations (16) and (17) are satisfied, however, equation (18) is not. This implies that in the intermediate states the local contact angle condition... 

Figure 9. (a) A height map of the underside of the drop, (b) a profile across a bubble, taken along the black line indicated in (a). The left and right dips correspond to actual elevations in the surface while the middle dip corresponds to a trapped air bubble, cf. Fig. 2. The dashed lines are used to show the local contact angle at the former three-phase line. Using this method it is possible to obtain quantitative information about the geometry of the liquid-gas interface.

A profile taken perpendicular to a former three-phase contact line shows the local contact angle at that point (Fig. 9b). 

It should be emphasized that the local contact angle is no longer 90°. The situation no longer complies with Young s equilibrium. Indeed, at... 

Conclusion. The chemical model is somewhat fuzzy in its details. Just what is the molecular process involved Is the local contact angle the same as the macroscopic one Notwithstanding these difficulties, it is clear that microscopic mechanisms in the immediate vicinity of the line can be important for large angles Od- A hybrid model, in which the hydrodynamic and molecular dissipations are simply added together, has been proposed. Nevertheless, the assumption that the two contributions are additive is far from being obvious. 

One the first attempts at understanding the influence of roughness on wetting is due to Wenzel (1936). We assume that the local contact angle is given by Young s relation [equation (9.1)], and we seek to determine the... 

Finally, given that pressure on the boundary is directly related to the local contact angle [20], we again use experi-... 

From (4.2) the local contact angle at the contact line is given by cos0y for (x,y, 0) e CL. 

S. Iliev and N. Pesheva, Nonaxisymmetric drop shape analysis and its application for determination of local contact angles, J. Golloid Interface Sci. 301, 677-684 (2006). 

The SEM was used to demonstrate and confirm these theoretical projections [306,309]. In the early study [306], molten drops of PE and PMMA were allowed to spread and solidify on a paper substrate prior to standard preparation for SEM. Later, poly(phenyl ether) (PPE) vacuum pump oil (Santovac 5-Monsanto Chemicals), which is not volatile, was used for dynamic studies. The PPE was fed through a hole in the sample stub, from outside the specimen chamber, and the wetting experiment was video tape recorded [309]. Mori et al. [310] used freshly cleaved mica surfaces as steps 60 nm in height inhibit wetting. Surface roughness has a major effect on the local contact angle between the liquid and the substrate of interest. 

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