Modeling of pressure and shear-driven flows in open rectangular microchannels

Analytical expressions are derived for the mean velocity of a liquid flowing in an open rectangular microchannel. Solutions are decomposed into additive components driven by pressure gradients and by shear stresses on the liquid/vapor interface. Speeds are computed numerically for meniscus contact angles ranging from 0° to 90°, arbitrary channel aspect ratios, and for wetting regimes ranging from liquid-full to nearly-dry corner flows. These numerical results are used to guide the development of several analytical expressions that apply in asymptotic limits of fluid depth and contact angle. The resulting asymptotes are then blended analytically to obtain relatively simple, accurate, and comprehensive expressions for the mean velocity.