Reynolds

The coefficient of friction between two unlubricated solids is generally in the range of 0.5-1.0, and it has therefore been a matter of considerable interest that very low values, around 0.03, pertain to objects sliding on ice or snow. The first explanation, proposed by Reynolds in 1901, was that the local pressure caused melting, so that a thin film of water was present. Qualitatively, this explanation is supported by the observation that the coefficient of friction rises rapidly as the remperarure falls, especially below about -10°C, if the sliding speed is small. Moreover, there is little doubt that formation of a water film is actually involved [3,4]. 

Reynolds C, King P M and Richards W G 1992 Free energy calculations in molecular biophysics Mol. Phys. 76 251... 

It is essential for the rotating-disc that the flow remain laminar and, hence, the upper rotational speed of the disc will depend on the Reynolds number and experimental design, which typically is 1000 s or 10,000 rpm. On the lower lunit, 10 s or 100 rpm must be applied in order for the thickness of tlie boundary layer to be comparable to that of the radius of the disc. 

Flammond B L, Lester W A and Reynolds P J 1994 Monte Cario Methods in Ab initio Quantum Chemistry (Singapore World Scientific)... 

Reynolds J A, Gilbert D B and Tanford C 1974 Empirieal eorrelation between hydrophobie free energy and aqueous eavity surfaee area Proc. Natl Acad. Sc/. USA 71 2925-7... 

The phenomenon of thermal transpiration was discovered by Osborne Reynolds [82], who gave a clear and detailed description of his experiments, together with a theoretical analysis, in a long memoir read before the Royal Society in February of 1879. He experimented with porous plates of stucco, ceramic and meerschaum and, in the absence of pressure gradients, found that gas passes through the plates from the colder to the hotter side. His experimental findings were summarized in the following "laws" of thermal transpiration. 

In the second part of hla memoir Reynolds gave a theoretical account of thermal transpiration, based on the kinetic theory of gases, and was able CO account for Che above "laws", Chough he was not able to calculate Che actual value of the pressure difference required Co prevent flow over Che whole range of densities. ... 

Reynolds also discussed transpiration under the Influence of a pressure difference alone and gave an account of the phenomenon of Impulsion In a Crookes radiometer, an effect of great Interest to 19ch century scientists. 

The date of this Appendix is given as May 1879, and we know that Maxwell had, at chat time, seen an abstract of Reynolds memoir [82]. 

This point was taken up by Reynolds in a letter addressed to G. G. Stokes, in the latter s capacity as Secretary of the Royal Society [83]. Reynolds pointed out that Maxwell s theory evaluated the effects of thermal transpiration only in circumstances where they were too small to be measured, and complained that Maxwell had misrepresented his own theoretical treat ment of the phenomenon. However, this incipient controversy never developed... 

Ferenczy G G, C A Reynolds and W G Richards 1990. Semi-Empirical AMI Electrostatic Potentials and AMI Electrostatic Potential Derived Charges - A Comparison with Ah Initio Values. Journal of Computational Chemistry 11 159-169. 

Reynolds C A, J W Essex and W G Richards 1992. Atomic Charges for Variable Molecular Conformations. Journal of the American Chemical Society lli 9075-9079. 

Calculations of relative partition coefficients have been reported using the free energy perturbation method with the molecular dynamics and Monte Carlo simulation methods. For example, Essex, Reynolds and Richards calculated the difference in partition coefficients of methanol and ethanol partitioned between water and carbon tetrachloride with molecular dynamics sampling [Essex et al. 1989]. The results agreed remarkably well with experiment... 

Essex J W, C A Reynolds and W G Richards 1989. Relative Partition Coefficients from Partition Functions A Theoretical Approach to Drug Transport. Journal of the Chemical Society Chemical Communications 1152-1154. 

The convection term in the equation of motion is kept for completeness of the derivations. In the majority of low Reynolds number polymer flow models this term can be neglected. 

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

B. L. Hammond, W. A. Lester, Jr., P. J. Reynolds, Monte Carlo Methods in Ah Initio Quantum ChemistryScientific, Singapore (1994). 

Quantum Monte Carlo (QMC) methods are computations that use a statistical integration to calculate integrals which could not be evaluated analytically. These calculations can be extremely accurate, but often at the expense of enormous CPU times. There are a number of methods for obtaining excited-state energies from QMC calculations. These methods will only be mentioned here and are explained more fully in the text by Hammond, Lester, and Reynolds. 

Computer-Aided Molecular Design Applications in Agrochemicals, Materials and Pharmaceuticals C. H. Reynolds, M. K. Holloway, H. K. Cox, Eds., American Chemical Society, Washington (1995). 

The simplest case of fluid modeling is the technique known as computational fluid dynamics. These calculations model the fluid as a continuum that has various properties of viscosity, Reynolds number, and so on. The flow of that fluid is then modeled by using numerical techniques, such as a finite element calculation, to determine the properties of the system as predicted by the Navier-Stokes equation. These techniques are generally the realm of the engineering community and will not be discussed further here. 

The Reynolds number for flow in a tube is defined by dvpirj, where d is the diameter of the tube, V is the average velocity of the fluid along the tube, p is the density of the fluid, and rj is its dynamic viscosity. At flow velocities corresponding with values of the Reynolds number of greater than 2000, turbulence is encountered. 

Reynolds number Re Reynolds numbers Reynolds stresses Rezipas... 

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