Molecular kinematics

These values of e may be compared with the value of the molecular kinematic viscosity v (1 x 10 6 m2/s). e is nearly three orders of magnitude larger than v. 

Conditions in the fully turbulent outer part of the turbulent boundary layer are quite different. In a turbulent fluid, the shear stress f is given by equation 1.95. As illustrated in Example 1.10, outside the viscous sublayer and buffer zone the eddy kinematic viscosity e is much greater than the molecular kinematic viscosity v. Consequently equation 1.95 can be written as... 

Viscosity of the continuous phase, kg/m s Molecular kinematic viscosity of the liquid, m /s Turbulent kinematic viscosity, m /s... 

Cartesian coordinate vector (x, y, z) Molecular thermal diffusivity Turbulent thermal diffusivity Molecular kinematic viscosity Turbulent kinematic viscosity Karman constant Mass density See Eq. (26)... 

A simple closure for Uf <8 Uf]f in Eq. (4.92) that includes the effects of the microscale fluid-velocity fluctuations is to replace it with Uf 8 Uf, and then to model Sf as a Newtonian fluid for the fluid velocity Uf with an effective viscosity equal to the sum of the molecular kinematic viscosity of the fluid (vf) and a microscale effective kinematic viscosity (Veff). This leads to Sf = -pf + Tf, where pi is the pressure in the fluid phase (e.g. that found from an equation of state) and Tf = 2gi(V( + Vefr)[Df - trace(Df) ]... 

M = molecular weight j/joo = kinematic viscosity at lOOT Tff = pour point temperature... 

Fig. 9. Oil absorption vs. oil MW. 1x1x0.050 inch coupons of SBS (Stereon 841A) were immersed in paraffinic process oils of varying molecular weight (kinematic viscosity) for 300 days.

Iaing75a] Laing, R. Artificial Molecular Machines A Rapproachment Between Kinematic and Tessellation Automata, in Proceedings of the International Symposium on Uniformly Structured Automata and Logic, Tokyo (1975). 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

A gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm2/s, is Mowing through a pipe 0.25 nt internal diameter and 5 km long at the rate of 0.4 nt3/s and is delivered at atmospheric pressure, Calculate the pressure required to maintain this rate of flow under isothermal conditions. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

The ab initio molecular dynamics study by Hudock et al. discussed above for uracil included thymine as well [126], Similarly to uracil, it was found that the first ultrafast component of the photoelectron spectra corresponds to relaxation on the S2 minimum. Subsequently a barrier exists on the S2 surface leading to the conical intersection between S2 and Si. The barrier involves out-of-plane motion of the methyl group attached to C5 in thymine or out-of-plane motion of H5 in uracil. Because of the difference of masses between these two molecules, kinematic factors will lead to a slower rate (longer lifetime) in thymine compared to uracil. Experimentally there are three components for the lifetimes of these systems, a subpicosecond, a picosecond and a nanosecond component. The picosecond component, which is suggested to correspond to the nonadiabatic S2/S1 transition, is 2.4 ps in uracil and 6.4 ps in thymine. This difference in the lifetimes could be explained by the barrier described above. 

W = net mass flux of vapor into bubble M = molecular weight of vapor v = kinematic viscosity of liquid... 

Fig. 9. Kinematic viscosity v = r /p (r viscosity, p density) divided by S2/M (S2 = mean square radius of gyration, M molecular mass) as a function of M for polyethylene melts at the same monomeric friction coefficient. (Reprinted with permission from [48]. Copyright 1987 American Chemical Society, Washington)...

In the discussion above, we have considered only the velocity field in a turbulent flow. What about the length and time scales for turbulent mixing of a scalar field The general answer to this question is discussed in detail in Fox (2003). Here, we will only consider the simplest case where the scalar field 4> is inert and initially nonpremixed with a scalar integral length scale that is approximately equal to Lu. If we denote the molecular diffusivity of the scalar by T, we can use the kinematic viscosity to define a dimensionless number in the following way ... 

In summary, the rheological studies of PATE are consistent with a proposed molecular association model for PATE solutions. Kinematic viscosity evaluation shows that at concentrations of 15% to 20% solids, a gelatinous solution results. The apparent viscosity measurements illustrate that network formation can be overcome by heating indicating that the association is electrostatic in nature. 

The fluid density appearing in (1.27) is denoted by p and is assumed to be constant. The molecular-transport coefficients appearing in the governing equations are the kinematic... 

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