Diffusion time constant

Diffusion time constant (s) Acceleration time constant (s)... 

Diffusion provides an effective basis for net migration of solute molecules over the short distances encountered at cellular and subcellular levels. Since the diffu-sional flux is linearly related to the solute concentration gradient across a transport barrier [Eq. (5)], a mean diffusion time constant (reciprocal first-order rate constant) can be obtained as the ratio of the mean squared migration distance (L) to the effective diffusivity in the transport region of interest. 

Observe the response time of the reactor for changes in the operating parameters SF, F and KLa. Is the biofilm always the slowest to respond Relate the response to the diffusion time constant L2/D. 

Fig. 3. Measured orientational diffusion time constants ror of the solvation shells of CD, Br . and T as a function of temperature. The solid curves represent fits of the data using Eq. (1).

In Fig. 3, the orientational diffusion time constants ror of the first solvation shell of the halogenie anions CD. Br, and D are presented as a function of temperature. From the observation that ror is shorter than rc, it follows that the orientational dynamics of the HDO molecules in the first solvation shell of the Cl ion must result from motions that do not contribute to the spectral diffusion, i.e. that do not affect the length of the O-H- -Cl hydrogen bond. Hence, the observed reorientation represents the orientational diffusion of the complete solvation structure. Also shown in Fig. 3 are fits to the data using the relation between ror and the temperature T that follows from the Stokes-Einstein relation for orientational diffusion ... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

Thus, frequency analysis provides the diffusion time constant <5F/ >F. Combining that value with the steady state determination of Dv/Sf yields a separate estimate of [Pg.237]

It must be expected that a polymer material having a much lower conductivity than polyaniline will give impedance responses revealing the effect of the three time constants obtained in the model. The system investigated was chosen for this reason since pECBZ conductivity and redox capacity [94] correspond to DE = 10 7cm2,s 1 and therefore, for the same layer thickness (500nm), the diffusion time constant would be 0.025 s. Electron diffusion should therefore be detectable in the a.c. and even in the EHD frequency domain. 

The fitted parameters are the amplitude at zero frequency (I/2Q), the diffusion time constant through the film 02/DE, and the capacitive time constant (7 E+ ti)A.F (Table 6-2). 

TDFRS allows for experiments on a micro- to mesoscopic length scale with short subsecond diffusion time constants, which eliminate almost all convection problems. There is no permanent bleaching of the dye as in related forced Rayleigh scattering experiments with photochromic markers [29, 30] and no chemical modification of the polymer. Furthermore, the perturbations are extremely weak, and the solution stays close to thermal equilibrium. 

For the moment, it is sufficient to know that the sample response, which is the time dependent diffraction efficiency after switching off the optical grating, contains at least a fast contribution from heat and a slow one from mass diffusion. The corresponding diffusion time constants depend on the grating constant and are typically of the order of 10 /rs and 100 ms, respectively. 

T = (Dq2) 1 is the collective diffusion time constant, DT the thermal diffusion coefficient. In Eq. (18), the low modulation depth approximation c( M c0, resulting in c(x,t)(l-c(x,t)) c0(l-c0)y has been made, which is valid for experiments not too close to phase transitions. Eqs. (16) and (20) provide the framework for the computation of the temperature and concentration grating following an arbitrary optical excitation. 

Equation (25) holds for monodisperse samples with a single diffusion time constant t, and the diffraction efficiency in response to the most fundamental excitation, a step function where the grating amplitude is switched from 0 to 1 at f = 0, is [27,28,35,45]... 

The corresponding time domain experiment with a long exposure pulse is shown in the insert. Both measurements have been normalized to the amplitude of the signal from the temperature grating. The amplitudes of the concentration signal and the diffusion time constant % agree between both experiments within the experimental error (Table 2). 

The sampling time At must be sufficiently short to avoid aliasing from signal intensity at frequencies above the Nyquist frequency (0Ny = n I At, which are folded back into the frequency interval -0)Ny < (0 < 0)Ny As a rule, At < Tm( /10 should be fulfilled, where Tmin is the shortest diffusion time constant. 

If the signal can be expressed as a sum over exponentials, as in the case of solutions of polydisperse polymers, high-, low-, and band-pass filters which are exponentials in the time domain influence the amplitudes, but not the diffusion time constants of the respective modes [80,81]. 

Diffusion time (diffusion time constant) — This parameter appears in numerous problems of - diffusion, diffusion-migration, or convective diffusion (- diffusion, subentry -> convective diffusion) of an electroactive species inside solution or a solid phase and means a characteristic time interval for the process to approach an equilibrium or a steady state after a perturbation, e.g., a stepwise change of the electrode potential. For onedimensional transport across a uniform layer of thickness L the diffusion time constant, iq, is of the order of L2/D (D, -> diffusion coefficient of the rate-determining species). For spherical diffusion (inside a spherical volume or in the solution to the surface of a spherical electrode) r spherical diffusion). The same expression is valid for hemispherical diffusion in a half-space (occupied by a solution or another conducting medium) to the surface of a disk electrode, R being the disk radius (-> diffusion, subentry -> hemispherical diffusion). For the relaxation of the concentration profile after an electrical perturbation (e.g., a potential step) Tj = L /D LD being - diffusion layer thickness in steady-state conditions. All these expressions can be derived from the qualitative estimate of the thickness of the nonstationary layer... 

Figure 7. pa-GFP dynamics by parallel 2P-epifluorescence microscopy (64 foci, 920 nm, 240 mW) in a tobacco BY-2 protoplast. Quantitative analysis of the decrease of nuclear pa-GFP 2P-epifluorescence, giving a diffusion time constant of 123 s. 

Figure 2. (a) EquiKbiium isotherms and (b) Diffusion time constants of three pure gases at 303K. 

With QENS, both the rotational and translational motions of CH4 can be observed. It was found that the rotational motion of CH4 in ZSM-5 can be described by an isotropic rotational diffusion model with a rotational diffusion time constant, Dr (72). The values of Dr for CH4 adsorbed at 250 K in ZSM-5 are of the order of 5 x 10 s . In MD simulations at 400 K, Dr was found to be of the order of 10 s (73). This difference is due to the fact that a radius of gyration of 0.15 nm was used in the computer fits of the QENS profiles. This radius is intermediate between a simple rotation model, with 0.11 nm for the distance between the protons and the center of mass of the methane molecule, and the radius of the channel in which the molecule performs oscillations. 

Octacalciumphosphate - for the chemical formula see Table 2 Cross-polarization time constant for the I-S model Proton diffusion time constant... 

Fig. 10.19. Measurement of the interpolymer spin-diffusion time constant for PS/PVME cast from toluene (Bt) and chloroform (Be), respectively. The deviation of the methine/methoxy line intensity of PVME from the equilibrium value obtained for > T, is plotted in arbitrary units vs. T after selective inversion of the aromatic PS line. (Reprinted with permission from Ref. [119]. 1986 American Chemical Society, Washington, DC.)...

Figure 5.27. Photochemical lifetime of odd hydrogen radicals, as well as the time constants for transport by the zonal and meridional winds, and a onedimensional diffusive time constant.

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