Study of “blind point” and mass sensitivity of a magnetostrictive biosensor with asymmetric mass loading

Abstract

The existence of “blind point” lowers the mass sensitivity and reliability of magnetostrictive particle (MSP) based biosensors. In addition, asymmetric distribution of mass loading (e.g. bacteria) will cause the shift of “blind point” and change of mass sensitivity of an MSP based biosensor. In this work, a modal analysis method was introduced and conducted to derive the governing vibration equation for an MSP biosensor with asymmetric mass loading. The effects of asymmetric mass loading on the “blind point” shift and mass sensitivity were unveiled by solving the governing vibration equation. It was found that the plot of “blind point” shift showed an “M” shape with the valley located at a/l ∼ 0.5 and two peaks located at a/l ∼ 0.25 and a/l ∼ 0.75. In addition, the theoretical results showed that the resonance frequency shift (Δf) depends on the value of a/l (i.e. both the attached mass and mass distribution) and their relationship is nonlinear. Based on the definition of mass sensitivity (Sm), the values of Sm were derived for the selected values of a/l. The results showed that Sm decreased initially with increasing a/l, reaching the minimum, and then increased until a/l = 1. That is, the maximum mass sensitivity is obtained when a/l equals to a critical value Xc (0 < Xc < l). Based on the result, an optimal mass loading distribution design criterion for developing a more sensitive MSP based biosensor was proposed.

Mass Load Distribution Dependence of Mass Sensitivity of Magnetoelastic Sensors under Different Resonance Modes

“…The kinetic energy ( T ) and potential energy ( V ) of the MS with the layer of mass load can be expressed as [ 19 ]: where ρ s , E s , ν s , and A s represent the density, Young’s modulus, Poisson’s ratio and cross-sectional area ( w × h s ) of the MS, respectively; ρ m , E s , ν s and A m represent the density, Young’s modulus, Poisson’s ratio and cross-sectional area ( w × h m ) of the mass load layer. In general, the second term in Equation (2) can be neglected [ 19 ].…”

“…The displacement function for the n th-order resonance is expressed as [ 19 ]: where φ n ( x ) is the mode shape function of the n th-order resonance of the MS; q nn ( t ) is the element of generalized coordinate which is a n × n matrix.…”

“…In this study, the first four mode shape functions are used and studied. The governing vibration equation is derived based on the Lagrange equation as expressed as [ 19 ] where K , M and ω n represent stiffness matrix, mass matrix and generalized eigenvalue. The element M ij in M is defined as and the element K ij in K is defined as .…”

“…Though some experiments and simulations have been carried out to study the behavior of mass sensitivity, few theoretical studies were done on the fundamentals behind the experimental phenomena. In our previous work, we theoretically derived the mass sensitivity and the “nodal point” position for different mass load distribution using a modal analysis method [ 19 ]. It is found that the mass sensitivity as well as the “nodal point” position changes with mass load distribution.…”

Location Dependence of Mass Sensitivity for Acoustic Wave Devices

“…Therefore, the governing vibration equation is derived to determine the n th order resonant frequency ( f n ) of an MSP with a concentrated mass load. Based on these, and using the same procedure as described by Zhang et al [ 19 ], the numerical simulation can be carried out to determine the resonance frequency of an MSP with a concentrated mass load. For the numerical simulation, MATLAB software was used with the properties and dimension of the MSP listed in Table 1 .…”