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Resonator response to Non-Newtonian fluids
The thickness-shear mode (TSM) resonator typically consists of a thin disk of AT-cut quartz with circular electrodes patterned on both sides. An RF voltage applied between these electrodes excites a shear mode mechanical resonance when the excitation frequency matches the crystal resonant frequency. When the TSM resonator is operated in contact with a liquid, the shear motion of the surface generates motion in the contacting liquid. The liquid velocity field, v{sub x}(y), can be determined by solving the one-dimensional Navier-Stokes equation. Newtonian fluids cause an equal increase in resonator motional resistance and reactance, R{sub 2}{sup (N)} = X{sub 2}{sup (N)}, with the response depending only on the liquid density-viscosity product ({rho}{eta}). Non-Newtonian fluids, as illustrated by the simple example of a Maxwell fluid, can cause unequal increases in motional resistance and reactance. For the Maxwell fluid, R{sub 2}{sup (M)} > X{sub 2}{sup (M)}, with relaxation time {tau} proportional to the difference between R{sub 2}{sup (M)}and X{sub 2}{sup (M)}. Early results indicate that a TSM resonator can be used to extract properties of non-Newtonian fluids.