Tham khảo tài liệu 'bio-mems technologies and applications - wang and soper (eds) part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 146 Bio-MEMS Technologies and Applications mean flow velocity lengths are nondimensionalized to a characteristic length LC such as a channel hydraulic diameter time is nondimensionalized to a characteristic time scale of the flow TC and pressure is nondimension-alized to a characteristic pressure The nondimensional Navier-Stokes equation may be written as follows Re 1 du _ u Vu St dt -Vp V2 u where St is the Strouhal number Te- st 77-- LC UC where Tc is a characteristic time scale of the transient fluid behavior. In the case of microscale phenomena related to fluid flows the characteristic length scale is on the order of microns. Thus the Reynolds number is usually on the order of 1 or For most microfluidic problems the flow is assumed to be in a quasi-steady state so that the flow is either steady or slowly changing so that the Strouhal is equal to 1. Then as the Reynolds number becomes small Re 1 Re st 1 the inertial terms become negligible compared to the viscous forces. Thus the left-hand terms of Equation disappear relative to the righthand terms and the viscous force balances the pressure force which is known as the creeping flow limit 12 . Vp V2 u A physical interpretation of Equation is that the left-hand terms correspond to body or inertial forces of the fluid and the right-most term is a surface viscous term through which the fluid transmits shear on a boundary. As the characteristic length scale of a flow decreases the volume of the fluid in the channel decreases so there is less mass through which body forces may act. At the same time the relative surface area of the flow geometry increases leading to greater surface forces which become more dominant in 1 Water-filled p 1000 Kg m3 LI Pa-s channel with a hydraulic diameter L of m traveling at an average velocity U of m s . 2007 by Taylor Francis Group LLC Micropump Applications in Bio-MEMS 147 determining the flow mechanics. Equation is merely a .
