Effective Salt Diffusion Coefficients Research Articles

Membrane efficiency and diffusive tortuosity of a dense prehydrated geosynthetic clay liner

In this study, a series of membrane/diffusion tests were conducted on specimens of a dense prehydrated geosynthetic clay liner (DPH GCL) subjected to KCl solutions (source concentration, Co = 8.7–160 mM) in rigid-wall cells. The source KCl solutions and de-ionized water (DIW) were circulated across the top and bottom specimen boundaries, respectively, and membrane efficiency coefficients, ω, were measured based on the differential pressures induced across the specimens due to prevention of liquid flux. Also, effective salt-diffusion coefficients, Ds∗, and apparent tortuosity factors, τa, were determined for each specimen based on the steady-state diffusive Cl− flux measured at the exit (bottom) boundary. The DPH GCL specimens exhibited higher ω and lower Ds∗ (and, likewise, lower τa) relative to conventional (granular, non-prehydrated) GCL specimens tested under similar conditions. The results were consistent with the lower hydraulic conductivities, k, measured for the DPH GCL specimens and are attributed primarily to the higher bentonite dry densities in the DPH GCL specimens (1.1 Mg/m3) relative to the conventional GCL specimens (∼0.4 Mg/m3), although differences in bentonite texture (powdered versus granular), bentonite type (treated versus untreated), and testing apparatus (rigid wall versus flexible wall) may have been contributing factors. Both the DPH GCL and the conventional GCL exhibited similar trends of decreasing τa with increasing ω. The τa values are considered to be a function of both a matrix tortuosity factor, τm, that accounts for the geometry of the interconnected pores, and a restrictive tortuosity factor, τr, that accounts for solute exclusion due to membrane behavior. Whereas the DPH GCL exhibited a lower τm relative to the conventional GCL, both GCLs exhibited similar trends of decreasing τr with increasing ω. The relationship between τr and ω for both GCLs is reasonably well represented by τr = 1 – ω, an expression that has been proposed for clay membranes in previous theoretical and experimental studies.

Size dependence of the salting process for dry salted sea cucumber (Stichopus japonicus)

The dry-salting kinetics of three groups of sea cucumber (SC) categorized by body weight as A (14.1–18.0 g), B (18.1–22.0 g) and C (22.1–26.0 g) were investigated. The effective salt diffusion coefficients (De) were estimated by mass transfer models describing dry–salting process of SC. The absolute values of the kinetic parameters for total and water weight changes during salting increased with decreasing SC weight. The values of De decreased with an increasing weight of SC because of the relatively thick thickness. De values calculated based on salt content were larger than those based on the liquid phase in both solutions. The effective salt diffusion coefficients based on a series of error functions (De1) and on the form of a trigonometric series (De2) varied from 1.37 to 1.95 and 3.91 to 5.55 × 10−10 m2/s, respectively. The axial diffusion coefficients (Dz) were higher than the radial diffusion coefficients (Dr).

Restricted salt diffusion in a geosynthetic clay liner

The influence of semipermeable membrane behaviour on salt diffusion through a geosynthetic clay liner (GCL) was investigated by conducting multi-stage membrane tests on four GCL specimens at different effective stresses (σ′ = 34·5–242 kPa) in flexible-wall cells. Each test was conducted by circulating five source potassium chloride solutions, sequentially from lowest to highest concentration (Co = 3·9, 6·0, 8·7, 20, 47 mM), across the top specimen boundary, while circulating de-ionized water across the bottom boundary. Membrane efficiency coefficients (ω) were determined from differential pressure measurements, and effective salt-diffusion coefficients [Formula: see text] were inferred from boundary electrical conductivities. Increases in [Formula: see text] with increasing Co were observed for all specimens and were correlated to decreases in ω. In each case, [Formula: see text] decreased linearly toward zero as ω → 1, regardless of the applied σ′. These results support the hypothesis from pore-scale physical modelling that [Formula: see text] for GCLs exhibiting membrane behaviour may be expressed as a linear function of the quantity 1 − ω.

Determination of Salt Diffusion Coefficient in Rainbow Trout (Oncorhynchus mykiss)

ABSTRACTThe diffusion properties of sodium chloride in rainbow trout muscle during dry salting at 10°C were investigated. The average initial dry matter content of the samples increased from 27.80 ± 0.10 to 36.01 ± 0.16%, and the average salt content increased to 17.98 ± 0.38 g NaCl/100 g dry matter at the end of the 10-h dry salting process. The analytical solution of Fick’s second law considering one-dimensional diffusion through an infinite slab was used to calculate effective salt diffusion coefficients (Deff). The Deff values in rainbow trout fillets decreased with increasing salting time and ranged from 6.64 × 10−10 to 16.45 × 10−10 m2/s.

Explicit and implicit coupling during solute transport through clay membrane barriers

Simulations of salt (KCl) flux through a 1-m-thick clay membrane barrier (CMB) based on coupled solute transport theory are compared to simulated fluxes based on traditional advective–dispersive transport theory. The simulations are based on measured values for the effective salt-diffusion coefficient ( D s*) and chemico-osmotic efficiency coefficient ( ω) for a bentonite-based barrier material subjected to KCl solutions. The results indicate that the exit salt flux is reduced due to both explicit coupling (hyperfiltration and chemico-osmotic counter-advection) and an implicit coupling effect resulting from the decrease in D s* due to a decrease in the apparent tortuosity factor, τ a, with an increase in ω. Implicit coupling is shown to be more significant than explicit coupling for reducing and retarding salt flux through a CMB under diffusion-dominated conditions. Failure to account for the implicit coupling effect may result in unrealistic results, such as the existence of salt flux through a perfect (ideal) clay membrane (i.e., ω=1).

Predicting Solute Flux through a Clay Membrane Barrier

Measured solute flux breakthrough curves ~FBCs! from column tests performed on a semipermeable clay membrane subjected to KCl solutions are compared with predicted FBCs using independently measured flow and transport properties. The predicted FBCs are based on three scenarios: ~1! Advective-dispersive transport that neglects membrane behavior; ~2! advective-dispersive transport that accounts for the concentration dependency of the effective salt-diffusion coefficient (D s) resulting from membrane behavior, referred to as partially coupled transport; and ~3! fully coupled transport that includes both the explicit coupling terms ~e.g., hyperfiltration, chemico- osmosis! associated with clay membrane behavior and the concentration dependency of Ds . The FBCs predicted by fully coupled transport agree best with the measured FBCs. However, for the diffusion-controlled conditions of the column tests, the steady-state solute fluxes predicted by partially coupled transport are only 23- 69% higher than the measured steady-state fluxes. The results imply that the advective-dispersive transport theory can be used to provide reasonably accurate, albeit somewhat conservative, estimates of steady-state solute flux through clays that behave as semipermeable membranes, provided diffusion is a significant, if not dominant, solute transport process and the concentration dependency of D s are taken into account.

Flow and transport through clay membrane barriers

Flux equations for liquid and solute migration through clay barriers that behave as semi-permeable membranes used in waste containment and remediation applications, known as clay membrane barriers (CMBs), are discussed. The results of a simplified analysis of flow through a geosynthetic clay liner (GCL) using measured values for the chemico-osmotic efficiency coefficient ( ω) of the GCL indicate a total liquid flux that counters the outward Darcy (hydraulic) flux due to chemico-osmosis associated with clay membrane behavior of the GCL. Also, the solute (contaminant) flux through the GCL is reduced relative to the solute flux that would occur in the absence of membrane behavior due to chemico-osmotic counter advection and solute restriction. Since diffusion commonly controls solute transport through GCLs and other low-permeability clay barriers, the implicit (empirical) correlation between ω and the effective salt-diffusion coefficient of the migrating contaminant is an important consideration with respect to contaminant restriction in CMBs.

Salting kinetics and salt diffusivities in farmed Pantanal caiman muscle

The legal Pantanal caiman (Caiman crocodilus yacare) farming, in Brazil, has been stimulated and among meat preservation techniques the salting process is a relatively simple and low-cost method. The objective of this work was to study the sodium chloride diffusion kinetics in farmed caiman muscle during salting. Limited volumes of brine were employed, with salting essays carried at 3, 4 and 5 brine/muscle ratios, at 15%, 20% and 25% w/w brine concentrations, and brine temperatures of 10, 15 and 20ºC. The analytical solution of second Fick's law considering one-dimensional diffusion through an infinite slab in contact with a well-stirred solution of limited volume was used to calculate effective salt diffusion coefficients and to predict the sodium chloride content in the fillets. A good agreement was obtained between the considered analytical model and experimental data. Salt diffusivities in fillets were found to be in the range of 0.47x10-10 to 9.62x10-10 m²/s.

Theory for reactive solute transport through clay membrane barriers

The theoretical development for one-dimensional, coupled migration of solutes with different ionic mobilities through clay soils that behave as ion-restrictive membranes, referred to as clay membrane barriers (CMBs), is presented. The transport formulation is based on principles of irreversible thermodynamics and accounts explicitly for coupling effects of hyperfiltration (ultrafiltration) and chemico-osmotic counter-advection associated with clay membrane behavior in the absence of electrical current. Since, by definition, no solute can enter a “perfect” or “ideal” membrane, the concept of an implicit coupling effect, such that the effective salt-diffusion coefficient, D s* approaches zero as the chemico-osmotic efficiency coefficient, ω approaches unity is introduced. The theoretical development also illustrates that, even in the absence of membrane behavior, traditional advective–dispersive transport theory based on a constant value of D s* for the solutes may not be appropriate for simulating transient transport in reactive (ion exchanging) systems. This potential limitation is illustrated through simulations for solute mass flux involving the migration of a binary salt solution (KCl) through a clay barrier with exchange sites saturated with a single exchangeable cation (e.g., Na +) that enters the pore solution upon ion exchange with the salt cation (K +).

Coupling effects during steady-state solute diffusion through a semipermeable clay membrane.

Two separate coupling effects are evaluated with respect to steady-state potassium chloride (KCl) diffusion through a bentonite-based geosynthetic clay liner (GCL) that behaves as a semipermeable membrane. Both of the coupling effects are correlated with measured chemico-osmotic efficiency coefficients, omega, that range from 0.14 to 0.63 for the GCL. The first coupling effect is an explicit (theoretical) salt-sieving effect expressed as a coupled effective salt diffusion coefficient, Domega*, that is lower than the true (uncoupled) effective salt diffusion coefficient, Ds*, because of the observed membrane behavior. However, the maximum difference between Domega* and Ds* based on measured chloride concentrations is relatively small (i.e., = 10%), and the difference decreases with decreasing omega (i.e., Domega* --> Ds* as omega --> 0). The second coupling effect is implicit (empirical) and is characterized by the measurement of concentration-dependent effective salt diffusion coefficients that results in an degrees 300% decrease in Ds* as omega increases from 0.14 to 0.63. The decrease in Ds* resulting from implicit coupling is attributed to solute exclusion described in terms of a restrictive tortuosity factor.

Optimisation strategies for the preparation of bipolar membranes with reduced salt ion leakage in acid–base electrodialysis

The salt ion fluxes across commercial bipolar membranes (BPMs) result in the salt contamination of the produced acids or bases especially at increased product concentrations. Often, bipolar membrane electrodialysis can only be applied when these fluxes are reduced. Here, a model is presented to predict the salt impurities using the limiting current density measured for a single bipolar membrane. The model is extended to relate the limiting current density to the experimentally determined properties of the separate membrane layers. A direct dependence has been found for the salt ion fluxes across the bipolar membrane on the square of the solution concentration and the effective salt diffusion coefficient. Further, the salt ion transport is inversely dependent on the fixed charge density and the thickness of the layers. The latter is not trivial — the thickness in general does not play a role in the selectivity of separate anion or cation exchange membranes. The dependence of the salt ion transport on the membrane layer properties has been verified experimentally by characterising membranes prepared from commercially available anion exchange membranes and tailor-made cation-permeable layers. The presented model has proven to be both, simple and accurate enough to guide bipolar membrane development towards increased selectivity.