Abstract
The pressure that develops between the two sides of a Donnan system is equal to the difference between the osmotic values of the two solutions, even though permeant ions may constitute a significant part of that difference. This is amply documented for the case of membranes that allow water movement through them by single molecules diffusing in isolation or in series through specific proteins (such as aquaporins). In this article, the development of pressure was analysed for a system in which membranes contain a few bulk aqueous pores that prevent charged polymers from entering them due to their size. It is shown analytically that the pressure that develops by the action of the electric field on the net charges in the pores is equal to the difference in the osmotic values of the solutions contributed by the permeant ions. Thus, the sum of the pressures that develop in the system due to the action of the electric field in the pores (a pushing force) and the concentration of the impermeant polymers at the interface (a sucking force), accounts for the total colloid osmotic pressure in these systems.
Highlights
Where φieq is the equilibrium potential for permeant ion i, Ci–∞ and Ci∞ are the molar concentrations of permeant ion i far from the membrane in solution 1 and solution 2, respectively, R is the gas constant, T is the absolute temperature, F is the Faraday number and zi is the valence of ion i
The course of the potential across the membrane is well understood when the membrane is a classical bimolecular lipid membrane (BLM) that is inherently permeable to water[3] or whose permeability to water can be increased significantly by specific water channels, referred to as aquaporins[4]
A Donnan system seemingly challenges the concept that for a membrane to be able to develop a pressure that matches the full difference in osmotic values between two solutions, it must be an ideal semipermeable membrane
Summary
The pressure that develops between the two sides of a Donnan system is equal to the difference between the osmotic values of the two solutions, even though permeant ions may constitute a significant part of that difference. The first surprise to emerge from the numerical analysis was that the action of the electric field on the charge in the water within the pores generates a pressure that is equal to the difference between the osmotic values of the two solutions contributed by the permeant ions. The pressure that develops across a porous membrane in a Donnan system has two components: a pushing force from side 1 to side 2 driven by the action of the potential gradient on the charges in the pores, and a sucking force acting from side 2 that originates from the concentration of the impermeant polymer at the interface of solution 2 with the pores[6].
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