Effect of roughness

The work done by different forces acting on the contact line due to the displacement can be written similar to equation (5.8) as 

Note that r is not used in the second term of right-hand side as it does not involve any roughness contribution. For equilibrium, the energy should be minimum. Hence, we have 

It may be noted that equation (5.19) is same as Young s equation for contact angle equation (5.8). Substituting equation (5.19) in equation (5.18), we have 

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Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

Some of the effects of roughness on the spreading of a liquid may be predicted from Eqs. 4, 6 and 20, providing the liquid does not trap air as it moves over the surface. These are summarised in Table 1. 

In recent years there has been a renewed appreciation of potential beneficial effects of roughness on a macroscale. For example Morris and Shanahan worked with sintered steel substrates bonded with a polyurethane adhesive [61]. They observed much higher fracture energy for joints with sintered steel compared with those with fully dense steel, and ascribed this to the mechanical interlocking of polymer within the pores. Extra energy was required to extend and break these polymer fibrils. 

In the previous section it was assumed that the surface of the flow duct was smooth. In reality duct surfaces are rough to varying degrees, which has an effect on the magnitude of friction. Thus Eqs. (4.47) and (4.49) represent the lowest possible levels of f in other words, the effect of roughness is zero. 

To allow for the effect of roughness one can use the results of empirical tests in ducts that have been artificially roughened with particles glued on the surface. This approach allows roughness levels to be determined as a function of the particle diameter k. The following friction factor equation has been derived for large Reynolds numbers ... 

One of the possible ways to account for the effect of roughness on the pressure drop in a micro-tube is to apply a modified-viscosity model to calculate the velocity distribution. Qu et al. (2000) performed an experimental study of the pressure drop in trapezoidal silicon micro-channels with the relative roughness and hydraulic diameter ranging from 3.5 to 5.7% and 51 to 169 pm, respectively. These experiments showed significant difference between experimental and theoretical pressure gradient. 

The effect of roughness on pressure drop in micro-tubes 620 and 1,067 pm in diameter, with relative roughness of 0.71, 0.58 and 0.321% was investigated by Kandlikar et al. (2003). For the 1,067 pm diameter tube, the effect of roughness on pressure drop was insignificant. For the 620 pm tube the pressure drop results showed dependence on the surface roughness. 

When the film thickness is of the order of roughness heights, the effects of roughness become significant which have to be taken into account in a profound model of mixed lubrication. The difficulty is that the stochastic nature of surface roughness results in randomly fluctuating solutions that the numerical techniques in the 1970s are unable to handle. As... 

The Moody diagram illustrates the effect of roughness on the friction factor in turbulent flow but indicates no effect of roughness in laminar flow. Explain why this is so. Are there any restrictions or limitations that should be placed on this conclusion Explain. 

As a final point, we note that typical surfaces are usually not crystalline but instead are covered by amorphous layers. These layers are much rougher at the atomic scale than the model crystalline surfaces that one would typically use for computational convenience or for fundamental research. The additional roughness at the microscopic level from disorder increases the friction between surfaces considerably, even when they are separated by a boundary lubricant.15 Flowever, no systematic studies have been performed to explore the effect of roughness on boundary-lubricated systems, and only a few attempts have been made to investigate dissipation mechanisms in the amorphous layers under sliding conditions from an atomistic point of view. 

The comparison of continuum and atomistic models by Luan and Robbins demonstrates that the atomic details of this contact can have a significant influence on the calculated friction. However, those calculations did not explore atomically rough surfaces, which are most likely found in real engineering contacts. The effect of roughness has been investigated recently by Qi et al. in a study of the friction at the interface between two Ni(100) surfaces.85 Two models were considered in that work. In the first model, both surfaces were atomically flat i.e., the rms roughness was 0.0 A. In the... 

Davies (D3) found that roughened spheres behave rather differently at Re = 9 X 10". Both Cl> and Cl rose steadily with increasing vJU, presumably due to the effect of roughness in displacing the critical transition to lower Re (see Section II). It is therefore possible that rough spheres show negative lift at somewhat lower Re, but this has not been confirmed. 

Refs 1) B. Lewis G. von Elbe,. Combustion, Flame, and Explosion of Gases , Oxford Univ Press, London (1938) la) K.I. Shchelkin, DoklAkadN 23, 636(1939) (On the theory of detonation initiation for gaseous mixtures in pipes) lb) K.I. Shchelkin, ZhEksper i TeoretFiz 10, 823(1940) (The effect of rough-... 

Effect of Roughness on the Detonation Velocity of Various Mixtures... 

Bewersdorff HW, Berman NS (1987) Effect of roughness on drag reduction for commercially smooth pipes J. Non-Newton Fluid Mech 24 365... 

There are numerous reports of investigations of the effects of roughness on flow in open channels. For instance, Reinius (R4) has reported on the effects of surfaces covered with various types of roughnesses (spheres, sand, etc.) on the flow of water in open channels, while Hama (HI) has reported... 

Claassen (CIO), 1918 Experimental studies of film flow of water, NaCl solutions, and molasses on vertical tubes. Measurements of film thickness, liquid adhering after draining, effects of roughness. 

Smooth Pt and Rh electrodes have been compared [105, 269] with electrodepos-ited layers to investigate the effect of roughness (which may be of the order of 103). While electrodeposited Pt absorbs hydrogen and bright Pt does not, no surface area effect has been observed as for hydrogen evolution. This indicates that the internal surface (pores) of rough electrodes does not work because of exclusion due to gas formation. Thus, the porosity of the active layers also needs to be characterized. It has been shown that in the case of Raney Ni [270] this can be conveniently done by means of impedance measurements [271]. 

Degasne, I., Basle, M. F., Demais, V., Hure, G., Lesourd, M., Grolleau, B., Mercier, L., and Chappard, D., Effects of roughness, fibronectin and vitronectin on attachment, spreading, and proliferation of human osteoblast-like cells (Saos-2) on titanium surfaces. Calcified Tissue International 64 (6), 499-507 (1999). 

The effect of roughness on the apparent contact angle of a solid surface has been given quantitative form by R. N. Wenzel.8 If r, the roughness factor , is the ratio between the real and the apparent area of the surface, then... 

Birkebak, R. D., and E. R. G. Eckert Effects of Roughness of Metal Surfaces on Angular Distribution of Monochromatic Radiation, J. Heat Transfer, vol. 87, p. 85, 1965. 

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