Smooth surfaces relationship

This relationship holds reasonably well for values of y+ up to about 5, and it applies to both rough and smooth surfaces. 

There are two predictive relationships based on wind speed. Liss and Merlivat (1986) used a physical rationale to explain the increase in the Kl versus wind speed slope at higher wind velocities in wind-wave tunnel and lake measurements, resulting in a piecewise linear relationship with two breaks in slope. These breaks are presumed to occur at the transition between a smooth surface and a rough surface and between a rough surface and breaking waves. In dimensionless form, this relationship is given as... 

For a perfectly smooth surface with c/F ss = 2 at all scales, Eq. (33) predicts a = 1, i.e., purely capacitive behavior. In other limit as c/F ss = 3, a = 0.5 which is de Levie s well-known result for the electrode with cylindrical pore. Eq. (33) also implies that the surfaces with different morphologies but with same surface fractal dimension are equivalent as far as the impedance is concerned. The relationship between dFss and a is dependent upon the model used in the fractal characterization of the electrode. 

In general, previous studies confirmed the notion that regardless of grain size, diamond coatings with a smooth surface finish provide very low friction coefficients to mating surfaces. Figure 9 illustrates the close relationship between surface roughness and friction coefficients of diamond films. 

Higa et al. [13,14] studied the restitution coefficient of an ice ball of radius in the range 0.14 < r-p < 3.6 cm at impact velocities Vi in the range 1 < Vi < 700 ctn/s and temperatures T in the range 113 < T < 269 K. Figure 9.4 shows the result obtained for ice balls with a smooth surface. They found a relationship between restitution coefficient and ice strength. Their results show that the restitution coefficient drops suddenly at a critical velocity for each temperature and impactor size. Beyond the critical velocity, Vc the coefficient 8 can be fit by the empirical equation. 

The relationship thus brought out is very attractive in particular it tempts us to try to interpret a particle of matter as a wave packet due to the superposition of a number of wave trains. This tentative interpretation, however, comes up against insurmountable difficidties, since a wave packet of this kind is in general very soon dissipated. We need only consider the corresponding case in water waves. If we produce a wave crest at any point of an otherwise smooth surface, it is not long before it spreads out and disappears. 

When steady-state conduction occurs within and outside solids, or between two contacting solids, it is frequently handled by means of conduction shape factors and thermal contact conductances (or contact resistances), respectively. This chapter covers the basic equations, definitions, and relationships that define shape factors and the thermal contact, gap, and joint conductances for conforming, rough surfaces, and nonconforming, smooth surfaces. 

For a liquid that rests on a smooth surface with a finite contact angle, one can determine the relationship between the interfacial tensions at the different interfaces from consideration of the balance of surface forces at the line of contact of the three phases (solid, liquid, and gas). Remembering that the interfacial tension always exerts a pressure tangentially along the surface, the surface free-energy balance (a... 

Theoretically, the Cassie-Baxter model assumes that the droplet partially contacts with the air trapped in the pores of the surface when it sits on the peaks of surface feature [22]. This relationship between the apparent contact angle observed on a rough surface and the equilibrium contact angle 0 obtained on a smooth surface is based on the same chemical composition [13,14] ... 

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