Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Periodic polymer photonic bandgap structures for on-chip optical cavities

Integrated on-chip optical platforms enable high performance in applications of high-speed all-optical or electro-optical switching, wide-range multi-wavelength on-chip lasing for communication, and lab-on-chip optical sensing. Integrated optical resonators with high quality factor are a fundamental component in these applications. Periodic photonic structures (photonic crystals) exhibit a photonic band gap, which can be used to manipulate photons in a way similar to the control of electrons in semiconductor circuits. This makes it possible to create structures with radically improved optical properties. Compared to silicon, polymers offer a potentially inexpensive material platform with ease of fabrication at low temperatures and a wide range of material properties when doped with nanocrystals and other molecules. In this research work, several polymer periodic photonic structures are proposed and investigated to improve optical confinement and optical sensing. We developed a fast numerical method for calculating the quality factor of a photonic crystal slab (PhCS) cavity. The calculation is implemented via a 2D-FDTD method followed by a post-process for cavity surface energy radiation loss. Computational time is saved and good accuracy is demonstrated compared to other published methods. Also, we proposed a novel concept of slot-PhCS which enhanced the energy density 20 times compared to traditional PhCS. It combines both advantages of the slot waveguide and photonic crystal to localize the high energy density in the low index material. This property could increase the interaction between light and material embedded with nanoparticles like quantum dots for active device development. We also demonstrated a wide range bandgap based on a one dimensional waveguide distributed Bragg reflector with high coupling to optical waveguides enabling it to be easily integrated with other optical components on the chip. A flexible polymer (SU8) grating waveguide is proposed as a force sensor. The proposed sensor can monitor nN range forces through its spectral shift. Finally, quantum dot - doped SU8 polymer structures are demonstrated by optimizing spin coating and UV exposure. Clear patterns with high emission spectra proved the compatibility of the fabrication process for applications in optical amplification and lasing.

Numerical calculation of diffraction coefficients from building edges using FDTD method

Finite Difference Time Domain (FDTD) Method and software are applied to obtain diffraction waves from modulated Gaussian plane wave illumination for right angle wedges and Fast Fourier Transform (FFT) is used to get diffraction coefficients in a wideband in the illuminated lit region. Theta and Phi polarization in 3-dimensional, TM and TE polarization in 2-dimensional cases are considered respectively for soft and hard diffraction coefficients. Results using FDTD method of perfect electric conductor (PEC) wedge are compared with asymptotic expressions from Uniform Theory of Diffraction (UTD). Extend the PEC wedges to some homogenous conducting and dielectric building materials for diffraction coefficients that are not available analytically in practical conditions. ^