Instabilities in the flow generated by a finite-size rotating disk

A rotating disk is the canonical experiment for measuring surface reaction rates in geochemical and electrochemical systems. Using the similarity solution for laminar flow around an infinite disk, the mass transfer coefficient can be simply related to the intrinsic reaction rate at the surface. However, measurements of mass transfer rates use a finite-size disk within a larger container of solution. Numerical simulations suggest that the flow around a finite-size disk becomes time dependent at Reynolds number below 1000, which is much smaller than the typical values in mass-transfer measurements (Re ~ 10⁴). We observe the formation of coherent structures in the flow, which suggest the possibility of a non-uniform mass transfer at the disk surface. In the specific geometry studied, a rotating-disk flow follows a similar sequence of instabilities to the Taylor-Couette flow: a centrifugal instability leading an axisymmetric, time-invariant flow, followed by a Hopf bifurcation to a time-periodic flow.. Increasingly chaotic flows at higher Reynolds number eventually lead to turbulence at Reynolds numbers between 3000 and 5000.