Time scales thermal diffusion

The tetrahedral arrangement that characterizes the local ordering of water molecules in the V structure dissipates after about 10 s (at 283 K) because the nearest neighbors of a given molecule are relatively free to change their positions in response to thermal perturbations. This relaxation time is about one order of magnitude smaller than the time scale for diffusive translational and rotational motion of the molecules in liquid water at 283 K, as can be inferred from Table 2.2. The physical meaning of... 

The thermal diffusivity for aluminum is = 5.2 x 10 m s [50]. Use this value to determine the time necessary for substantial temperature change over the length scale of 10 following creation of shear bands in the shock front. Should the temperature evolution of the shear band be included in a constitutive description on time scales of compression and release ... 

E.g. tryptophane residues of proteins excite at 290-295 mn but they emit photons somewhere between 310 and 350 mn. The missing energy is deposited in the tryptophane molecular enviromuent in the form of vibrational states. While the excitation process is complete in pico-seconds, the relaxation back to the initial state may take nano-seconds. While this period may appear very short, it is actually an extremely relevant time scale for proteins. Due to the inherent thermal energy, proteins move in their (aqueous) solution, they display both translational and rotational diffusion, and for both of these the characteristic time scale is nano-seconds for normal proteins. Thus we may excite the protein at time 0 and recollect some photons some nano seconds later. With the invention of lasers, as well as of very fast detectors, it is completely feasible to follow the protein relax back to its ground state with sub-nano second resolution. The relaxation process may be a simple exponential decay, although tryptophane of reasons we will not dwell on here display a multi-exponential decay. 

The Peclet number compares the effect of imposed shear (known as the convective effect) with the effect of diffusion of the particles. The imposed shear has the effect of altering the local distribution of the particles, whereas the diffusion (or Brownian motion) of the particles tries to restore the equilibrium structure. In a quiescent colloidal dispersion the particles move continuously in a random manner due to Brownian motion. The thermal motion establishes an equilibrium statistical distribution that depends on the volume fraction and interparticle potentials. Using the Einstein-Smoluchowski relation for the time scale of the motion, with the Stokes-Einstein equation for the diffusion coefficient, one can write the time taken for a particle to diffuse a distance equal to its radius R, as... 

Since the length scales associated with the thermal lens are on the order of 10 to 1000 times the grating constant, their characteristic time scale interferes with polymer diffusion within the grating. Such thermal lensing has been ignored in many FRS experiments with pulsed laser excitation [27,46] and requires a rather complicated treatment. A detailed discussion of transient heating and finite size effects for the measurement of thermal diffusivities of liquids can be found in Ref. [47]. 

The dec8y rate of the order-parameter fluctuations is proportional to the thermal diffusivity in case of pure gases near the vapor-liquid critical point and is proportional to the binary diffusion coefficient in case of liquid mixtures near the critical mixing point (6). Recently, we reported (7) single-exponential decay rate of the order-parameter fluctuations in dilute sugercritical solutions of liquid hydrocarbons in CO for T - T 10 C. This implied that the time scales associated with thermal diffusion and mass diffusion are similar in these systems. 

To analyse bond breakage under steady loading, we take advantage of the enormous gap in time scale between the ultrafast Brownian diffusion (r 10 — 10 s) and the time frame of laboratory experiments ( 10 s to min). This means that the slowly increasing force in laboratory experiments is essentially stationary on the scale of the ultrafast kinetics. Thus, dissociation rate merely becomes a function of the instantaneous force and the distribution of rupture times can be described in the limit of large statistics by a first-order (Markov) process with time-dependent rate constants. As force rises above the thermal force scale, i.e. rj-t> k T/x, the forward transition... 

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