The zero-field viscosity of model ER fluids consisting of glass beads in silicone oil was determined as a function of average particles size ( = 3–75 μm), volume fraction (ϕ = 0.1–0.3) and bimodal mixtures of two sizes. The viscosity increased with ϕ and decreased with . The viscosity of the suspensions ηs in all cases was described reasonably well by the following relation:
where ηs,o(ϕ) and b(ϕ) are constants which increase with ϕ. Reasonable agreement with the Mooney crowding equation occurred for the single size particles, giving for the crowding factor k = 1.3 + 1.5/. For ϕ < 0.2 the viscosity of the bimodal mixtures could be described by a modification of the Mooney equation
where ηo is the viscosity of the silicone oil, ϕi the volume fraction of each particle size Di and ki the normal crowding factor for that size. At ϕ = 0.3 the measured values of ηs for the bimodal mixtures became appreciably larger than those calculated from the modified equation. The decrease in particle size leads to both an increase in surface area of the particles per unit volume of the suspension and to a decrease in spacing (crowding); both factors probably contributed to the increase in ηs.
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