Mass Transport of Binary Electrolytes in Membranes. Concentration Dependence for Sodium Chloride Transport in Cellulose Acetate

Abstract

Equations describing the transport of water and a binary salt through semipermeable membranes are presented. Methods of experimentally determining the resulting six independent transport parameters have been tested. Measurements of these parameters on Loeb-type membranes are presented for curing temperatures of 75°, 84°, and 95°C. If the membrane concentration is characterized by the geometric mean activities of adjacent solutions, the osmosis parameters as defined are concentration-independent up to 0.1 M. They are also independent of the pressure difference across the membrane up to 600 p.s.i.g. Above 600 p.s.i.g. compaction causes a decrease in the transport parameters. Coupling between the different driving forces is quantitatively measured. During reverse osmosis the water flux is not influenced by coupling and can be described by one parameter. The salt flux shows coupling to the water flow and requires two parameters to describe its variations. The reciprocal relations are valid to within at least an order of magnitude. Since water flux coupling is small, the uncertainty in the magnitude of the corresponding coupling parameter is large. Electrical conductivity in a membrane is one third or one fourth of that in the adjacent solution. The transference number of the sodium ion decreases from 0.85 at 0.0035M to about 0.3 at 0.075M.[Equations describing diffusive flow of water and a binary " salt through a semipermeable membrane are presented. The six independent transport parameters defined by these equations have been measured for sodium chloride and water flow through Loeb-type cellulose acetate membranes (Loeb and

Scope and limitations of the irreversible thermodynamics and the solution diffusion models for the separation of binary and multi-component systems in reverse osmosis process

“…To describe the transport phenomenon of water and a single solute in a binary electrolyte system through semi-permeable membranes, Bennion and Rhee (1969) have integrated a set of thermodynamic water and solute flux equations by assuming the water flux is not influenced by coupling the salt flux during reverse osmosis, while the salt flux shows coupling to water flow. The proposed water flux equation as follows:…”

“…They argued that there is no significant solute-solute interaction in multi-component systems. In fact, they based their thinking on the model of Bennion and Rhee (1969), which describes the fluxes of water and solute for a single solute system and modified this model in order to make it compatible for a system with two ionic and non-ionic solutes, which is given by:…”

Mass Transfer of Binary Electrolytes in Membranes at High Concentrations

“…Michaels et al (1964) performed reverse osmosis experiments on various water-salt systems. They varied the applied pressure and found that salt flux, Ne, had the following pres- This is merely a special case of the more general equations proposed by Sherwood et al (1967), Bennion (1966), and Bennion and Rhee (1969).…”

“…In a frictional membrane model, the driving force on a species is related to a linear sum of frictional interactions between the various species and the membrane. Spiegler (1958), Kedem and Katchalsky (1961), Bennion (1966), Wills and Lightfoot (1966), and Bennion and Rhee (1969) have provided extensive treatments of frictional membrane models. Spiegler (1958) and Wills and Lightfoot (1966) both proposed different methods applicable to ion exchange membranes where one ionic species is absent from the membrane.…”

Ion and Solvent Transport in Ion‐Exchange Membranes: I . A Macrohomogeneous Mathematical Model

“…For the sulfuric-acid/Nafion-ll7' system, our experimental results (6) indicate that dilutesolution equations are suitable. For membrane-electrolyte systems in which dilute-solution theories cannot be apphed, transport models based on the principles of irreversible thermodynamics have proven useful (29)(30)(31)(32)(33)(34)(35), although a large number of unknown coefficients must be evaluated if no restrictive approximations are introduced. Equation [1] can be derived for transport in a homogeneous medium by making use of Eyring's absolute-reactionrate theory for diffusion processes (36)(37)(38).…”