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Zero shear viscosity is the viscosity of a material when it is effectively at rest. Despite the misnomer, zero shear viscosity describes a plateau value which you can sometimes see when you use a high-powered rheometer to measure viscosity under extremely low shear conditions. The procedures involving extrapolation of the natural logarithm of the apparent viscosity to zero characteristic shear stress is the most reliable technique for obtaining an estimate of the zero-shear-rate viscosity.