Anyone who has flown in an airplane knows about turbulence, or when the flow of a fluid — in this case, the flow of air over the wings — becomes chaotic and unstable. For more than a century, the field of fluid mechanics has posited that turbulence scales with inertia, and so massive things, like planes, have an easier time causing it. Now, research led by engineers at the University of Pennsylvania has shown that this transition to turbulence can occur without inertia at all.
One of the most fundamental concepts in fluid dynamics is the Reynolds number, which describes the ratio between viscous forces and inertial forces for given fluids and the conditions they are flowing in. Low Reynolds numbers are associated with “laminar” flow, which is smooth and orderly, while high Reynolds numbers are associated with turbulent flow, which is nonlinear and chaotic.
The transition from smooth to turbulent has obvious implications for massive things, such as airplanes, but surprisingly, it also has an impact on small scales where mass should theoretically not play a factor. It is relevant to the flow of blood in capillaries, or in extracting oil or natural gas from porous rock, as is the case with fracking.
To explain how turbulence could arise even in the absence of inertia, the team set out to conduct an experiment similar to Reynolds’ famous one, but instead of changing the inertia of the fluid, they changed the fluid itself. In their study, they pumped a polymer-infused fluid through a pipe at a constant rate. Polymers are a common feature of non-Newtonian fluids — such as blood, ketchup or yogurt — which have flow properties that change under certain conditions. One of the main features of non-Newtonian fluids is that their material properties, such as viscosity, are nonlinear — there is not a direct relationship between the amount of force exerted on them and the speed at which they flow.
Beyond medical or industrial applications, understanding the interplay between non-Newtonian fluids and turbulence is an important contribution to the fundamentals of fluid mechanics.