Journal of the Chinese Institute of Engineers, Vol. 25, No. 1, pp. 57-65 (2002) 57 THE ZEROTH ORDER SOLUTION OF THE VELOCITY FIELD AROUND MICRO COMB STRUCTURES WITH LATERAL OSCILLATION Chi-Yuan Lee 1 , Lung-Jieh Yang 2 and Ping-Hei Chen 1 * 1 Department of Mechanical Engineering National Taiwan University Taipei, Taiwan, 106, R.O.C. 2 Department of Mechanical Engineering Tamkang University Tamsui, Taiwan, 251, R.O.C. Key Words: damping ratio, micro comb structure, micro-electro-me- chanical systems (MEMS). ABSTRACT This work models the flow around the comb structure of a sur- face-machined microaccelerometer as a two-dimensional, time-periodic, incompressible flow with periodic boundary conditions. The corre- sponding two-dimensional Navier-Stokes equation generally has no analytical solution. However, using small-size scaling, the dominant diffusion mechanism of the micro flow pattern simplifies the govern- ing equations into one set of diffusion equations. Moreover, this in- vestigation presents an analytical approximation combined with the method of separating variables in a complex-variable domain, to solve the two-dimensional diffusion equation of the velocity field. The pre- cise analysis of air damping herein could predict the frequency response of the micro comb structures dynamic behavior. *Correspondence addressee I. INTRODUCTION In recent decades, semiconductor microaccelero- meters, fabricated using micro-electro-mechanical systems (MEMS) technology, have made a large im- pact on the design of high resolution and high preci- sion semiconductor micro-sensors. The commercial- ized ADXL-05 and -50, developed by the Analog Device Corp., are classical examples of successful products developed using this technology. For these accelerometers, the involved techniques include ca- pacitive-sensing, electrostatic force feedback, and comb-shaped electrodes with length scales in the µm range; these techniques are necessary, and must be guaranteed, for the good performance of micro sensors. Therefore, not only the evaluation of capaci- tance and the electrostatic force of the micro comb- structure have to be precisely controlled, but also the damping effect due to the flow field around the comb- structure must be investigated to ensure the efficient dynamic behavior of the accelerometer (Howe et al ., 1996; Kuehnel and Sherman, 1994). Previous studies have discussed the damping effect of micro accelerometers fabricated through the use of silicon bulk micromachining. In those accelerometers, the gap between the seismic mass and