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비대칭형 막기공을 통한 뉴톤 유체의 발산흐름(diverging flow)에 대한 심도있는 해석 결과를 제시하였다. 막기공 모델의 일반적 형태인 슬릿(slit)과 원뿔(cone)형 채널에 대해 미동흐름(creeping flow)을 적용하여 유속분포 관계식을 구하였다. 유속분포의 고찰로부터 발산각도 αlongrightarrow0 인 경우는 윤활근사법(lubrication approximation)이 적용되어 Poiseuille 흐름으로 되는 것을 확인하였고, 발산각도가 증가할수록 벽면부근에서의 유속분포는 결핍(depletion)됨과 아울러 전체유속은 감소하였다. 구해진 속도분포와 압력분포의 관계식으로부터 투과유량에 대한 이론식을 도출하였다. 예측된 결과는 기공의 비대칭성이 증가할수록 그에 따른 투과유량은 점차 증가하는 거동을 보였다. 본 연구의 이론결과는 궁극적으로 막여과에의 응용 측면과 밀접하게 연관되어 있다.
The extended analysis on the diverging flow through asymmetric membrane pores has been performed in this study. Afore rigorous equations of velocity profile relevant to the divergent slit and cone shaped channels, which are widely used as a general pore model, have been obtained by employing a creeping flow approach of Newtonian fluids. As a degree of asymmetry (i.e., diverging angle) is increased, the predicted flow function shifts Toward the center region due to the incorporated wall effect, so that the overall velocity profile becomes decreased. It is true, as expected, that when the divergent channel is in the low diverging angle limit, the channel flow results in the Poiseuillean fashion by utilizing a lubrication approximation. The flow rate equation of each type of channel has been developed from the combined solution of velocity profile and pressure fields. The effect of diverging flow on the flow rate enhancement has been remarkably predicted, in which the flow rate increases with the increase of pore asymmetry. The advantage of our theoretical results lies in the analytical expression for the diverging flow behavior through pore channels as well as its ability to play a fundamental role on the related membrane filtrations such as microfiltration and ultrafiltration.
