An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes

The work in this paper concerns the axisymmetric pipe ow of a Herschel-Bulkley uid, with the aim of determining a relation between the critical velocity (de ning the transition between laminar and turbulent ow) and the pipe diameter in terms of the Reynolds number Re3. The asymptotic behaviour for large and small pipes is examined and simple expressions for the leading order terms are presented. Results are then compared with experimental data. A nonlinear regression analysis shows that for the tested uids the transition occurs at similar values to the Newtonian case, namely in the range 2100 < Re3 < 2500.