The development of pressure across membranes in Donnan systems

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.