Strong roughness

Aluminum Sheet steel, strong rough oxide layer 75 0.80... 

Fig. 3 Schematic representation of a slight (a) and a strong (b) roughness. The profile of slight roughness is described hy the fimction z = L is the effective thickness of the porous film that represents strong roughness. (From [27])...

It is impossible at the present time to provide a unified description of the response of the QCM for non-uniform solid-liquid interfaces with arbitrary geometrical structure. Below we summarize results obtained for the limiting cases of slight and strong roughness. 

Fig. 5 Dependence of the parameter AF/pf on the velocity decay length points experimental data, line 1 in both plots indicates an ideally smooth surface, a Influence of strong roughness according to Eq. 44 for different values of -2 69, 3 172, 4 276 nm) and L = 506 nm. b The same for different values of L 2 460, 3 506, 4 690 nm and fn = 172 nm. Line 5 in both plots was calculated for slight roughness (roughness factor R = 1.3, Eqs. 34 and 39). (From [27])...

Figure 5 shows that there is no way to fit the experimental data assuming that only one type of roughness is presented on the surface. We are thus forced to conclude that, in these experiments the surface has a multiscale roughness, shown schematically in Fig. 6. The structure of this rough surface is a combination of a slight and a strong roughness shown in Fig. 3a,b. When this is taken into account, it is possible to use Eqs. 33, 34,43, and 44 to calculate the shift in resonance frequency and shift in the width of the resonance, and fit the experiments to the calculated curves with properly chosen values of the parameters of strong roughness. The result of such a fit is shown in Fig. 4, curves 2 and 3. For details of the fitting procedure, the limitations associated with the use of a simplified model, and the comparison with STM data see [27].

Fig. 6 Schematic representation of multiscale roughness. This structure is a combination of a slight and a strong roughness shown in Fig. 3a,b. (From [27])...

Surface roughness is of paramount importance in the use of the QCM in liquids. The existing theories provide a description of the QCM response for rough surfaces in two limiting cases of sHght and strong roughness. How-... 

Characterizing roughness by a geometrical RF, as the ratio of the true surface area and the apparent cross-section area, Eq. (29), one distinguishes typically the cases of weak, moderate, and strong roughness, depending on whether / — 1<<1,/ —... 

Christison, who heard his lectures in 1820, says Thenard was a tall, powerful man, with the head, front, curls and eyes of a bull, and a conformable voice, strong, rough and commanding. His matter was excellent but the incessant vigour made one long for a little of his friend s [Gay-Lussac s] no less persuasive quiet occasionally (see p. 77). 

Perturbation theory cannot be applied to describe the effect of the strong roughness. An approach based on Brinkman s equation has been used instead to describe the hydrodynamics in the interfacial region [82]. The flow of a liquid through a nonuniform surface layer has been treated as the flow of a liquid through a porous medium [83-85]. The morphology of the interfacial layer of thickness, L, has been characterized by a local permeability, that depends on the effective porosity of the layer, (j). A number of equations for the permeability have been suggested. For instance, the empirical Kozeny-Carman equation [83] yields a relationship... 

FIG. 19. Dependence of the parameter Tjpf on the velocity decay length Points—experimental data. Lines la and lb, ideally smooth surface 2a-4a, influence of strong roughness according to Eq. (49) for different values of (2a—... 

At least in two dimensions, one can see how friction facilitates this transition to shear jamming. Consider particles that are part of a force chain that has formed due to shear strain. Particles that are members of a force chain typically experience two strong, roughly diametric contacts. Idealizing this situation, we consider a particle that is in force and torque balance and that experiences exactly two... 

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