Nonlinear behavior of micro electro-mechanical systems

This dissertation covers the study of nonlinear behavior in micro electromechanical systems (MEMS). Three problems relating to MEMS devices for cell biomechanics and microfluidics were solved, showing that detailed descriptions of the materials and device behavior offers new understanding of these systems and the opportunity to numerically optimize their performance.; Droplet formation in microfluidic systems is not well understood; without a better understanding it is hard to optimize system design and realize the full potential of these devices. Droplet formation in microfluidic T-junction devices was studied using experimental and numerical methods. The simulations agree well with experimental data from PDMS devices; they show that droplet pinch-off is controlled not by viscous stress, but caused rather by pressure buildup after channel blockage due to the second phase. The period of droplet formation is dependent on velocity of the flow, but not viscosity or interfacial tension of the fluids. Dimensionless period, which is identical to the dimensionless length of the droplets, is controlled primarily by water fraction, but also affected by velocity of the flow following a power law. Higher values of capillary number tend to extend the distance between the droplet pinch-off location and the T-junction. Droplet length does depend on flow velocity at low velocities, but reaches a relatively constant length at higher flow velocities. The coefficient of variation of droplet volume increases with increasing capillary number.; High density arrays of Polydimethylsiloxane (PDMS) cantilevers to measure basolateral cell forces offer new insight into cell mechanics and motility, but the equations used to convert displacement measurements to force often violate the basis for several simplifications in the deformation theories. Theoretical and numerical solutions for PDMS cantilever deflection are presented, incorporating bath shear strain and large-deflection theory. Numerical solutions of large deformation that also incorporate shear strain were necessary for PDMS cantilevers with aspect ratio L/D smaller than 10.; Applying small forces (in the pN to nN range) for experiments with single cells and strong molecular interactions is challenging. Electromagnetic needles (EMN) can be used with magnetic microparticles to apply forces in the nN range. The cores of the electromagnets in these devices are often tapered with sharp tips, in order to concentrate magnetic energy toward the particle. Existing devices have been designed based on generalities of magnetic theory and linear simplifications of the material properties. A detailed numerical study using finite element analysis associated with nonlinear magnetization curves of both the core and particle materials shows that optimal tip radii, to maximize applied force, is not the smallest radii possible. The effective range of the tip sharpness is a nonlinear function of the working distance. Furthermore, numerical optimization of the device geometry, using a direct search algorithm, resulted in an improvement in force production by an additional 10-fold over previous efforts.