School of Mechanical Engineering Seminar
Monday, July 9 2018 at 14:00
Tokhna Building of Mechanical Engineering, Room 103

Design of the wall surface wetting properties for stabilization of desired separated flow configurations in micro channels.

Dmitriy Goykhman

M.Sc. student of Prof. Neima Brauner and Prof. Amos Ullmann

Stratified flow of two immiscible phases can be found in a variety of processes and equipment. In the last two decades, the microfluidics discipline has seen a phenomenal growth with increasing ranges of applications. Naturally, in macro systems, it is always the heavier fluid that forms the lower layer. In mini and micro channels, the role of gravity diminishes and surface tension and wall adhesion forces, along with viscous forces, become dominant. The flow pattern in the channel can be affected by the affinity of the fluids and the channel surface. This study examines to what extent the design of the wall surface wetting properties can be used as a mean to stabilize a desired separated flow configuration in micro channels. For example, performance considerations of the microfluidic system may show advantages of stabilizing configurations where the heavier phase flows above the light phase.

A practical design tool is obtained by introducing the constant curvature approximation to represent the shape of the phases interface and their stable location (e.g., top light or top heavy). The stable configuration is considered as the one associated with the lower free (gravitational and surface) energy. The closure obtained for the interface curvature via the approximate solution is combined with the available exact solution for stratified two-phase laminar flows with curved interfaces to obtain the corresponding phase flow rates and the associated flow characteristics. Finally, the assumption of constant interface curvature is relaxed, and an exact solution for the interface shape is presented by a solution of the Young-Laplace equation. This enables validation of the conclusions obtained based on the approximate constant curvature solution.

Electrostatically Actuated Bistable Cantilevers for Resonant Acceleration Sensing

Omer HaLevy

School of Mechanical Engineering, Faculty of Engineering,

Tel Aviv University, Ramat Aviv, 69978, Israel

omerlev1@mail.tau.ac.il

Resonant accelerometers incorporating vibrating beams demonstrate higher sensitivity and better robustness when compared to their statically operated counterparts. Operation of these devices in the vicinity of the critical instability points, often achieved by means of electrostatic softening, can result in an enhanced performance of resonant sensors. While double-clamped curved bistable beams can serve as resonant acceleration sensors, they suffer from high sensitivity to temperature and residual stress. Cantilevers are distinguished by low sensitivity to the thermal stress but their stiffness tuning is challenging.

In this research we report on a feasibility study of a displacement/acceleration sensor incorporating an electrostatically actuated bistable resonant cantilever as the sensing element. The concept is based on the tailoring of the device geometry and the actuating force in such a way that the beam in its initial “as fabricated” configuration is already positioned near the critical point.  Our reduced order Galerkin and coupled finite elements models results show that the frequency to deflection sensitivity of the L = 150 mm long, h = 16 mm wide and d = 1 mm thick cantilever can reach 20 Hz/nm. This is equivalent to the frequency to acceleration sensitivity of 388 Hz/g, obtained for the case of a 4 mm × 4 mm × 20 mm proof mass. The devices incorporating ≈ 50 mm thick electrodes and ≈ 6 µm thick cantilevers were fabricated from a silicon on insulator (SOI) wafer using deep reactive ion etching (DRIE). We discuss the fabrication process and present preliminary experimental results. The second part of the work is focused on the exploration of the synchronization (lock-in) phenomenon in resonant sensors. The lock-in effect often limits the performance of differential resonant sensors containing two oscillators and operated in an anti-phase (tuning fork) mode. We present a reduced order model of a generic tuning fork device. The model accounts for the geometric nonlinearity of the vibrating beams and for the nonlinear coupling. The results of the numerical investigation are presented and role of various parameters on the device behavior is discussed.

School of Mechanical Engineering Seminar
Monday, June 25, 2018 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

Shear stress induced by a fluid on the surface of a hydraulically driven crack.

Energy release rate in hydraulic fracture: Should or should not one take the phenomenon of the shear stress into account?

Professor Gennady Mishuris
Royal Society Wolfson Research Merit Award Holder
Department of Mathematics, IMPACS, Aberystwyth University
http://www.aber.ac.uk/en/maths/staff-list/staff_profiles/?login=ggm 

The talk consists of two parts.

In the first one, we briefly overview recent advance in the mathematical and numerical modelling of Hydraulic Fracture leading to an explicit level set algorithm based in particular on the accurate accounting for the solution asymptotics.

Then, in the second part, we discuss a novel HF model which accounts for the hydraulically induced shear stresses at the crack faces. It utilizes a general form of the elasticity operator alongside a revised fracture propagation condition based on the critical value of the energy release rate. 

We show that the revised formulation is always in agreement with the linear elastic fracture mechanics. We show that the phenomenon may play a significant role in the case of so-called small toughness and viscosity dominated regimes while in the other regimes it provides the analogous result as the classic model. We have also found that the small toughness regime should be no longer considered as a computational challenge. Finally, in those regimes, predicted crack redirection angle may change dramatically in comparison with the classic approach. We believe that the modified formulation opens new ways to analyse the physical phenomenon of HF, as well as improving the reliability and efficiency of its numerical simulation (our numerical simulations have already highlighted advantages of the model).