Stokes-Einstein equation variables

In the absence of hydraulic or wind forces, the water becomes quiescenf but natural or free convection processes remains operative. Driven by bottom residing thermal or concentration gradients. Equations 12.14 and 12.15 may be used for estimating these low-end MTCs. The chemical diffusion coefficient in the porewaters of the upper sediment layer is the key to quantifying the sediment-side MTC. Use Archie s law. Equation 12.18, to correct the aqueous chemical molecular diffusivity for the presence of the bed material. Bed porosity is the key independent variable that determines the magnitude of the correction factor. See Table 12.7 for typical porosity values in sedimentary materials. Eor colloids in porewaters. Equation 12.18 applies as well. The Stokes-Einstein equation (Equation 12.19) is recommended and some reported particle Brownian diffusion coefficients appear in Tables 12.9 and 12.10. Under quasisteady-state conditions, Equation 12.23 is appropriate for estimating the bed-side MTCs. 

The critical nucleus of a new phase (Gibbs) is an activated complex (a transitory state) of a system. The motion of the system across the transitory state is the result of fluctuations and has the character of Brownian motion, in accordance with Kramers theory, and in contrast to the inertial motion in Eyring s theory of chemical reactions. The relationship between the rate (probability) of the direct and reverse processes—the growth and the decrease of the nucleus—is determined from the condition of steadiness of the equilibrium distribution, which leads to an equation of the Fourier-Fick type (heat conduction or diffusion) in a rod of variable cross-section or in a stream of variable velocity. The magnitude of the diffusion coefficient is established by comparison with the macroscopic kinetics of the change of nuclei, which does not consider fluctuations (cf. Einstein s application of Stokes law to diffusion). The steady rate of nucleus formation is calculated (the number of nuclei per cubic centimeter per second for a given supersaturation). For condensation of a vapor, the results do not differ from those of Volmer. 

---