Experimental study of the instability of laminar flow in a tube with deformable walls

Abstract

The onset of instability of laminar flow in a tube with deformable walls is studied experimentally in order to characterize how the onset is affected by the elastic (shear) modulus of the deformable wall. To this end, rectangular blocks of polydimethylsiloxane (PDMS) gels of different shear moduli are fabricated with a cylindrical hole (of diameter 1.65 mm) in which the fluid (water) flow occurs due to an imposed pressure difference. The shear moduli of the PDMS gels were in the range of 21 - 608 kPa. When fluid flows through the deformable tube, we find that the tube radius changes slowly as a function of distance along the flow, and this change is a function of Reynolds number (Re). The pressure drop between the two ends of the tube is measured, and the friction factor is calculated from this pressure drop. The friction factor vs. Re data shows that the expected laminar flow relation (f = 64/Re) for flow in a rigid tube is seen in a deformable tube at lower Re, but there is a deviation from this relation at Re < 2000. We identify the Re at which the deviation occurs as the Reynolds number at which the laminar flow in the deformable tube becomes unstable. This transition Reynolds number is as low as 500 for the 21 kPa PDMS gel, the softest gel studied in this work, and this value is much lower than the critical Reynolds number (∼2000) for transition in a rigid tube. The onset of the transition is also independently corroborated using a dye-stream visualization method, and the transition Reynolds number obtained with this method agrees well with the Reynolds number at which there is a deviation in the friction-factor data from the laminar relation. This transition in a deformable tube which happens at Reynolds number much lower than 2000 could be potentially exploited in improving mixing in microscale devices.