Shear frictional force

N = 0 value. This is an unfortunate drawback of the experimental technique the estimate for the Nq is essential for an understanding of the mechanisms of the influence of surfactants and polymers on the friction between fibers and on the pulp rheology. This estimate can be obtained from direct measurements of cohesive forces in contacts between crossed fibers. The molecular component of the cohesion, p, in the contact between two fibers can be obtained as the force necessary to rupture the fiber-fiber contact. The shear friction force can then be determined as the product of the previously determined friction coefficient, p, and the normal force Nq. In the absence of an external load, the value of Nq is solely the result of the molecular attraction forces, that is, F = iNq = pp. 

The component of the shear friction force in contact, F, due solely to molecular attraction, can be obtained from the measured values of the cohesive forces, p, using the values of the friction coefficients, p, shown in Figure 2.21. These data are illustrated in Figure 2.24, which shows the friction force, F = pp as a function of the PEI concentration. In the concentration interval c 10" -10" M, the addition of PEI results in an increase in the friction force up to a maximal value observed in the concentration interval between c 10 M0 M. At PEI concentrations greater than 10 M, the friction force decreases and reaches values nearly two times less than in water. 

FIGURE 2.24 The molecular component of the shear friction force between cellulosic fibers in water as a function of the PEI concentration. (Redrawn from Amelina, E.A. et al., Kolloidnyi Zh., 63, 132, 2001.)... 

The radioautographic work suggests another model illustrated in Fig. XII-11. The load is supported over area A, with metal contacts of shear strength s over a portion of the area ctA and film-film contacts of shear strength Sf over the rest of the area. In analogy to Eq. XII-9, one can write the total frictional force, F as... 

Carpick R W, Agrait N, Ogletree D F and Salmeron M 1996 Measurement of interfacial shear (friction) with an ultrahigh vacuum atomic force microscope J. Vac. Sc/. Technol. B 14 1289... 

The fundamental principle of Hquid disiategration Hes ia the balance between dismptive and cohesive forces. The common dismptive forces ia atomizer systems iaclude kinetic energy, turbulent fluctuation, pressure fluctuation, iaterface shearing, friction, and gravity. The cohesive forces within the Hquid are molecular bonding, viscosity, and surface tension. 

As we said in the introduction, friction absorbs a lot of work in machinery and as well as wasting power, this work is mainly converted to heat at the sliding surfaces, which can damage and even melt the bearing. In order to minimise frictional forces we need to make it as easy as possible for surfaces to slide over one another. The obvious way to try to do this is to contaminate the asperity tips with something that (a) can stand the pressure at the bearing surface and so prevent atom-to-atom contact between asperities (b) can itself shear easily. 

Carpick, R.W., Ogletree, D.F. and Salmeron, M., Lateral stiffness A new nanomechanical measurement for the determination of shear strengths with friction force microscopy. Appl. Phys. Lc//., 70(12), 1548-1550(1997). 

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

All sliding friction forces are dramatically affected by surface contamination. If the surface is covered with a material that prevents the adhesive forces from acting, the coefficient is reduced. If the material is a liquid which has low shear viscosity the condition exists of lubricated sliding where the characteristics of the liquid control the friction rather than the surface friction characteristics of the materials. It is possible by the addition of surface materials that have high adhesion to increase the coefficient of friction. 

For the flow of a fluid in a pipe of length / and diameter d, the total frictional force at the walls is the product of the shear stress R and the surface area of the pipe (Rndl). This frictional force results in a change in pressure A Pf so that for a horizontal pipe ... 

The shear stresses within the fluid are responsible for the frictional force at the walls and the velocity distribution over the cross-section. A given assumption for the shear stress at the walls therefore implies some particular velocity distribution. It will be shown in Chapter 11 that the velocity at any point in the cross-section will be proportional to the one-seventh power of the distance from the walls if the shear stress is given by the Blasius equation (equation 3.11). This may be expressed as ... 

For planar flow in a viscous fluid, frictional forces between the flow planes give rise to shear stress across the planes of the flow. For flow along x, the shear stress across an area A is... 

The conhned liquid is found to exhibit both viscous and elastic response, which demonstrates that a transition from the liquid to solid state may occur in thin hlms. The solidihed liquid in the him deforms under shear, and hnally yields when the shear stress exceeds a critical value, which results in the static friction force required to initiate the motion. 

During the friction and wear tests of PTFE Him, two zones can be classified according to the load. One is the load below 70 nN, the friction force which was created in friction and wear tests is too small to make the PTFE film to shear. Within this zone the friction force increases linearly with the load, and there are no transfer of atoms and no worn marks. The second zone is when the load is above 70 nN, and the friction force created in the friction and wear tests is large enough to force the PTFE molecular atom to slip. So there were obvious worn mark and projection in the film, and the friction force stayed almost constant with load. 

A measure of the frictional resistance that a fluid in motion offers to an apphed shearing force. Let F be the frictional force, and let S be the area of the interface between a stationary surface plane and a fluid with velocity dv/dr. Then the resisting or frictional force is given as ... 

Spring-bead models relate frictional force to the relative velocity of the medium at the point of interaction. The entanglement friction coefficient above is defined in terms of the relative velocity of the passing chain. Since the coupling point lies, on the average, midway between the centers of the two molecules involved, the macroscopic shear rate must be doubled when applying the result to a spring-bead model. Substitution of 2 CE for Con in the Rouse expression for viscosity yields... 

The droplet simultaneously experiences a frictional force due to the dynamics of the surrounding fluid that opposes its movement. Under laminar flow conditions, the frictional force is given by Ff = 67tr orv, where ri0 is the shear viscosity of the medium and vthe velocity with which the droplet moves. Under steady-state conditions, the so-called Stokes velocity (v) emerges from the force balance ... 

Figure 11.5 Dependence of friction on load for a single microcontact. The friction force between a silica sphere of 5 //in diameter and an oxidized silicon wafer is shown (filled symbols). Different symbols correspond to different silica particles. The solid line is a fitted friction force using a constant shear strength and the JKR model to calculate the true contact area (based on Eq. (6.68)). Results obtained with five different silanized particles (using hexamethylsililazane) on silanized silica are shown as open symbols. Redrawn after Ref. [467].

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