Interfaces flatness

Examples are the onter menisci in Fignres 5.7b and 5.8. In this case the action of gravity cannot be neglected insofar as the gravity keeps the interface flat far from the contact line. The capillary pressnre is... 

Figure 6.3. Configuration of the interface (flat, fixed and with no polarization)...

Aubouy, M., Guiselin, O., Raphael, E. Scaling description of polymer interfaces flat layers. Macromolecules 29(22), 7261-7268 (1996)... 

The preceding evidence for orientation at the interface plus the considerations given in Section III-3 make it clear that the polar end is directed toward the water and the hydrocarbon tails toward the air. On the other hand, the evidence from the study of the Gibbs monolayers (Section III-7) was that the smaller molecules tended to lie flat on the surface. It will be seen that the orientation... 

In the mean field considerations above, we have assumed a perfectly flat interface such that the first tenn in the Hamiltonian (B3.6.21) is ineffective. In fact, however, fluctuations of the local interface position are important, and its consequences have been studied extensively [, 58]. 

One can regard the Hamiltonian (B3.6.26) above as a phenomenological expansion in temis of the two invariants Aiand//of the surface. To establish the coimection to the effective interface Hamiltonian (b3.6.16) it is instnictive to consider the limit of an almost flat interface. Then, the local interface position u can be expressed as a single-valued fiinction of the two lateral parameters n(r ). In this Monge representation the interface Hamiltonian can be written as... 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

Interfacial Forces. Neighboring bubbles in a foam interact through a variety of forces which depend on the composition and thickness of Hquid between them, and on the physical chemistry of their Hquid—vapor interfaces. For a foam to be relatively stable, the net interaction must be sufficiently repulsive at short distances to maintain a significant layer of Hquid in between neighboring bubbles. Otherwise two bubbles could approach so closely as to expel all the Hquid and fuse into one larger bubble. Repulsive interactions typically become important only for bubble separations smaller than a few hundredths of a micrometer, a length small in comparison with typical bubble sizes. Thus attention can be restricted to the vapor—Hquid—vapor film stmcture formed between neighboring bubbles, and this stmcture can be considered essentially flat. 

Fig. 3. Two-dimensional schematic illustrating the distribution of Hquid between the Plateau borders and the films separating three adjacent gas bubbles. The radius of curvature r of the interface at the Plateau border depends on the Hquid content and the competition between surface tension and interfacial forces, (a) Flat films and highly curved borders occur for dry foams with strong interfacial forces, (b) Nearly spherical bubbles occur for wet foams where...

Radiographic. Radiography is an exceUent nondestmctive test (NDT) method for evaluating the bond of Al—steel electrical and Al—Al—steel stmctural transition joints. It provides the capabiHty of precisely and accurately defining all nonbond and flat-bond areas of the Al—steel interface, regardless of size or location (see Surface and interface analysis). 

Fig. 8. Microhardness profile across interfaces of two types of explosion clads that show widely divergent response resulting from the inherent cold-work hardening characteristics where Q represents the 3.2-mm type 304L stainless/28.6-mm, A 516-70 control (before cladding) ( ) = clad + flat ...

Transition Joints. Use of explosion-clad transition joints avoids the limitations involved in joining two incompatible materials by bolting or riveting. Many transition joints can be cut from a single large-area flat-plate clad and deflvered to limit the temperature at the bond interface so as to avoid undesirable diffusion. Conventional welding practices may be used for both similar metal welds. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

These equations assume that there is no drag force at the gas/liquid interface, such as would be produced by gas flow. For a flat surface inclined at an angle 0 with the horizontal, the preceding equations may be modified by replacing g by g sin 0. For films falhng inside vertical tubes with film thickness up to and including the full pipe radius, see Jackson AlChE1, 231-240 [1955]). 

FK . 15-22 Uqiiid agitation by a disc flat blade turbine in the presence of a gas-liquid interface a) without wall baffles, (h) with wall baffles, and (c) in full vessels without a gas-bqiiid interface (continuous flow) and without baffles. [Couitesy Treyhal, Mass Transfer Operations, 3rd ed., p. 148, McGraw-Hill, NY,... 

FIG. 15-23 Power for agitation impellers immersed in single-phase liquids, baffled vessels with a gas-liquid surface [except curves (c) and (g)]. Curves correspond to (a) marine impellers, (h) flat-blade turbines, w = dj/5, (c) disk flat-blade turbines witb and without a gas-liquid surface, (d) curved-blade turbines, (e) pitcbed-blade turbines, (g) flat-blade turbines, no baffles, no gas-liquid interface, no vortex. 

The reacting sohd is in granular form. Decrease in the area of the reaction interface occurs as the reaction proceeds. The mathematical modeling is distinguished from that with flat surfaces, which are most often used in experimentation. 

It is generally observed that the interface between two solids which results from the growth of one phase by condensation to form a film on die other is one in which the number of nearest neighbour bonds between the two phases is maximized. The close-packed planes tend to be found at the interface, which is consequently usually nearly atomically flat and this minimizes die interfacial... 

Though a powerfiil technique, Neutron Reflectivity has a number of drawbacks. Two are experimental the necessity to go to a neutron source and, because of the extreme grazing angles, a requirement that the sample be optically flat over at least a 5-cm diameter. Two drawbacks are concerned with data interpretation the reflec-tivity-versus-angle data does not directly give a a depth profile this must be obtained by calculation for an assumed model where layer thickness and interface width are parameters (cf., XRF and VASE determination of film thicknesses. Chapters 6 and 7). The second problem is that roughness at an interface produces the same effect on specular reflection as true interdiffiision. 

In the JKR experiments, a macroscopic spherical cap of a soft, elastic material is in contact with a planar surface. In these experiments, the contact radius is measured as a function of the applied load (a versus P) using an optical microscope, and the interfacial adhesion (W) is determined using Eqs. 11 and 16. In their original work, Johnson et al. [6] measured a versus P between a rubber-rubber interface, and the interface between crosslinked silicone rubber sphere and poly(methyl methacrylate) flat. The apparatus used for these measurements was fairly simple. The contact radius was measured using a simple optical microscope. This type of measurement is particularly suitable for soft elastic materials. 

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