Kinetic Modeling of Temperature Driven Flows in Short Microchannels

The temperature driven gas flow in a two-dimensional finite length microchannel and a cylindrical tube are studied numerically with the goal of performance optimization of a nanomembrane-based Knudsen compressor. The numerical solutions are obtained using direct simulation Monte Carlo method and discrete ordinate method for BGK model kinetic equation in a wide range of Knudsen numbers from 0.05 to 50. The lengthto-height ratios from 5 to 30 were examined. Three different wall temperature distributions were considered, namely, linear, stepwise, and a non-monotonic profile typical for a radiantly heated Knudsen compressor membrane. The short channel end effects are characterized, and the sensitivity of the mass flow rate to a non-monotonic temperature distribution is shown. INTRODUCTION Lab on a chip technology is drawing the attention of scientists from many disciplines. Recent advances in MEMS manufacturing have made it possible to construct microscale analytical sensors such as integrated gas chromatography systems, miniature spectrometers, and mass spectrometers. The miniatur∗Address all correspondence to this author. ized detection devices will require microscale roughing pumps to provide sensor elements with gas samples at necessary environmental conditions. A pumping mechanism that can be exploited at microscale is thermal transpiration, a rarefied gas effect that drives the gas flow along the temperature gradient in a tube or channel. The main goal of this paper is the numerical study of thermal transpiration flows in short microchannels to aid in the performance optimization of a transpiration based microscale roughing pump known as the Knudsen compressor [1]. In early 1900s M. Knudsen built and studied the first transpiration based compressor, consisting of a series of differentially heated and cooled capillaries. Each stage of the compressor had a capillary section where the wall temperature increases, causing a thermomolecular pressure build-up at the high-temperature end of the capillary. The capillaries are followed by a connector stage of a significantly larger cross-sectional area, where the pressure is almost constant and temperature is decreased to its original value at the beginning of the stage. The modern version of Knudsen compressor was suggested by Pham-Van-Diep et al [2] and demonstrated by Vargo and Muntz [3]. The most critical element of the Knudsen compressor developed at USC is the thermal transpiration membrane made of porous materials, such as aerogel, with pore diameters on the order of the mean free 1 Copyright c © 2005 by ASME Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.