Interface profiles

Fig. 3.1a, b. Interface profiles for simple low molecular weight materials predicted using computer simulation, a A smooth surface with few steps or vacancies, b A rough surface. Values of the energy of breaking a bond are given in units of kT. (from [163], Copyright 1980 by the AAAS.)... 

A modification of Eq. (65) was applied128 to melt — solid interfaces. The treatment was restricted to interfaces of a single curvature, so that l/R was used instead of the general term (l// j) + (l// 2). Let the interface profile be as indicated in Fig. 16, that is, at large values of x, the melt - solid boundary is flat and lies in the... 

Minimizing T = / /( , S7 )dV produces equilibrium interface profiles (r). An equilibrated planar interface is characterized by its excess energy per unit area, 7,... 

When two fluid interfaces have a high radius of curvature, such as in the pseudoemulsion film, the distance between the interference patterns is too small to be measured by common reflected light interferometry. In this case, differential interferometry can be used for imaging the interface profile [40-45]. (Another technique for studying curved films is the controlled drop tensiometer, as was shown in section 2.)... 

FIGURE 4.6. The interface profile (relative to the interface position at r = 0) for an alkane drop in water with a silica probe at an axial separation distance Do of 6.5 and 4.5 nm. The dots denote the coiresponding disjoining pressure value at the marked radial distance. The inset is the disjoining pressure (electrostatic and van der Waals) for a water/aUtane/silica system with a univalent (non-surface-active) electrolyte ( " = 30 nm ijfo = 50 mV). Reprinted from Ref. [67], with permission from Elsevier. 

Figure 1 Schematic representation of the propagation of Interface profiles in solid-state reactions between components A and B. Hatched areas denote reaction product.

J. E Joanny, Dynamics of wetting Interface profile of a spreading liquid. J. Mec. Theor. Appl. Special Issue, 249-71 (1986). 

Figure 14. Interface profile for arachidic acid determined from the reflectivity data shown...

Fig. 7.51 Interface profile of intergranular corrosion when the precipitate phase is anodic to the matrix phase, (a) Preferential corrosion of continuous AB2 phase, (b) Preferential corrosion of discontinuous DE3 phase...

Fig. 7.52 Interface profile of intergranular corrosion when solute-depleted zone is anodic to precipitate and undepleted matrix, (a) Intergranular attack when precipitateand solute-depleted zone iscontinuous. (b) Intergranular attack when precipitate and depleted zones are discontinuous...

A mass balance enforced by the continuity equation governs the equation for the air-polymer interface profile ... 

The first term in the flux expression provides an artificial compression that keeps the interface profile sharp the second term provides a small amount of viscosity that controls the final thickness of the interface. The combined equation is thus of the form... 

Buehrle J, Heiminghaus S, Mugele F (2003) Interface profiles near three-phase contact lines in electric fields. Phys Rev Lett 91(8) 086101... 

Fig. 12. Interface profile at various Bond numbers (based on tube radius, r) [after Concus (9)].

In summary, therefore, a well-defined interface profile of the van der Waals type does not exist in principle for infinitely large systems in complete equilibrium, but it... 

Fig. 1 Interface profile from computer simulations part a is an overview and part b expands the central part for comparison with Eq. (4)...

Fig. 4 Nonequilibrium steady state interface profiles (density contours at n, = 0.5), for liquid drops in sheared microcapillaries. (a) = 0.02. (b) w =...

Once the interface profile is known, the excess free energy in the interface follows from eqn [40] and gives the interface tension as... 

Equation (5.4) gives the flow rate of a liquid that is due to a volumetric force Vp. In the present case, the force is determined both by the weight of the liquid, which is pgdejdx per unit volume, and by the Laplace force - yd e/dx induced by the surface curvature. The force, and hence the flow rate, can thus easily be deduced from the interface profile [equation (5.9)]. Invoking the flow rate equation (5.6) leads to an equation describing the evolution of the interface ... 

Profiles Q Interface Profiles Q Efficiencies and HETP Q Transfer Coefficients... 

Fig. 7 shows the variation of the maximum value of the dimensionless axial depth of gas invasion with shaft speed for the case of AP = 0.005 MPa. The larger the eccentricity ratio, the lower the shaft speed at which the gas invasion starts. However both the theory and the measurements show that the Interface reaches the oil end of the seal at the same shaft speed (Njj), regardless of z, though the Invasion starts at different speeds. Predictions are in good agreement with measurements. The calculation of the interface profile turned to be unstable with the increase in shaft speed, that is, with the... 

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