Dynamic response of a cantilever in liquid near a solid wall

The dynamic response of a Bimorph(TM) cantilever (10 mm x I mm x 0.5 mm) is investigated experimentally in air and in Fluorinert(TM) (3M(TM)) liquids with varying viscosity but nearly the same density. The gap height d between the cantilever and a solid surface is varied from millimeter to micrometer range and the response of the cantilever is interpreted in terms of added mass m(a) and viscous damping coefficient c(v). Key dimensionless parameters based on the Navier-Stokes (N-S) equations include the kinetic Reynolds number R-k = omegab(2)/4eta (omega is the circular frequency and eta the kinematic viscosity) and the dimensionless gap height d/b, where b is the cantilever width. The added mass increases (and resonance frequency decreases) with increasing fluid density and decreasing d/b, where the dimensionless Gap height d/b has a stronger effect. The added mass coefficient is independent of R-k for R-k > 270 and d/b > 0.01. The N-S equations can be linearized when d/b > 0.1. In liquids, the viscous damping coefficient increases (and the Q-factor decreases) with increasing dynamic viscosity (decreasing R-k) and decreasing d/b. In general, the viscous terms in the N-S equations affect the viscous damping coefficient at all Gaps. The implications of the results on sensor design are briefly discussed. (C) 2003 Elsevier Science B.V. All rights reserved.