The first finite‐element analysis of the forces between particles in electrorheological fluids is presented. The shear modulus for chains of particles arrayed on a square lattice is calculated. Two limiting cases are considered: (1) dielectric particles in a dielectric fluid and (2) infinitely conducting particles in an insulating fluid. In (1), the modulus increases linearly with the ratio of dielectric constants Kp/Kf as the ratio becomes large, contrary to expectations from a simple dipole approximation where it would saturate. For case (2), the modulus depends sensitively on the interparticle spacing and diverges when the particles touch.

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