@article { Dubasch2010, title = {An oscillatory instability in microchannel flows of thermally responsive fluids}, journal = {Journal of Engineering Mathematics }, volume = {71}, year = {2011}, month = {08/2011}, pages = {31-53}, abstract = {A simple asymptotic model for the flow of a thermally responsive fluid in a microtube is derived. At low temperatures these fluids behave as a Newtonian fluid; however, above a critical temperature they (reversibly) form gel-like structures. Also, because of the small length scales involved in microfluidic flows, viscous heating can become significant. This can lead to gelation simply from the temperature change due to viscous heating. Our model takes into account viscous heating, as well as possible conduction through the channel walls. The rheology of the thermally responsive fluid is modelled using a bi-viscosity model, with the gel phase being represented by a constant large viscosity. The model is then used to show that, when the viscous heating exceeds a critical level, an oscillatory flow behaviour can occur. These oscillations eventually become damped out as the system reaches a steady state; however, the time it takes for this to occur can become excessively large. The physical mechanisms that cause the oscillatory behaviour are examined, and the criteria for the oscillatory flow to occur are determined. Some analysis of the oscillations and the timescales involved therein are also presented. }, URL = {http://www.springerlink.com/content/2xhn5tk47rk16r38/}, author = {Neville Dubash and Ian A. Frigaard and Boris Stoeber} }