Roughness factors

The friction factor is given by Rounds equation with a roughness factor e = 0.00015 ft. 

Contact angle, 0, and spreading coefficient for a liquid on a solid surface comparison of spreading coefficient S for a smooth surface with S for a surface of roughness factor r... 

Where the surface roughness is not very great it might be adequately expressed by a simple Wenzel roughness factor [27,28],... 

It is important to appreciate the assumption implicit in the concept of roughness factor chemical nature and local environment of surface molecules on the rough surface and on smooth surface are the same. 

Consider the roughness factor, r (Eq. 19), for such a fractal surface ... 

Obviously the roughness factor is similarly arbitrary, but it is of interest to use Eq. 25 to compute its value for some trial values of D and a. This is done in Table 2. In order to map the surface features even crudely, the probe needs to be small. It can be seen that high apparent roughness factors are readily obtained once the fractal dimension exceeds 2, its value for an ideal plane. 

Roughness factor calculated for a fractal surface, according to the fractal dimension D and probe area a... 

As was shown above (Section 2.2, Eq. 5), Young s equation (Eq. 4) may be derived by considering the small displacement from equilibrium of a sessile drop on a plane surface. If the same derivation is applied to the situation where the solid surface has a roughness factor (Eq. 19) of r, it is readily seen that Eq. 5 becomes [28]... 

As long as the liquid actually wets the rough surface, a less contentious approach linking the roughness factor to the extent of contact would seem to be via the spreading coefficient as shown in Eq. 20 and summarised in Table 1. If air is trapped within pits by the liquid, a composite surface is produced. 

Figure 2-11. Relative roughness factors for new clean pipe. Reprinted by permission from Pipe Friction Manual, 1954, The Hydraulic Institute. Also see Engineering Data Book, 1st Ed., 1979, The Hydraulic Institute. Data from L. F. Moody, see note Figure 2-3.

Figure 2-24. Friction loss for flow of water in steel pipes. Note C = pipe roughness factor. See Tables 2-9 and 2-22. Courtesy of Carrier Corp.

Type of Pipe Degree of Roughness Velocity ft/min Roughness Factor (Use as multiplier)... 

This conclusion was additionally confirmed by Palczewska and Janko (67) in separate experiments, where under the same conditions nickel-copper alloy films rich in nickel (and nickel films as well) were transformed into their respective hydride phases, which were proved by X-ray diffraction. The additional argument in favor of the transformation of the metal film into hydride in the side-arm of the Smith-Linnett apparatus consists of the observed increase of the roughness factor ( 70%) of the film and the decrease of its crystallite size ( 30%) after coming back from low to high temperatures for desorbing hydrogen. The effect is quite similar to that observed by Scholten and Konvalinka (9) for their palladium catalyst samples undergoing the (a — j8) -phase transformation. 

Effect of Material and Load The sieving constant, C, increases geometrically with load. In addition there is a shape factor, a roughness factor, and a density factor such that ... 

It is important to distinguish clearly between the surface area of a decomposing solid [i.e. aggregate external boundaries of both reactant and product(s)] measured by adsorption methods and the effective area of the active reaction interface which, in most systems, is an internal structure. The area of the contact zone is of fundamental significance in kinetic studies since its determination would allow the Arrhenius pre-exponential term to be expressed in dimensions of area"1 (as in catalysis). This parameter is, however, inaccessible to direct measurement. Estimates from microscopy cannot identify all those regions which participate in reaction or ascertain the effective roughness factor of observed interfaces. Preferential dissolution of either reactant or product in a suitable solvent prior to area measurement may result in sintering [286]. The problems of identify-... 

A new approach to the double-layer capacitance of rough electrodes has been given by Daikhin et al.m m The concept of a Debye length-dependent roughness factor [i.e., a roughness function R LD) that deter-... 

Leikis et al,223 used the Parsons-Zobel method to obtain the roughness factor fpz for pc/Ag electrodes. It was found that /pz 1.2, which was explained by the geometric inhomogeneity of the pc-Ag electrode surface. A more detailed analysis is given in Section II.2. Thus it should be noted that in the case of pc electrodes with appreciable differences of EamQvalues for the various planes (AEff o > 100 mV), it is impossible to obtain the true roughness coefficient, the actual Ea=0, and the inner-layer capacity. 

Data for the pc-Au/DMF + LiC104 interface have been collected by Borkowska and Jarzabek.109 The value of ffa0was found to be 0.27 V (SCE in H20) and the roughness factor / = 1.3 (Table 8). Unlike Hg, Bi, In(Ga), and Tl(Ga) electrodes and similarly to the Ga/DMF interface, the inner-layer capacity for pc-Au in DMF depends weakly on a, and thus the effect of solvent dipole reorientation at pc-Au is less pronounced than at In(Ga), Bi, and other interfaces. 

Electroreflectance data for pc-Cu579 confirm that the capacity minimum at E- -0.2 to -0.3 V (SCE) is due to the oxidation of the electrode surface. According to impedance data,564,565 as for pc-Ag and pc-Au,63 67 74 roughness factor for a pc-Cu electrode is approximately 2, which has been explained by the high surface inhomogeneity of the electrode surface. 

The R of electropolished Zn single-crystal face electrodes has been obtained from the shape of the adsorption-desorption peak of cyclohex-anol at various Zn and Hg surfaces.154 The roughness factor of Zn electrodes has been found to increase in the order Zn(0001) < Zn(lOlO) < Zn(llZO) with values in the range 1.1 to 1.25. 

---