Theory of Viscoelasticity in Temporarily Crosslinked Polymers (1) Treatment in Single Relaxation Time

1963 ◽  
Vol 18 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Shizuo Hayashi
Keyword(s):  
Relaxation Time ◽  
Crosslinked Polymers ◽  
Single Relaxation Time ◽  
Theory Of Viscoelasticity

The dielectric behaviour of dipolar mixtures I: chlorobenzene–nitrobenzene mixtures

1986 ◽  
Vol 64 (11) ◽  
pp. 1534-1536 ◽  
Author(s):  
F. F. Hanna ◽  
K. N. Abdel-Nour ◽  
A. M. Ghoneim
Keyword(s):  
Relaxation Time ◽  
Thermodynamic Parameters ◽  
Relaxation Times ◽  
Dielectric Behaviour ◽  
Dilute Solutions ◽  
Single Relaxation Time ◽  
Microwave Region ◽  
Dielectric Absorption

The dielectric absorption of dilute solutions of nitrobenzene, chlorobenzene, and their mixtures in cyclohexane and Decalin® have been measured in the microwave region at three temperatures between 20 and 40 °C. The relaxation times and thermodynamic parameters are determined. A single relaxation time is found for the mixtures, and the results are discussed.

Simulation of Flow Past a Square Cylinder by Parallel Lattice Boltzmann Method using Multi-Relaxation-Time Scheme

2006 ◽  
Vol 22 (1) ◽  
pp. 35-42 ◽  
Author(s):  
J.-S. Wu ◽  
Y.-L. Shao
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Numerical Results ◽  
Channel Height ◽  
Blockage Ratio ◽  
Square Cylinder ◽  
Single Relaxation Time ◽  
Boltzmann Method

AbstractThe flows past a square cylinder in a channel are simulated using the multi-relaxation-time (MRT) model in the parallel lattice Boltzmann BGK method (LBGK). Reynolds numbers of the flow are in the range of 100 ∼ 1,850 with blockage ratio, 1/6, of cylinder height to channel height, in which the single-relaxation-time (SRT) scheme is not able to converge at higher Reynolds numbers. Computed results are compared with those obtained using the SRT scheme where it can converge. In addition, computed Strouhal numbers compare reasonably well with the numerical results of Davis (1984).

Ultrasonic relaxation of the vibrational specific heat of carbon dioxide, sulphur hexafluoride, nitrous oxide, cyclo propane and methyl chloride in the liquid state

1958 ◽  
Vol 247 (1249) ◽  
pp. 168-185 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Nitrous Oxide ◽  
Relaxation Time ◽  
Specific Heat ◽  
Methyl Chloride ◽  
Substantial Part ◽  
Sulphur Hexafluoride ◽  
Single Relaxation Time ◽  
Full Analysis ◽  
Liquid States

Measurements have been made of the ultrasonic absorption and the velocity of propagation in a number of liquefied gases at temperatures from 0 to 50°C and over the frequency range 1 to 50 Mc/s. The observations in liquid carbon dioxide cover the major part of a relaxation region, centred about a frequency of approximately 10 Mc/s, and a full analysis is therefore possible in this case. The results are adequately described in terms of a relaxation of the total vibrational specific heat associated with a single relaxation time. For sulphur hexafluoride, nitrous oxide, cyclo propane and methyl chloride it was not possible to cover a substantial part of the relaxation region. In each case, however, the results are consistent with the assumption that the observed non-classical absorption is entirely due to vibrational relaxation and that the total vibrational specific heat relaxes with a single relaxation time. The corresponding characteristic frequencies are calculated and fall within the range 60 to 250 Mc/s. Comparisons are made between the values of the product, density ( ρ ) times relaxation time at constant temperature (ז T ), in the gaseous and liquid states for the above substances and for others, where adequate data is available. It is found that for a given temperature the ratio ( ρז T ) liquid ( ρז T ) gas is greater than, but close to, unity. It is concluded that vibrational transitions in liquids which are not highly associated occur by the mechanism of binary collisions between molecules. The quantity ( ρז T √ T ) –1 , which can be taken as a measure of the collision efficiency, increases with increasing temperature for non-polar liquids, but appears to depend very little on temperature for highly polar ones.

Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy’s flows

2016 ◽  
Vol 27 (04) ◽  
pp. 1650037 ◽  
Author(s):  
Pietro Prestininzi ◽  
Andrea Montessori ◽  
Michele La Rocca ◽  
Sauro Succi
Keyword(s):  
Porous Media ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Physical Dependence ◽  
Single Relaxation Time ◽  
Flows In Porous Media ◽  
Percent Accuracy ◽  
Boltzmann Method

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

Dielectric dispersion in pure polar liquids at very high radio-frequencies II. Relation of experimental results to theory

1952 ◽  
Vol 213 (1115) ◽  
pp. 473-492 ◽  
Keyword(s):  
Relaxation Time ◽  
Viscous Flow ◽  
Frequency Factor ◽  
Dielectric Dispersion ◽  
Resonance Absorption ◽  
Millimetre Wave ◽  
Polar Liquids ◽  
Single Relaxation Time ◽  
Observed Behaviour ◽  
Very High

The results of the measurements at centimetre and millimetre wave-lengths on the dielectric properties of water, methyl alcohol and ethyl alcohol described in part I are analyzed. There is no evidence that, for any of these liquids, more than a single relaxation time as a function of temperature is required to account for the dispersion arising from dipole rotation. It is suggested that the observed behaviour of the two alcohols at wave-lengths near to 1 cm, which appears not to conform with the hypothesis of a single relaxation time, is in fact the consequence of resonance absorption. If it is supposed that in dipole rotation and viscous flow the molecules have to surmount potential energy barriers, then it appears that, in each of the liquids examined, the heights of the barriers concerned in the two processes are identical; but the ‘frequency factor’ associated with such processes is much larger for viscous flow than for dipole rotation.

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