Abstract
Steady flow through curved ducts has numerous applications in the chemical engineering sciences. A recent example is within the field of microfluidics in which curved ducts have cross-section dimensions much smaller than one millimetre. The validation of steady fluid flow through curved microfluidic ducts is a crucial part of verifying any experimental work or numerical modelling in this field. Of particular interest is a measure of the secondary flow which consists of a counter-rotating vortex pair in the cross-sectional plane. We develop a new model for the magnitude of the secondary flow velocity within curved ducts having rectangular cross-sections. Our modelling respects the scaling at asymptotically small flow rates while carefully considering how this is modified for increasing Dean number. Lastly, we discuss why this new model is a more appropriate benchmark of the secondary flow than a power law model commonly found throughout the literature.
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