Transport relaxation time

In EHD impedance studies, the relaxation times for the different transport processes are obtained by variation of the modulation frequency of the flow. The utility of the technique relies on being able to separate out individual transport relaxation times. This is possible because, with EHD, each relaxation time will have a different functional dependence upon the perturbation. The theory and methodology were first developed for sinusoidal modulation of the flow velocity in a tube [20, 22]. The results... 

Transport coefficients are given in terms of the following moments of the transport relaxation time t([Pg.363]

Fig. 2 Dependence of the transport relaxation time on the time between bursts and the molecular relaxation time...

We define the linear adsorption regime such that the activity coefficient/ = 1. In this case, one can solve Eq. (131) under quasistationary conditions by postulating that the characteristic surface-transport relaxation time is very small, as estimated earlier. An integration of Eq. (131) leads to the following expression for the particle flux [112,115] ... 

Here, the angular frequency tu = 2tr/ is of the sinusoidal electric field applied to the solution. According to the theoretical analysis [149b], the relaxation time t of is given as follows by a harmonic mean of the rotational relaxation time r, and the transport relaxation time T of carriers along the polymer chain ... 

Figure 22. Transport relaxation time Tmof the MF mode as a function of of PHT in dichloro-methane with Cp = 0.004 wt%.

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

Russel J. D., Bernstein R. B., Curtiss C. F. Transport properties of a gas of diatomic molecules. VI. Classical trajectory calculations of the rotational relaxation time of the Ar-N2 system, J. Chem. Phys. 57, 3304-7 (1972). 

Human skin is the largest organ in the human body. It is fundamentally important to health as the semi-permeable barrier - the first line of defence - between the body and the external world. However, it remains relatively inaccessible to conventional magnetic resonance imaging, firstly because it is thin and therefore requires high spatial resolution, and secondly because it is characterized by relatively short T2 relaxation times, particularly in the outermost stratum comeum. Conventional studies have not usually achieved a resolution better than 70-150 pm, with an echo time of the order of a millisecond or so. As a planar sample, skin has proved amenable to GARField study where it has been possible to use both a shorter echo time and achieve a better spatial resolution, albeit in one direction only. Such studies have attracted the interest of the pharmaceutical and cosmetic industries that are interested in skin hydration and the transport of creams and lotions across the skin. 

An entirely different type of transport is formed by thermal convection and conduction. Flow induced by thermal convection can be examined by the phaseencoding techniques described above [8, 44, 45] or by time-of-flight methods [28, 45]. The latter provide less quantitative but more illustrative representations of thermal convection rolls. The origin of any heat transport, namely temperature gradients and spatial temperature distributions, can also be mapped with the aid of NMR techniques. Of course, there is no direct encoding method such as those for flow parameters. However, there are a number of other parameters, for example, relaxation times, which strongly depend on the temperature so that these parameters can be calibrated correspondingly. Examples are described in Refs. [8, 46, 47], for instance. 

This relative importance of relaxation and diffusion has been quantified with the Deborah number, De [119,130-132], De is defined as the ratio of a characteristic relaxation time A. to a characteristic diffusion time 0 (0 = L2/D, where D is the diffusion coefficient over the characteristic length L) De = X/Q. Thus rubbers will have values of De less than 1 and glasses will have values of De greater than 1. If the value of De is either much greater or much less than 1, swelling kinetics can usually be correlated by Fick s law with the appropriate initial and boundary conditions. Such transport is variously referred to as diffusion-controlled, Fickian, or case I sorption. In the case of rubbery polymers well above Tg (De < c 1), substantial swelling may occur and... 

Kusumi, A., W. K. Subczynski, and J. S. Hyde. 1982b. Oxygen transport parameter in membranes as deduced by saturation recovery measurements of spin-lattice relaxation times of spin labels. Proc. Natl. Acad. Sci. USA 79 1854-1858. 

In both experimental and theoretical investigations on particle deposition steady-state conditions were assumed. The solution of the non-stationary transport equation is of more recent vintage [102, 103], The calculations of the transient deposition of particles onto a rotating disk under the perfect sink boundary conditions revealed that the relaxation time was of the order of seconds for colloidal sized particles. However, the transition time becomes large (102 104 s) when an energy barrier is present and an external force acts towards the collector. 

A number of studies (9,10) have demonstrated that the valence of coordination of vanadium in typical vanadia catalysts changed with gas composition in contact with the catalyst. As we discuss below, changes at the surface are partially offset by transport of oxygen from interior strata of the catalyst. We believe it is the diffusion of oxygen, as an ion, which is responsible for the relaxation time observed. 

Most pigmented systems are considered viscoelastic. At low shear rates and slow deformation, these systems are largely viscous. As the rate of deformation or shear rate increases, however, the viscous response cannot keep up, and the elasticity of the material increases. There is a certain amount of emphasis on viscoelastic behavior in connection with pigment dispersion as well as ink transportation and transformation processes in high-speed printing machines (see below). Under periodic strain, a viscoelastic material will behave as an elastic solid if the time scale of the experiment approaches the time required for the system to respond, i.e., the relaxation time. Elastic response can be visualized as a failure of the material to flow quickly enough to keep up with extremely short and fast stress/strain periods. 

Another transport property of interfacial water which can be studied by MO techniques is the dipole relaxation time. This property is computed from the dipole moment correlation function, which measures the rate at which dipole moment autocorrelation is lost due to rotational motions in time (63). Larger values for the dipole relaxation time indicate slower rotational motions of the dipole... 

Monte Carlo and Molecular Dynamics simulations of water near hydrophobic surfaces have yielded a wealth of information about the structure, thermodynamics and transport properties of interfacial water. In particular, they have demonstrated the presence of molecular layering and density oscillations which extend many Angstroms away from the surfaces. These oscillations have recently been verified experimentally. Ordered dipolar orientations and reduced dipole relaxation times are observed in most of the simulations, indicating that interfacial water is not a uniform dielectric continuum. Reduced dipole relaxation times near the surfaces indicate that interfacial water experiences hindered rotation. The majority of simulation results indicate that water near hydrophobic surfaces exhibits fewer hydrogen bonds than water near the midplane. 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

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