On the nonlinear dynamics of a piezoresistive based mass switch based on catastrophic bifurcation

This research investigates the feasibility of mass sensing in piezoresistive MEMS devices based on catastrophic bifurcation and sensitivity enhancement due to the orientation adjustment of the device with respect to the crystallographic orientation of the silicon wafer. The model studied is a cantilever microbeam at the end of which an electrostatically actuated tip mass is attached. The piezoresistive layers are bonded to the vicinity of the clamped end of the cantilever and the device is set to operate in the resonance regime by means of harmonic electrostatic excitation. The nonlinearities due to curvature, shortening and electrostatic excitation have been considered in the modelling process. It is shown that once the mass is deposited on the tip mass, the system undergoes a cyclic fold bifurcation in the frequency domain, which yields a sudden jump in the output voltage of the piezoresistive layers; this bifurcation is attributed to the nonlinearities governing the dynamics of the response. The partial differential equations of the motion are derived and discretized to give a finite degree of freedom model based on the Galerkin method, and the limit cycles are captured in the frequency domain by using the shooting method. The effect of the orientation of the device with respect to the crystallographic coordinates of the silicon and the effect of the orientation of the piezoresistive layers with respect to the microbeam length on the sensitivity of the device is also investigated. Thanks to the nonlinearity and the orientation adjustment of the device and piezoresistive layers, a twofold sensitivity enhancement due to the added mass was achieved. This achievement is due to the combined amplification of the sensitivity in the vicinity of the bifurcation point, which is attributed to the nonlinearity and maximizing the sensitivity by orientation adjustment of the anisotropic piezoresistive coefficients.

Wettability and confinement size effects on stability of water conveying nanotubes

This study investigates the wettability and confinement size effects on vibration and stability of water conveying nanotubes. We present an accurate assessment of nanotube stability by considering the exact mechanics of the fluid that is confined in the nanotube. Information on the stability of nanotubes in relation to the fluid viscosity, the driving force of the fluid flow, the surface wettability of the nanotube, and the nanotube size is missing in the literature. For the first time, we explore the surface wettability dependence of the nanotube natural frequencies and stability. By means of hybrid continuum-molecular mechanics (HCMM), we determined water viscosity variations inside the nanotube. Nanotubes with different surface wettability varying from super-hydrophobic to super-hydrophilic nanotubes were studied. We demonstrated a multiphase structure of nanoconfined water in nanotubes. Water was seen as vapor at the interface with the nanotube, ice shell in the middle, and liquid water in the nanotube core. The average velocity of water flow in the nanotube was obtained strongly depend on the surface wettability and the confinement size. In addition, we report the natural frequencies of the nanotube as functions of the applied pressure and the nanotube size. Mode divergence and flutter instabilities were observed, and the activation of these instabilities strongly depended on the nanotube surface wettability and size. This work gives important insights into understanding the stability of nanotubes conveying fluids depending on the operating pressures and the wettability and size of confinement. We revealed that hydrophilic nanotubes are generally more stable than hydrophobic nanotubes when conveying fluids.

Bubble accumulation and its role in the evolution of magma reservoirs in the upper crust

Volcanic eruptions transfer huge amounts of gas to the atmosphere. In particular, the sulfur released during large silicic explosive eruptions can induce global cooling. A fundamental goal in volcanology, therefore, is to assess the potential for eruption of the large volumes of crystal-poor, silicic magma that are stored at shallow depths in the crust, and to obtain theoretical bounds for the amount of volatiles that can be released during these eruptions. It is puzzling that highly evolved, crystal-poor silicic magmas are more likely to generate volcanic rocks than plutonic rocks. This observation suggests that such magmas are more prone to erupting than are their crystal-rich counterparts. Moreover, well studied examples of largely crystal-poor eruptions (for example, Katmai, Taupo and Minoan) often exhibit a release of sulfur that is 10 to 20 times higher than the amount of sulfur estimated to be stored in the melt. Here we argue that these two observations rest on how the magmatic volatile phase (MVP) behaves as it rises buoyantly in zoned magma reservoirs. By investigating the fluid dynamics that controls the transport of the MVP in crystal-rich and crystal-poor magmas, we show how the interplay between capillary stresses and the viscosity contrast between the MVP and the host melt results in a counterintuitive dynamics, whereby the MVP tends to migrate efficiently in crystal-rich parts of a magma reservoir and accumulate in crystal-poor regions. The accumulation of low-density bubbles of MVP in crystal-poor magmas has implications for the eruptive potential of such magmas, and is the likely source of the excess sulfur released during explosive eruptions.