Ionic flows through a single homogeneous membrane : A thermodynamic analysis

Area of Science:

• Physical Chemistry
• Membrane Science
• Transport Phenomena

Background:

• The Kedem-Katchalsky (KK) equation models mono-monovalent salt flow across permselective membranes.
• It's derived as an expansion of the Kirkwood-Bearman-Spiegler (KBS) equations.
• Assumptions include concentration-independent frictional coefficients.

Purpose of the Study:

• To present a first-order expansion of the KBS equations for salt flow.
• To explore the validity conditions for this expansion.
• To derive a more general ionic flow equation applicable when impermeable salts are present.

Main Methods:

• Integration of the Kirkwood-Bearman-Spiegler equations under specific assumptions.
• Derivation of a generalized ionic flow equation.
• Comparison with the existing Kedem-Katchalsky and Goldman equations.

Main Results:

• A first-order expansion of the KBS equations, closely related to the Goldman equation, is presented.
• Conditions for the validity of this expansion are established.
• A new, more general ionic flow equation is derived, encompassing situations with impermeable salts where KK parameters may be ill-defined.

Conclusions:

• The derived general equation offers a broader framework for understanding ionic flow across membranes.
• The Kedem-Katchalsky equation for salt flow is shown to be a special case of this more general formulation.
• This work refines the understanding of transport phenomena in charged membranes, especially under complex solution conditions.