Modelling laminar pulsed flow in rectangular microchannels

Fully developed laminar pulsed flow of an incompressible Newtonian fluid through rectangular ducts has been modelled and analyzed using Green functions. Based on the solutions for the velocity profile presented previously [Fan, C., Chao, B.-T., 1965. Unsteady, laminar, incompressible flow through rectangular ducts. Zeitschrift für Angewandte Mathematik und Physik 16, 351–369], exact analytical solutions in series form for wall shear stress and volumetric flow rate have been obtained. Various flow effects in periodic pulsed flow through rectangular microchannels, including flow reversal, phase shift and wall shear stress enhancement were calculated indicating that a substantial increase in local wall shear stress can be achieved with a modest increase of average flow rate over a cycle. The analytical solutions and the calculated results will help optimize parameters in cleaning of microfluidic devices by pulsed flow.