Transversely Oscillating MEMS Viscometer: The “Spider”1

The analysis of a new viscometer that takes the form of an oscillating plate, fabricated from silicon using the methods of micro-electro-mechanical-systems (MEMS) is considered. The instrument is designed principally for experimental use in the oil industry. The plate is 1.6mm wide, 2.4mm long, and 20μm thick. It is suspended from a 0.4mm thick support by 48 square cross-section legs, each of length 0.5mm width and depth of 20μm. The process of lithography is used to deposit layers atop the silicon. These layers can then be formed into resistors and metallic tracks. The tracks traverse the supporting legs to provide connections between the plate and external electronics. The oscillating plate is a mechanical element that can be set in motion by the force produced by the interaction between an electric current flowing in the plate and an externally applied magnetic field. The viscometer can be operated either in forced or transient mode and is intended for use in both Newtonian and non-Newtonian fluids. The motion of the viscometer is analyzed for incompressible fluids, using the Navier–Stokes equations to model the flow for both a Newtonian viscous fluid and a viscoelastic fluid where the stress is modeled by a reduced form of Maxwell’s equations.