It is known that the Brownian motion is concerned with the aggregation of particle- chains in electrorheological fluids (ERF) under external field. In this paper we suggest a two-sphere model in which we assume that there is internal motion between two spheres but they keep separation from each other for simplifying particle-chain in ERF. Analysing the properties of the Brownian motion of the two-sphere system the result of its trace fractal dimension less than 2 is obtained. In view of the dimension of motion-trace a qualitative explanation of the aggregation of particle-chains in ERF subjected to external electric field, i.e. ,phase separation,is given.