Study Of The Effect Of Elasticity Of The Added Mass In Mass Sensing Using Resonant Peak Shift Technique

Abstract

Micromachined biosensors are used in chemical and biological applications. A biosensor which uses mass based transduction is called a mass sensor. Mass sensors are used to detect extremely small mass of biomolecules such as proteins, viruses or even parts of DNA in the range of femtograms (10-15 gm) to zeptograms (10−21 gm). Highly effective and reliable microcantilevers are used for detecting the mass of biomolecules using either static deflection or dynamic resonant peak shifts. The main objective of our work is to investigate the effect of elasticity of the attached mass on the shift in the resonant frequency and examine the validity of the rigid mass assumption used in the literature. The natural frequencies of a resonator are either found by solving the governing differential equation or approximately using Rayleigh-Ritz method. The mass of a body, attached to a resonator beam is determined using resonant frequency shift method. In our study, we derive an analytical expression for ‘δm’ based on the shift in frequency ‘δf’ that accounts for the elasticity of the added mass and the location of the mass on the beam. We study the simplest model to incorporate these effects where the added mass is itself modeled as a single degree of freedom spring-mass system. The entire system is represented as a 2-DOF lumped model of cantilever and the attached elastic mass. The natural frequencies are obtained using eigenvalue analysis. We study the mass estimation of Escherichia Coli (E. Coli), a food borne pathogen, using experimental results reported in the literature. We treat E.Coli as an elastic mass and model it as a single degree of freedom system to account for its elasticity. We use the elastic model as well as the rigid mass model to check the results available in the literature and point out the difference that results in mass estimation using the two models. To demonstrate the effect of elasticity on mass sensing using the resonant peak shift technique, we conduct mesoscale experiments. Since the fundamental principle does not depend on any phenomenon exclusively dependent on micro scales, the mesoscale experiments are justified. For this purpose, an experimental set-up with metallic cantilevers and flexible rubber strands as attached masses are used. We also use our experimental set-up to study the effect of positional inaccuracy of the added mass (rigid) in the computation of its mass from the shift in the resonance frequency. The results obtained show that elasticity of the added mass as well as its position on the resonator affect the computed mass but this effect is dependent on the relative stiffness and mass of the resonator and the added mass. We also observe the limitations of the experiments in carrying out studies over the desired range of parameters. We also create a computational model of the system and carry out simulations to explore a larger range of parameter values. In particular, we create an FEM model of our system in ANSYS, and carry out modal analysis for the cantilever beam resonator with and without the added mass, varying the relative stiffness and mass of the two components (the cantilever beam and the added mass). We compare the results of shift in the resonant frequency with those obtained from the rigid mass model. The results show the effect of elasticity clearly in certain ranges of relative stiffness and mass.