Significance for Diffusivity

The significance of a rapid test for determining sample conductivity is the relationship between bulk conductivity and bulk diffusivity. The Nernst-Einstein[9] equation can be used to relate the bulk diffusion coefficient D_i for ion species i to the bulk conductivity σ_B:

$$\frac{D_i}{D^{o}_i} = \frac{\sigma_{\mbox{\tiny B}}}{\sigma_{\mbox{\tiny P}}}$$ (6)

The quantity D^o_i is the diffusivity of ion species i in bulk water, and the quantity σ _P is the sample pore fluid conductivity. Since the values of D^o_i can be obtained from tables [10], D_i could be calculated explicitly from bulk conductivity measurements if the value of σ_P could be determined using a technique such as pore fluid expression [28, 33].

The existing RCT could be made useful by being used to either measure scientifically useful quantities such as diffusivity or report empirical measurements that are directly related to physical processes. Unfortunately, it has been shown here that the results from the RCT six hour conduction test do not represent the true DC resistance, and so are not directly related to diffusivity, which is the process of interest. However, the initial current may be used to accurately estimate σ_B.

A second calculation shows that the RCT test does not simulate chloride transport either, and so does not simulate real-world conditions. The drift velocity v_D of the chloride ions through the RCT cell is calculated (in cgs units) from a modification of the Einstein equation [9]:

$$v_D = \frac{z e E D}{300\, k T}$$ (7)

The relevant quantities are the ion valence z, the electronic charge e (4.8 x 10⁻¹⁰ statcoulombs), the applied electric field (in units of volts per centimeter), the sample diffusivity D, the Boltzmann constant k (1.38 x 10 ⁻¹⁶ erg ºK⁻¹ ), and the absolute temperature T; the value of 300 converts from volts (MKS) to statvolts (cgs). This equation for the drift velocity v_D can be used to determine the time required for chloride ions to traverse a specimen, and is in agreement with the experimental results of both McGrath and Hooton [34] and Sugiyama et al. [35].

The drift velocity equation can be simplified using the geometry of the RCT cell (E = 12 V cm⁻¹) and assuming a constant temperature of 300 ºK:

$$v_D = D\ \times\ 464 \,\mbox{cm}^{-1}$$ (8)

This equation can be simplified further by expressing the diffusivity as a ratio of the chloride ion bulk diffusivity at 25 ºC (2.0 x 10 ⁻⁵ cm² s⁻¹ [10]) to the formation factor F [36,37]. The chloride ion penetration depth δ during the standard six hour RCT, as a function of the formation factor F, is simply the drift velocity v_D times 21600 seconds:

$$\delta = \frac{200}{F} \,\mbox{cm}$$ (9)

Since typical values of the formation factor F for 28-day specimens range from 100-1000 [38, 39], the chloride ions do not traverse the specimen during the rapid chloride test. Therefore, the standard six hour RCT does not simulate chloride transport through the specimen because the chloride ions typically penetrate only a fraction of the specimen thickness during the test.