Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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Stokes Flow Through a Microchannel with Projections of Constant Spacing

일정 간격의 돌출부를 갖는 마이크로채널 내의 스톡스 유동 해석

  • Son, JeongSu (Dept. of Mechanical Engineering, Chonnam Nat'l Univ.) ;
  • Jeong, Jae-Tack (Dept. of Mechanical Engineering, Chonnam Nat'l Univ.)
  • Received : 2014.10.13
  • Accepted : 2014.12.16
  • Published : 2015.04.01
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Abstract

In this study, we analyzed a two-dimensional Stokes flow through a microchannel containing projections with constant spacing attached to each wall. The projections on the top and bottom walls were semi-circular in shape, with in-phase locations. By considering the periodicity and symmetry of the flow, the eigenfunction expansion and least squared error method were applied to determine the stream function and pressure distribution. For some typical radius and spacing values, the streamline patterns and pressure distributions in the flow field are shown, and the shear stress distributions on the boundary walls are plotted. In addition, the average pressure gradients in the microchannel are also calculated and shown with the radius and spacing of the projections. In particular, the results for the case of extremely small gaps between the projections on the top and bottom walls are in good agreement with the lubrication results.

본 연구에서는 채널 벽면에 돌출물이 일정 간격으로 부착되어 있는 마이크로채널을 통과하는 2차원 스톡스 유동을 이론적으로 고찰한다. 상하 벽면에 부착된 돌출물들은 모두 반원 형상이고 서로 동일한 위상에 위치한다. 채널 내 유동의 주기성과 대칭성을 고려한 고유함수 전개법과 오차의 최소제곱법을 사용하여 유동장을 해석하여 유동함수 및 압력분포를 구하였다. 돌출물의 반경과 간격의 몇 가지 값들에 대하여 유동장 내의 유선 및 압력분포도를 보이고, 경계벽면에서의 전단응력 분포 등을 도시하였다. 또한, 돌출물의 반경과 돌출물 사이의 간격 변화에 따른 마이크로채널 내 평균 압력강하율의 변화를 계산하여 그림으로 나타내었다. 특히 상하 돌출물 사이의 틈새가 매우 작은 경우, 그 계산결과는 윤활이론의 결과와 아주 잘 일치함을 확인하였다.

Keywords

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  1. STOKES FLOW THROUGH A MICROCHANNEL WITH PROTUBERANCES OF STAGGERED ARRANGEMENT vol.20, pp.4, 2015, https://doi.org/10.6112/kscfe.2015.20.4.109