Fluid–structure interaction analysis of flow and heat transfer characteristics around a flexible microcantilever in a fluidic cell

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Abstract

This study analyzes the effect of the flow conditions and the geometric variation of the microcantilever’s bluff body on the microcantilever detection capabilities within a fluidic using a finite element fluid–structure interaction (FSI) model. Periodic steady-state results of the current investigation show that the magnitude of the inlet fluid velocity, elasticity of the microcantilever, random noise, and the height of the bluff body has respective profound effect on deflection of the microcantilever. Low inlet fluid velocity condition exhibits no vortices around the microcantilever. However, the introduction of a random noise in the fluidic cell may cause the microcantilever to oscillate in a harmonic mode at low velocity. The results of this study show that microcantilevers excite earlier for large height compared with smaller heights of the bluff body at high inlet fluid velocity. This work paves the road for researchers in the area microcantilever to design efficient microcantilevers that display least errors in the measurements.

Introduction

Microcantilever sensor systems have been receiving considerable attention in various areas of interest ranging from biomedical to thermal applications [1], [2], [3], [4], [5], [6], [7], [8]. In biological applications, microcantilever-based biosensors have been used in monitoring hazardous biological and chemical agents, and in screening patients for the presence of diseases and to determine its susceptibility to a given drug [2]. This is due to their fast responses, high sensitivity, and their potential for an inexpensive array-based sensing platform [3]. As such, accurately designed biosensors can provide fast and accurate detection of pathogens within a short period of time. A collection of miniaturized biosensors can be arranged on a solid substrate to perform many tests instantaneously so higher throughput and speed can be achieved. This collection of micro-arrays arrangement is often called a biochip. First applications of microcantilever arrays as tools for bimolecular detection have been illustrated in the field of DNA hybridization detection [5], [9].

In thermal applications, microcantilevers with integrated heaters have been used in various applications such as thermomechanical data storage [10], [11], high density data storage [12], [13], [14], [15], thermomechanical cantilever actuation [16], nanometer-scale manufacturing [17], [18], nanometer-scale thermal measurements [19], [20], [21], and vapor detection [22]. Majority of the studies on heat flow from the cantilever to the environment was limited to heat flow along the microcantilever and into the substrate while ignoring heat flow to the air environment [23], [24], [25]. However, several applications utilized heated microcantilevers that are suspended in air environment and away from a substrate [10], [11], [16], [17], [18], [22]. Recently, Kim and King [26] investigated transient heat conduction between a heated microcantilever and its air environment. Time-averaged heat flow from the cantilever leg to the air was determined to be two- to six fold greater than time-averaged heat flow from the cantilever heater to the air.

Changes in the physical properties of a microcantilever are used to detect changes in the environment surrounding it. Most often the deflection of the microcantilever is measured to indicate the presence or absence of a certain analyte. Moreover, microcantilevers are commonly made of silicon, silicon nitride, metal or combinations thereof. When the analyte molecules bind to the receptor, the side coated with the receptor will either become tensioned or relieved; thereby causing the microcantilever to deflect. The concentration of the analyte is related to the deflection of the microcantilever. The superior capabilities of microcantilevers to detect a specific substance are affected by many factors [27], [28], [29], [30], [31], [32]. For example, Khanafer and Vafai [27] studied numerically the effect of flow conditions and the geometric variation of the microcantilever’s supporting system on the microcantilever detection capabilities within a fluidic cell for various pertinent parameters assuming rigid microcantilever. Their results showed that the normal velocity was decreased when decreasing the height of the fluidic cell and consequently minimizing any unfavorable microcantilever deflection. Khanafer et al. [28] conducted a study to establish the minimum spacing distance between an array of the microcantilevers that produce similar flow conditions around each resulting in an optimum utilization of the biosensor. This minimum spacing distance was necessary for the microcantilevers to function independently of each other when they are used to detect concentrations of different analytes, i.e., species to be measured. Khaled et al. [31] investigated the main causes for the deflection of microcantilevers embedded in micromechanical bio-detection systems. The results of their investigation illustrated that oscillating flow conditions are found to produce significant deflections at relatively large frequency of turbulence. Also, bimaterial effects influencing the microcantilever deflections were found to be prominent at a relatively low frequency of turbulence. Meanwhile, Fritz et al. [32] reported experimentally that the deflection of the microcantilever due to flow disturbances and thermal effects could reach 5–10 times that due to analyte adhesion, respectively.

It is worth noting that efforts have been given toward fabricating more flexible microcantilevers to improve the sensitivity and throughput of microcantilever sensors in flowing fluids at higher flow rates [33]. However, higher flow rates may cause significant flow-induced bending and vibration of highly flexible microcantilevers and consequently affects sensing efficiency of the system. Thus, flow-induced bending of microcantilevers may hinder developing high resolution sensors for complex velocity fields [33]. Previous studies on the analysis of flow characteristics around microcantilevers in a fluidic cell assumed rigid microcantilevers. However, since microcantilevers are extremely small; they tend to deflect as a result of the flow turbulences in addition to the microcantilever’s deflection caused by binding the analyte (e.g., biological molecules, such as proteins or biological agents) with the receptor (each individual protein interacts with a unique receptor). Therefore, the main objective of this work is to employ the fluid–structure interaction analysis to study the effect of flow turbulences on the deflection of microcantilever as well as flow and heat transfer characteristics in a fluidic cell for various pertinent parameters. This study will enhance both design and the performance of microcantilevers in fluidic cells. Moreover, heat flow from and within the microcantilever governs its performance in all of its applications.

Section snippets

Mathematical formulation

Consider a two-dimensional, steady, incompressible flow through a fluidic cell having a length L and height H. It is assumed in this investigation that the flow is incompressible. The fluidic cell contains a microcantilever aligned along the centerline of the fluidic cell. The physical model and computational domain for such a fluidic cell are illustrated in Fig. 1. An arbitrary Lagrangian–Eulerian formulation was employed to describe the fluid motion in the FSI model. Furthermore, the

Conclusions

The current numerical investigation study the fluid–structure interaction model of fluid flow and heat transfer around a flexible microcantilever in a fluidic cell. The effect of varying inlet fluid velocity, height of the bluff body, elasticity of the microcantilever, and the introduction of an external noise on the deflection of the microcantilever was demonstrated in this investigation. The governing continuity, momentum and energy transfer equations are solved based on a Galerkin method of

Acknowledgement

The authors express their thanks to the reviewer for his valuable comments and suggestions.

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