Experimental studies on the flow through soft tubes and channels

Abstract

Experiments conducted in channels/tubes with height/diameter less than 1 mm with soft walls made of polymer gels show that the transition Reynolds number could be significantly lower than the corresponding value of 1200 for a rigid channel or 2100 for a rigid tube. Experiments conducted with very viscous fluids show that there could be an instability even at zero Reynolds number provided the surface is sufficiently soft. Linear stability studies show that the transition Reynolds number is linearly proportional to the wall shear modulus in the low Reynolds number limit, and it increases as the 1/2 and 3/4 power of the shear modulus for the ‘inviscid’ and ‘wall mode’ instabilities at high Reynolds number. While the inviscid instability is similar to that in the flow in a rigid channel, the mechanisms of the viscous and wall mode instabilities are qualitatively different. These involve the transfer of energy from the mean flow to the fluctuations due to the shear work done at the interface. The experimental results for the viscous instability mechanism are in quantitative agreement with theoretical predictions. At high Reynolds number, the instability mechanism has characteristics similar to the wall mode instability. The experimental transition Reynolds number is smaller, by a factor of about 10, than the theoretical prediction for the parabolic flow through rigid tubes and channels. However, if the modification in the tube shape due to the pressure gradient, and the consequent modification in the velocity profile and pressure gradient, are incorporated, there is quantitative agreement between theoretical predictions and experimental results. The transition has important practical consequences, since there is a significant enhancement of mixing after transition.