Swirling-annular-flow-induced instability of a micro shell considering Knudsen number and viscosity effects

This paper investigates the instability of the outer thin-walled micro shell subjected to the swirling flowing fluid, where flowing fluid passes through the annular space formed by both inner and outer shells. The inviscid fluid hydrodynamic pressure and steady viscous forces are obtained respectively. The equations of motion are derived by the Hamilton’s principle and solved with the zero-level contour and travelling-wave approaches. The impact of various parameters such as material parameters, fluid structure, fluid viscosity and Knudsen number, on the instability behaviors of this fluid-micro shell system is displayed. The findings of the research indicate that the elastic modulus is a prominent factor of affecting instability, and the shear couple forces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msub> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>γ</m:mi> </m:mrow> <m:mo>̄</m:mo> </m:mover> </m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mi>θ</m:mi> </m:mrow> </m:msub> </m:math> γ ̄xθ have the most stabilizing effect leading to the increase of critical flow velocity by 14.454 %. The synergistic effect of the fluid viscosity and Knudsen number reduces the stability of such system by 80 %. The research contributes to understand the complex dynamical behaviors of fluid-conveying micro shell in design of micro devices including micromixer, microreactor, micro heat pipe.