Vibrating wire rheometry

We describe the design and operation of a novel vibrating-wire rheometer. Our device consists of a tungsten wire under tension and immersed in a fluid in a magnetic field. When an alternating current is passed through the wire it vibrates at the driving frequency, and we measure the voltage induced across the wire as a function of frequency. The resonant frequency of the wire is of order 1000 Hz, and can be tuned by varying its length and the applied tension. We modify an analytic expression for the induced voltage, previously derived for Newtonian fluids, to include a complex viscosity, and determine the viscous and elastic modulus of complex fluids by fitting this expression to our data. Our device gives excellent results for the viscosity of Newtonian fluids and the viscoelastic moduli of aqueous polymer solutions, at frequencies higher than those accessible using a conventional shear rheometer. Because the amplitude of the wire's vibrations is on the order of a few microns, it can be used to probe the microrheology of fluids that are heterogeneous on that scale. We illustrate this by measuring the micron-scale moduli of a viscoplastic suspension of Laponite clay as it gels.