Frictional coefficient velocity

Thus the average velocity decays exponentially to zero on a time scale detennined by the friction coefficient and the mass of the particle. This average behaviour is not very interesting, because it corresponds to tlie average of a quantity that may take values in all directions, due to the noise and friction, and so the decay of the average value tells us little about the details of the motion of the Brownian particle. A more interesting... 

This expression shows diat if die detuning Acuj is negative (i.e. red detuned from resonance), dieii die cooling force will oppose die motion and be proportional to die atomic velocity. The one-diniensional motion of die atom, subject to an opposing force proportional to its velocity, is described by a damped haniionic oscillator. The Doppler damping or friction coefficient is die proportionality factor. 

Equation (Cl.4.35) yields two remarkable predictions first, tliat tire sub-Doppler friction coefficient can be a big number compared to since at far detuning Aj /T is a big number and second, tliat a p is independent of tire applied field intensity. This last result contrasts sharjDly witli tire Doppler friction coefficient which is proportional to field intensity up to saturation (see equation (C1.4.24). However, even tliough a p looks impressive, tire range of atomic velocities over which is can operate are restricted by tire condition tliat T lcv. The ratio of tire capture velocities for Doppler versus sub-Doppler cooling is tlierefore only uipi/uj 2 Figure Cl. 4.6 illustrates... 

Figure C 1.4.6. Comparison of capture velocity for Doppler cooling and Tin-periD-lin sub-Doppler cooling. Notice tliat tire slope of tire curves, proportional to tire friction coefficient, is much steeper for tire sub-Doppler mechanism. (After [17].)...

The friction coefficient determines the strength of the viscous drag felt by atoms as they move through the medium its magnitude is related to the diffusion coefficient, D, through the relation Y= kgT/mD. Because the value of y is related to the rate of decay of velocity correlations in the medium, its numerical value determines the relative importance of the systematic dynamic and stochastic elements of the Langevin equation. At low values of the friction coefficient, the dynamical aspects dominate and Newtonian mechanics is recovered as y —> 0. At high values of y, the random collisions dominate and the motion is diffusion-like. 

Flow coefficients and pressure coefficients can be used to determine various off-design characteristics. Reynolds number affects the flow calculations for skin friction and velocity distribution. 

Second, we take account of the frictional drag as the solute molecule moves through the solvent. The frictional force is taken to be proportional to the velocity of the particle, with a proportionality constant called the friction coefficient... 

Fig. 19—Friction coefficient and load on different substrates [48]. Velocity 15.6 mm/s Lubricant paraffin liquid.

Phenomenal studies were made to observe the frictional behavior of L-B films and SAMs and its dependence on applied load and sliding velocity, which has been summarized in a review article by Zhang [33]. It has been confirmed that in comparison to the bare surface of the substrates, the friction on molecular films is significantly reduced, with friction coefficients in a range of 0.05-0.1. Friction forces are found... 

The friction coefficient, n, is assigned with different values in different friction conditions. Fj is the relative sliding velocity of two contacting bodies. 

The process of transition from hydrodynamic to boundary lubrication can be described qualitatively by plotting the measured friction coefficients against film thickness, which depends on the operational conditions, such as load, sliding velocity and lubricant viscosity. A typical diagram known as the "Stribeck Curve is schematically shown in Fig. 27, in which the friction coefficients are given as a function of, ... 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

The friction coefficient at PVA gel/OTS modified quartz is 0.300 while that at PVA gel/unmodrfied quartz is 0.076. Frictions were measured by using a rheometer (ARES, TA instruments) as a function of sliding velocity in water and these values were calculated from the experimental resultsoflowestsbdingvelodty,7.5 x 10 m/s. 

Ni is Avogadro s number, / the particle friction coefficient, u the velocity and v the partial specific volume of the solute [79,80]. Inertial forces are negligible and the balancing of the above forces yields the sedimentation coefficient ... 

Silinsh et al. (1989) applied their thermalization procedure to naphthalene and anthracene at low temperatures, 35 K or less. A stationary state was envisaged in the presence of an external field. Calculations have been performed for the saturation drift velocity, friction coefficients, and effective mass as functions of the external field. The conclusions are almost the same as for pentacene. 

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