Macroscopic Conservation Equation Based
Model For Surface Tension Driven Flow
Author(s)
T. M. Adams & A. R. White
Abstract
Due to the small scales encountered in MEMS and microfluidic devices, surface
tension can play a significant role in the device physics. As such, many
microscale devices have exploited surface tension forces to serve as passive
valves and to move fluids. Surprisingly, few models for surface tension driven
flow seem to have been developed.
In this study a theoretical mathematical model for surface tension driven flow
through a capillary of an arbitrary cross section is derived. The model is based on
macroscopic mass and momentum balances, allowing for different physical
insights to be drawn compared to approaches starting with the Navier-Stokes
equations. Expressions for flow length and velocity are derived for both
frictionless flow and for flow with wall friction. For frictionless flow the result
of surface tension force is to increase the momentum of the fluid by constantly
drawing mass into the capillary at a constant characteristic velocity. In the case
of flow with wall friction, a characteristic time scale can be calculated. For times
on the order of the characteristic time scale, the flow velocity exponentially
decays from the characteristic velocity, whereas for larger times the velocity
shows an inverse power law dependence. The model well predicts flow
behaviour for previously published experiments in which the characteristic time
is small. For systems in which the characteristic time is larger, the model may
show improved performance over previous models.
Keywords: capillary, microchannel, microfluidics, surface tension.
1 Introduction
With the rapid development of microfluidic devices over the past decade, the
favourable scaling of surface tension with small dimensions has been exploited
Keywords
capillary, microchannel, microfluidics, surface tension.
Related Book
Other papers in this volume
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