Experimental Analysis of Salt Diffusion in Compacted Clays by Through-Diffusion and Half Cell Technique

Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 16)


The estimation of the model parameters namely effective diffusion coefficient and retardation factor of a potential landfill liner material was presented in this paper using the experimentally measured salt concentration data. Experimental data of concentration variation of time and spatial distance in compacted bentonite was obtained using two diffusion measurement techniques viz. through-diffusion and half cell technique, respectively. The bentonite was subjected to the same concentration gradient and compacted density in both the experimental methods to compare the results and understand underlying mechanism in the diffusion tests. The measured data from the laboratory diffusion techniques was analysed using a Graphical User Interface (GUI)-based Dot-net application CONTRADIS. The CONTRADIS was used to estimate the model parameters by the inverse analysis. The application uses the solution of the forward analysis and stochastic algorithm for the inverse analysis. The retardation factor obtained theoretically was validated using laboratory batch sorption tests.


Through-diffusion Half cell Clay CONTRADIS 

1 Introduction

The barrier materials used in the landfill liners are mostly clayey soil having very high plasticity and hydraulic conductivity as low as 10−9 cm/s. In such a case, the solute transport will be mostly governed by diffusion and the flow due to advection will be negligible (Barone et al. 1992; Rowe and Booker 1985; Shackelford et al. 1989). In most of the municipal solid waste landfills or highly toxic and hazardous waste landfills, flow due to diffusion is considered to be the significant transport mechanism (Kau et al. 1999). As such for the effective design of landfill liners, knowledge of the parameter governing the diffusive mechanism which is described by diffusion coefficient becomes essential. Also, flow through the plastic compacted clays is influenced by the sorption characteristics of the soils. The sorption potential is best described by a parameter known as retardation factor (Shackelford and Daniel 1991). Hence, proper estimation of both the model parameters which are the effective diffusion coefficient and retardation factors becomes important. Diffusion coefficients are obtained experimentally from laboratory diffusion tests, and the retardation factors are obtained from the equilibrium batch tests (Shackelford et al. 1989, 1991). However, estimation and comparison of the model parameters by different available methods are scarcely conducted.

In this paper, two different laboratory techniques namely through-diffusion and half cell technique were used to estimate the model parameters. The tests were performed on duplicate specimens at a particular density and under same concentration gradient to understand the migration rate of a particular type of ion, to have a comparative analysis of the model parameters, in which not much literature is available.

The paper also describes the development of a dot-net application-based software package CONTRADIS that was built for the purpose of analyzing experimental results obtained from through-diffusion and half cell technique. This software is capable of using the contaminant transport data from experiments and predicting the diffusion and linear sorption parameters of the soils.

2 Governing Mechanism

The governing equation describing the transport of solute through saturated soil is formulated utilizing Fick’s second law which is given as (Shackelford and Daniel 1991; Bharat 2014; Bharat et al. 2012):
$$\frac{\partial c}{\partial t} = \frac{{D^{*} }}{{R_{d} }}\frac{{\partial^{2} c}}{{\partial x^{2} }}$$
where Rd is the retardation factor, and \(D^{*}\) is the effective diffusion coefficient.

3 Materials and Methods

Bentonite soil rich in montmorillonite mineral having liquid limit of 393% was used in the present study. The specific surface area and the cation exchange capacity of the soil are 495 m2/g and 68 meq/100 g, respectively.

The diffusion cell, made of poly(methyl methacrylate) glass tubes having diameter of 2.5 cm and thickness of 1 cm, was used for the diffusion testing.

3.1 Through-Diffusion Technique

Bentonite soil compacted a particular density of 1.5 g/cc was placed in the diffusion cell and saturated for a period of 21 days. The clay plug was placed in contact with two reservoirs namely source and collector reservoir as depicted in Fig. 1. At the end of the saturation period, diffusion testing was started by placing NaCl solution of 0.2 M in the source reservoir and pure distilled water in collector reservoir. Due to this concentration gradient, one-dimensional diffusive mass flux would occur from source to collector reservoir. Both the reservoir concentrations were analysed with time to obtain the plot of relative concentration (c/c0) of sodium ions in both the reservoirs with time. c0 is the initial concentration which is 0.2 M or 12,000 ppm.
Fig. 1

Through-diffusion set-up

3.2 Half Cell Technique

Two half cells of diameter 3.9 and 4 cm length were used in this technique. In both the half cells, soil is compacted at 1.5 g/cc where one half cell was saturated with 0.2 M NaCl and the other half cell is saturated with pure distilled water. After saturation, both the cells were brought in contact with each other and diffusion process took place from the tagged half cell with NaCl to the untagged half cell (Fig. 2). At the end of the diffusion testing period, both the half cells were dismantled and the soil in the cells was sliced at 5 mm thickness and analysed for concentration variation along the length of the half cells.
Fig. 2

Half cell set-up

Based on various initial and boundary conditions, analytical solutions are developed for both the methods (Bharat 2014; Robin et al. 1987).

3.3 Batch Test

Batch study was carried out in the present study to determine one of the model parameters experimentally which is the retardation factor and compare with the theoretical result. The soil-to-solution ratio maintained in the test is 1:20. Batch equilibrium test was performed on air-dried soil to determine the sorption characteristics of the clay soil with respect to sodium ions. Ten gram of the soil is mixed with 200 mL of NaCl of different initial concentrations. Six different initial concentrations are maintained in six different soil samples having weight of 10 g. The six different initial concentrations that were analysed are 2, 4, 6, 8, 10 and 12 g/L. The soil solution is mixed thoroughly in an orbital shaker for 48 h as equilibrium time is assumed to be 48 h. After thorough mixing, the slurries are taken in a centrifuge tube and centrifuged for 2000 rpm for 10 min. The supernatant from each tube is analysed for the equilibrium concentration of the sodium ion by flame photometer. The results were plotted to determine the adsorption isotherm. The sorbed concentration of sodium ions in the soil was plotted against the equilibrium concentration of the ion in the solution to get the sorption isotherm which is given as:
$$q = \frac{{\left( {C_{0} - C_{e} } \right) \times V}}{{M_{\text{s}} }}$$
where V is the volume of the solution, and \(M_{\text{s}}\) is the mass of the soil sample.


The name CONTRADIS stands for “CONtaminant TRAnsport due to DIffusion in Soils.” CONTRADIS is a software package that was built for the purpose of analyzing the experimental readings obtained from various methods that have been used by the previous studies in the field of contaminant transport in soils.

This application-based software package was developed to overcome the shortcomings of the existing software POLLUTE which is a commercially available software and is based on semi-analytical solutions. However, the present application CONTRADIS can perform inverse analysis and estimate the model parameters using stochastic optimization algorithm (Bharat et al. 2012).

The CONTRADIS utilizes the analytical solutions (Bharat 2014; Robin et al. 1987) of both the above-described experimental methods and can generate theoretical concentration profile by performing inverse analysis. This software package was verified on the synthetic data obtained from the calculated concentration value as an input data. With the input parameter of D* and Rd, a theoretical concentration profile is obtained and the actual estimate of the model parameters are taken to be the one for which the experimental profile fits well the theoretical profile with minimum RMSE.

5 Results and Discussions

5.1 Results from Through-Diffusion Technique

The concentration profile was obtained for a period of 60 days for both the reservoirs. It was observed that the concentration in the source reservoir decreased with time and concentration in the collector reservoir increased with time. The experimental data was used in CONTRADIS for the inverse analysis which compares it with the theoretical obtained data by minimizing the RMSE error. The fitting of the theoretical and the experimental concentration profiles as obtained from the software by inverse analysis is given in Fig. 3. The effective diffusion coefficient so obtained is 7.7 × 10−6 cm2/s and retardation factor is 10.
Fig. 3

CONTRADIS conc. profile for through-diffusion test

5.2 Results from Half Cell Technique

After dismantling the half cells at the end of the diffusion testing period, the soil plugs were sliced and analysed for the sodium ion concentration after mixing the soil with 1 M ammonium acetate and mixing it for a period of 16 h. Ammonium acetate replaces all the adsorbed and the free exchangeable ions present in the soil layer. The mixture was then centrifuged and the supernatant so obtained was analysed for total sodium ion concentration for all the slices. The mobile ion or the free ion concentration was obtained by subtracting the total ion concentration from the adsorbed concentration for the same dried mass in the particular slice. A total of 16 soil slices were analysed. The concentration profile along the length of the two half cell obtained from the experimental half cell technique shows that the profile reaches to the ends of the half cell which is finite porous medium case. Hence, the theory of finite porous medium case is used in CONTRADIS, and the experimental data was analysed in the software package for getting the model parameters by inverse analysis. The theoretical data was fitted with the experimental data with minimum root mean square error. The best-fit curve showing the theoretical concentration data and experimental data is shown in Fig. 4. The effective diffusion coefficient so obtained is 1.51 × 10−5 cm2/s and retardation factor is 1.5.
Fig. 4

CONTRADIS conc. profile for half cell test

5.3 Results from Batch Test

Batch test results were utilised to obtain both linear and nonlinear sorption isotherms. Figures 5 and 6 show that the linear sorption isotherm does not fit the experimental data as accurately as nonlinear Freundlich model does. This is because of the fact that at higher concentration, the sorption isotherms are highly nonlinear. However for simplicity of solving the governing differential equation (1), the sorption isotherm is considered linear. Because of this assumption, we can see that in Figs. 3 and 4 experimental data and the theoretical data could not be as well-fitted as is expected. The equations describing the process to determine the retardation factor from linear and Freundlich model can be found elsewhere (Shackelford et al. 1989, 1991). The retardation factor from the linear model obtained experimentally is 4.8, and the retardation factor obtained from the linearized Freundlich model is 6.1.
Fig. 5

Linear isotherm model

Fig. 6

Freudlich isotherm model

6 Summary and Conclusions

Measured salt concentration profiles with time and length of the soil plugs were obtained for two different laboratory techniques viz. through-diffusion and half cell technique, respectively. A new software package named CONTRADIS was developed which utilizes the analytical solutions of the governing differential equation, for both these techniques to determine the model parameters by inverse analysis using optimization algorithm. In order to validate one of the model parameters namely retardation factor, laboratory batch equilibrium test was conducted. The test results show that the model parameters obtained by through-diffusion technique were more reliable as the retardation factor obtained experimentally nearly matched the theoretically obtained value. The results of the half cell technique might not be considered as realistic owing to experimental error like improper contact between the half cells. However, more tests need to be conducted on various contaminating species using both these techniques to understand the reliability of the model parameters which would be useful in the design of landfill liners.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringIIT GuwahatiGuwahatiIndia

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