Fibre suspensions in Hagen–Poiseuille flow: Transition from laminar plug flow to turbulence

• We examine the effect of plug during transitional flow for a fibre suspension.
• Using UDV, we estimated the yield stress and Reynolds stress of the suspension.
• With increasing Reynolds number the plug of fibres diminished in a complex manner.
• The plug size scales with the ratio of the Reynolds stress to yield stress.
• The yield stress varied non-monotonically with flow rate for each suspension tested.

The focus of the present work is an experimental study of the behaviour of semi-dilute, opaque fibre suspensions during fully-developed pressure-driven flow in a cylindrical pipe. We measure the instantaneous velocity profiles across the radius R   of the pipe, using ultrasound doppler velocimetry (UDV), as a function of the applied hydraulic pressure and concentration (0.75–1.75% (wt/wt)). In total 374 conditions were tested on three different flexible, non-Brownian fibre suspensions. The goal of the work was to gain insight into the role of the plug during transition to turbulence. From the UDV measurements, we estimated the radius of the plug rprp, the yield stress of the suspension τyτy, through knowledge of the pressure drop, as well as the Reynolds stress ρu′2‾. We find that the yield stress varied non-monotonically with flow rate for each suspension tested. At slow flow, i.e. when rp/R→1rp/R→1, we observe that plug densification, i.e. a contraction of the plug created by the growth of a lubricating film at the wall, caused the initial increase in yield stress. Yield stress was found to continue to increase with flowrate and its maximum was reached at 0.4