Ph.D Thesis

Ph.D StudentGat Amir
SubjectFlow in Shallow Micro-Channels
DepartmentDepartment of Aerospace Engineering
Supervisors PROFESSOR EMERITUS Itzchak Frankel
Full Thesis textFull thesis text - English Version


Micrometer-sized systems, made possible by modern micro-fabrication techniques, enable the reduction of weight, power consumption, and production costs of various systems. Many of these micro-systems involve gas or liquid flows through some or all of their components. Micro-systems have a potential to create entirely new applications and significantly contribute to future science and technology. In order to achieve these goals a comprehensive understanding of the physics of flows in the micro regime is needed.

Gaseous and liquid flows through straight and uniform micro-channels have been studied extensively by numerous researchers. However, many applications involve more complex geometries and networks of micro-channels which include elements such as channel bends, constrictions and junctions. The study of gaseous and liquid flows through non-uniform configurations and micro-channel networks is therefore of considerable interest and will be the focus of this thesis. Owing to the relative large influence of surface forces, micro-flows are typically characterized by small Reynolds numbers and nearly uniform temperatures. Furthermore, due to current manufacturing techniques, these flows often take place in the narrow gap between parallel planes. In this research we utilize these typically shallow geometries and small Reynolds numbers to develop a first-order asymptotic model for non-uniform geometries. The model includes the effects of weak rarefaction, low-Mach-number compressibility and various side wall geometries. A closed-form solution for channel configurations with general planform and side walls geometries was formulated via use of analytic-function theory and Green's functions. The general solution was then applied to obtain explicit analytic solutions describing the flow field within curved and sharp edged bends of various angles, bifurcations, junctions, constrictions and expansions.

Utilizing the computed viscous resistances of micro-channel bends and junctions, the flows through tree-like networks and parallel-channel networks are analyzed and optimized. Significant improvements of the optimization objectives are achieved by relatively small modifications to the networks geometries. The accuracy of the results was validated by comparisons to numerical simulations and existing experimental data. Our model gives quantitative solutions for realistic geometries with depth to width ratio of up to 1/3 and Reynolds numbers of up to 5. The analytic method presented in this thesis is general and can readily be applied to the design and optimization of a variety of other shallow geometries and to enable analysis and optimization of complex channel networks.