Tangential force constant

We define the first order tangential force constant by ... 

This equation imposes a constraint among the various first order tangential force constants. The parameters the second order derivatives of the potential, are defined by ... 

In a general description of relative motion, it is also desirable to consider the influence of higher derivatives of the relative displacement. As yet, no such specific effort is known to the author. Some experimental work has been done in which instead of prescribing a constant drive speed, a constant tangential force is applied. The ensuing motion then describes the relation between friction and speed. It has been noted by the author that the friction-speed relations obtained from the constant speed and the constant force tests are alike. A similar result has been found by the author using his theoretical model. These results suggest that the coefficient of friction is mainly dependent upon the speed. Moreover the coefficient is more likely to be a point function rather than a path function of speed. With the scant information available, the observation made here may only be looked upon as tentative. In the friction of metals, it has been stated by Rabinowicz that the past history of motion over a certain critical distance is an important factor. Such a path dependence has not yet been studied in detail. 

Consider an fee crystal with one atom in the primitive unit cell and with an interatomic potential (p(r) which extends only to neareast neighbours. Neglecting the tangential force constant, i.e., (y q) = there is then... 

Yabannavar et al. [81] proposed a proportionality relationship valid for spin-filters based on an analogy to Eq. (15). They defined the Reynolds number based on the tangential velocity at the screen surface. Since in spin-filters the permeation velocity, or perfusion flux, is given by Eq. (16), and it can be assumed that the screen porosity e will be maintained constant throughout the scale-up process, it is possible to write a proportionaHty relationship for the ratio from drag to lift force in spin-filters as given by Eq. (17). 

The shear stress applied to the top plate via the tangential force is r = Ft/A. For Newtonian fluids, it is found that the velocity gradient dv/dx is proportional to the shear stress1, the constant of proportionality being the viscosity of the fluid. Viscosity is thus defined ... 

By Newton s definition the viscosity or, more appropriately, the viscosity coefficient, jj, of a fluid in a laminar steady-state flow is expressed as the tangential force, F, per unit area. A, required to maintain a unit rate of shear (or velocity gradient), G, in the liquid. If the liquid fills the space between two parallel planes of area. A, one of which moves at a constant distance, r, from the other with a relative velocity, u, then we have... 

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