Magnetohydrodynamics and Fluid Structure Interaction Model for Flow in a Cantilever Microtube

Microtubes containing magnetic fluid have numerous applications in microfluidic and nanotechnology systems, including mixing, drug delivery, and microcantilever biosensors. The Lorentz force, induced by the interaction of flow velocity and magnetic field, can be used to guide or influence the flow within these microtubes. An important consideration and potential opportunity when using microtubes with magnetic fluid for biosensing applications is the vibration of the tube caused by fluid traction. In this work, we investigate the effect of a transverse magnetic field on the vibration and oscillations of cantilever microtubes conveying magnetic fluid, utilizing flow lubrication theory. We couple the Euler–Bernoulli beam model with the Navier-Stokes flow equations to derive a fluid-structure interaction (FSI) model for analyzing the vibrations of the cantilever microtube. The results indicate that a transverse magnetic field can significantly impact the flow motions and structural dynamics of the tube by increasing the system's natural frequencies and critical flow velocity, thereby contributing to the system's dynamic instability.