Quantification and prediction of capillary fluid flow in planar nanochannels is essential to the development of many emerging nanofluidic technologies. Planar nanochannels are typically produced using the standard nanofabrication processes of thermal bonding or sacrificial etching. Both approaches may yield nanochannels that are bowed and/or exhibit non-uniform (i.e. non-planar) wall spacing. These variations in wall spacing affect the transient dynamics of a liquid plug filling the nanochannel, causing deviations from the classical behavior in a parallel-plate channel as described by the Washburn model. Non uniform wall spacing impacts the overall frictional resistance and influences the meniscus curvature. In this thesis, a new analytical model that predicts the meniscus location over time in micro- and nanochannels as a function of channel height was compared to experimental filling data of well-characterized channels with different heights. The wall-to-wall spacing of the utilized nanochannels exhibited height variations between 60 and 300 nm. The model was also validated with microscale channels that were fabricated with a linear variation in the wall-to-wall spacing from 100 µm to 400 µm. The filling speed and meniscus shape during the filling process were determined by dynamic imaging of the meniscus front for several different liquids. A modified Washburn equation that utilizes an effective channel height to predict the filling speed corresponding to the location of the tallest height within a channel was derived. A model was also developed to predict the meniscus distortion encountered in a non-constant height channel, provided the cross-sectional channel heights and the distance from the channel entrance are known. The models developed herein account for induced transverse pressure gradients created by non-constant channel heights. The models are compared to experimental data derived from both nanoscale and microscale channels with good qualitative agreement. These results demonstrate that the capillary flow in nanochannels with non-parallel-plate, linear tapered, or parabolic cross sections can be predicted.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





capillary, microchannel, nanochannel, parabolic, linear, parallel, effective height, Washburn, modified, non-uniform