Osmotic Pressure and Maxwell Stress

Hydrostatic pressure is acting on a single uncharged particle in a liquid in the absence of electrolyte ions. When the particle is immersed in a liquid containing 

Biophysical Chemistry of Biointerfaces By Hiroyuki Ohshima Copyright 2010 by John Wiley Sons, Inc. 

N ionic species with valence Zt and bulk concentration (number density) nf (/ = 1, 2,. . . , N), in addition to the hydrostatic pressure p, the osmotic pressure is acting on the particle, which is obtained by integrating the osmotic pressure tensor over an arbitrary surface surrounding the particle. The osmotic pressure is given by the bulk osmotic pressure tensor Ho, 

further, the particle is charged, the particle charge and electrolyte ions (mainly counterions) form an electrical double layer around the particle, as shown in Chapter 1. The osmotic pressure becomes 

The electrolyte ions in the electrical double layer thus exert an excess osmotic pressure ATI(r) on the particle, which is given by 

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