Attraction force between slightly conducting spheres immersed in a dielectric liquid

We examine the interaction between slightly conducting solid particles suspended in an insulating liquid and subjected to a D.C. electric field with reference to the basic physical processes in electrorheological fluids. Measurements are performed using a scaled-up two-sphere experimental model for the particle interaction. Formulae of the attraction force between conducting spheres are recalled for moderate distances s between the spheres. For small distances an expression is derived by extending the conduction model as developed for spheres in contact, assuming a saturation regime of electrical conduction in the liquid