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

## Abstract

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.

## Keywords

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

*R*

_{d}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 m^{2}/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

*c*/

*c*

_{0}) of sodium ions in both the reservoirs with time.

*c*

_{0}is the initial concentration which is 0.2 M or 12,000 ppm.

### 3.2 Half Cell Technique

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

*V*is the volume of the solution, and \(M_{\text{s}}\) is the mass of the soil sample.

## 4 CONTRADIS

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 *R*_{d,} 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

^{−6}cm

^{2}/s and retardation factor is 10.

### 5.2 Results from Half Cell Technique

^{−5}cm

^{2}/s and retardation factor is 1.5.

### 5.3 Results from Batch Test

## 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.

## References

- Barone, F. S., Rowe, R. K., & Quigley, R. M. (1992). A laboratory estimation of diffusion and adsorption coefficients for several volatile organics in a natural clayey soil.
*Journal of Contaminant Hydrology,**10,*225–250.CrossRefGoogle Scholar - Bharat, T. V. (2014). Analytical model for 1D contaminant transport through clay barriers.
*Environmental Geotechnics,**1*(4), 210–221. (2013).CrossRefGoogle Scholar - Bharat, T. V., Sivapullaiah, P. V., & Allam, M. M. (2012). Robust solver based on modified particle swarm optimization for improved solution of diffusion transport through containment facilities.
*Expert Systems with Applications,**39*(12), 10812–10820.CrossRefGoogle Scholar - Kau, P. M. H., Binning, P. J., Hitchcock, P. W., & Smith, D. W. (1999). Experimental analysis of fluoride diffusion and sorption in clays.
*Journal of Contaminant Hydrology,**36,*131–151.CrossRefGoogle Scholar - Robin, M. J. L., Gillham, R. W., & Oscarson, D. W. (1987). Diffusion of strontium and chloride in compacted clay-based materials.
*Soil Science Society of America Journal,**51,*1102–1108.CrossRefGoogle Scholar - Rowe, R. K., & Booker, J. R. (1985). 1-D pollutant migration in soils of finite depth.
*Journal of Geotechnical Engineering,**111*(4), 479–499.CrossRefGoogle Scholar - Shackelford, C. D., & Daniel, D. E. (1991). Diffusion in saturated soil. II. Results for compacted clay.
*Journal of Geotechnical Engineering,**117*(3), 485–506.CrossRefGoogle Scholar - Shackelford, C. D., Daniel, D. E., & Liljestrand, H. M. (1989). Diffusion of inorganic chemical species in compacted clay soil.
*Contaminant Hydrology, Amsterdam, the Netherlands,**4*(3), 241–273.CrossRefGoogle Scholar