Hydrodynamic loading of microcantilevers vibrating in viscous fluids

Abstract

The hydrodynamic loading of elastic microcantilevers vibrating in viscous fluids is analyzed computationally using a three-dimensional, finite element fluid-structure interaction model. The quality factors and added mass coefficients of several modes are computed accurately from the transient oscillations of the microcantilever in the fluid. The effects of microcantilever geometry, operation in higher bending modes, and orientation and proximity to a surface are analyzed in detail. The results indicate that in an infinite medium, microcantilever damping arises from localized fluid shear near the edges of the microcantilever. Closer to the surface, however, the damping arises due to a combination of squeeze film effects and viscous shear near the edges. The dependence of these mechanisms on microcantilever geometry and orientation in the proximity of a surface are discussed. The results provide a comprehensive understanding of the hydrodynamic loading of microcantilevers in viscous fluids and are expected to be of immediate interest in atomic force microscopy and microcantilever biosensors.

Atomic-resolution imaging in liquid by frequency modulation atomic force microscopy using small cantilevers with megahertz-order resonance frequencies

“…Due to the hydrodynamic damping caused by the water squeezed between a cantilever and sample surface, significant reduction of Q is expected [26,27,28], which may cancel out the improvement obtained by the enhanced f 0 . Such "squeeze film effect" may become prominent when a small cantilever with a short tip is used.…”

“…In contrast, Q * shows much larger damping upon the tip approach (9.3-22.9%) owing to the squeeze film effect. Such Q damping caused by the solid surface has been extensively studied from theoretical and experimental aspects [33,34,26,27,28]. These previous studies suggested that the Q * of a rectangular beam starts to decrease at the lever-sample distance (d ls ) corresponding to the cantilever width.…”

“…Γ r and Γ i are the real and imaginary parts of the hydrodynamic function and given by [32,27] Γ r = 1.0553 + 3.7997…”

Experimental study of aerodynamic damping in arrays of vibrating cantilevers

“…Regardless of the scale under investigation, most prior studies have been primarily concerned with a single cantilever beam (Fu and Price 1987, Basak et al 2006, and Sader 1998. Fewer studies have focused on the hydrodynamic interaction of multiple beams vibrating in close proximity.…”

Correlation Force Spectroscopy for Single Molecule Measurements

“…These 46 techniques are most effective for 'soft' systems with elastic moduli < 100 Pa [82]. There are parallel efforts in microrheology measurements using microcantilevers [45,[86][87][88], following on recent success in understanding the dynamics of cantilevers in fluid [89][90][91][92][93][94][95][96][97][98]. A wide range of frequencies and viscous and elastic moduli can be explored by AFM microcantilevers.…”