Analytical Expressions for Thermo‐Osmotic Permeability of Clays

Abstract

In this study, a new formulation for the thermo‐osmotic permeability of natural pore solutions containing monovalent and divalent cations is proposed. The mathematical formulation proposed here is based on the theoretical framework supporting thermo‐osmosis which relies on water structure alteration in the pore space of surface‐charged materials caused by solid‐fluid electrochemical interactions. The ionic content balancing the surface charge of clay minerals causes a disruption in the hydrogen bond network when more structured water is present at the clay surface. Analytical expressions based on our heuristic model are proposed and compared to the available data for NaCl solutions. It is shown that the introduction of divalent cations reduces the thermo‐osmotic permeability by one third compared to the monovalent case. The analytical expressions provided here can be used to advantage for safety calculations in deep underground nuclear waste repositories.

Understanding Fast and Robust Thermo-osmotic Flows through Carbon Nanotube Membranes: Thermodynamics Meets Hydrodynamics

“…In particular, the molecular mechanisms of thermo-osmotic flows, generated at interfaces by thermal gradients, have been explored recently. , Notably, we have shown that standard descriptions of thermo-osmosis based on irreversible thermodynamics − had to be complemented to take into account interfacial hydrodynamics (stagnant layer or liquid–solid slip).…”

A semi‐analytical model for coupled THM consolidation of saturated clays improved by PVTD considering thermal contraction

“…Some theoretical estimations of the thermo-osmotic conductivity have been reported in literature. 48,49 On the basis of this, to explore the influence of the thermo-osmotic conductivity on the coupled THM consolidation response of the soil, 6 cases with different S w , are compared in Figures 14-16, where the smear effect is not considered and k represents the hydraulic conductivity of the soil. It can be observed from Figure 14 that altering the thermo-osmotic conductivity does not affect the development of the temperature increment.…”

Model of Non-Isothermal Consolidation in the Presence of Geobarriers and the Total Approximation Properties of its Finite Element Solutions

“…It is the clay soils used in geobarriers that are known to have the properties of semipermeable membranes [7,28]. A new theoretical explanation of thermo-osmotic filtration of solutions in clays is proposed in [11]. However, the authors do not deviate from the law for the rate of filtration known from the scientific literature which takes into account thermal osmosis:…”

“…According to the equation, the thermo-osmotic permeability is k T = k∇H/T (P a • m 2 /K) [11]. Most often, ∇H > 0 in clays, and fluid flow occurs in the direction of decreasing temperature, but negative values have also been reported.…”