Oscillations diffusion effects

P-08 -Transient uptake measurements using an oscillating microbalance effect of acid leaching on the diffusivity of -hexane in Pt/H-mordenite... 

We consider an isolated gas bubble in an unbounded incompressible liquid initially at rest. We neglecting diffusions effects and changes in temperature. The following differential equation describes the nonlinear oscillations of the spherical gas bubble boundary[3],[4]... 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

In combination with DFT calculations, the time- and depth-dependent phonon frequency allows to estimate the effective diffusion rate of 2.3 cm2 s 1 and the electron-hole thermalization time of 260 fs for highly excited carriers. A recent experiment by the same group looked at the (101) and (112) diffractions in search of the coherent Eg phonons. They observed a periodic modulation at 1.3 THz, which was much slower than that expected for the Eg mode, and attributed the oscillation to the squeezed phonon states [9]. 

When the same kind of electrode is introduced in a solution with a high pH (i.e., pH= 10) and a lower substrate concentration (first order kinetics), an oscillation in time of the measured pH inside the membrane spontaneously occurs. This enzyme, which has been extensively studied, does not give oscillation for any conditions of pH and substrate concentration. The period of oscillation is around one-half minute, and the oscillation is abolished by introducing an enzyme inhibitor. The phenomenon can be explained by the autocatalytic effect and by a feedback action of OH- diffusion in from the outside solution. The diffusion of this ion is quicker than the diffusion of the substrate. There is a qualitative agreement between the computer simulation and the experimental results. 

Before leaving this discussion, it is important to note that other forms of Peclet numbers are also possible and may be more appropriate depending on the type of convective influence studied. For example, in the case of oscillatory flows (as in oscillatory viscometers), it is more useful to define the Peclet number as (Rfa/D), where co is the frequency of oscillation. Regardless of the particular definition, the general significance of the Peclet number remains the same, i.e., it compares the effect of convection relative to diffusion. 

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