Microelectromechanical systems (MEMS) have widespread applications in medical, electronical and mechanical devices. These devices are characterized by the smallest dimension which is at least one micrometer and utmost one millimeter. Rapid progress in the manufacture and utilization of these microdevices has been achieved in the last decade. Current manufacturing techniques of such devices and channels include surface silicon micromachining; bulk silicon micromachining; lithography; electrodeposition and plastic molding; and electrodischarge machining (EDM). In recent years, electrostatic, magnetic, electromagnetic and thermal actuators, valves, gears and diaphragms of dimensions of hundred microns or less have been fabricated successfully. Sensors have been manufactured that can detect pressure, temperature, flow rate and chemical composition in such channels. Physical effects such as electrokinetics, pressure gradient and capillarity become prominent for channels where the length scales are of the order of hundreds of micrometers. Also, at such length scales, the application of conventional numerical techniques that use macroscale equations to describe the phenomenon is questionable as the validity of the no-slip boundary condition depends on the ratio of the mean free path of the fluid molecules to the characteristic dimension of the problem (called the Knudsen number). Macroscale equations can only be applied if Knudsen number is of the order of 10-3 or less. In recent years, the lattice Boltzmann method (LBM) has emerged as a powerful tool that has replaced conventional macroscopic techniques like Computational Fluid Dynamics (CFD) in many applications involving complex fluid flow. The LBM starts from meso- and microscopic Boltzmann's kinetic equation and can be used to determine macroscopic fluid dynamics. The origins of LBM can be drawn back to lattice gas cellular automata (LGCA) which lacked Galilean invariance and created statistical noise in the system. LBM on the other hand possesses none of these drawbacks of LGCA, and is easy to implement in complex geometries and can be used to study detailed microscopic flow behavior in complex fluids/fluid mixtures. Nor does it have any of the drawbacks of the Navier-Stokes solvers of implementing the slip boundary condition on the surface of a solid. It has also been found to be computationally fast and an alternative to Navier-Stokes equations. In this study, LBM is used to simulate two-fluid flows such as bubbles rising in a liquid, droplet impingement on a dry surface and creation of emulsions in microchannels. Simulation of disperse flows in a continuous medium using simple boundary condition methods lays the foundation of conducting complex simulations for the formation of droplets past a T-junction microchannel in the framework of this statistical method. Simulations in a T-junction illustrate the effect of the channel geometry, the viscosity of the liquids and the flow rates on the mechanism, volume and frequency of formation of these micron-sized droplets. Based on the interplay of viscous and surface tension forces, different shapes and sizes of droplets were found to form. The range of Capillary numbers simulated lies between 0.001 [less than or equal to] Ca [less than or equal to] 1.0. Different flow regimes are observed that can be described based on the Capillary number of the flow. A flow regime map that lists where droplet or parallel flow may occur has been created based on the flow rate ratio and Capillary number for a purely laminar flow in the microchannel.

Graduation Date





Kumar, Ranganathan


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Mechanical, Materials, and Aerospace Engineering









Release Date

April 2012

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)