Abstract: Based on the point- dipole model, we have calculated the free energy of electrorheological fluid by using statitical method. The phase transition from liquid to solid is investigated by considering the osmotic pressure of particles in the suspension. Our results show that the osmotic pressure become negative when the applied field exceeds acritical value E_c and then the liquid experiences a phase transition to a solid phase.

Key words: electrorheological fluid, free energy, critical field, osmotic pressure