(318j) Transport Limits on Dissolution from a Rotating Disk –Effects of Instabilities in the Flow

A rotating disk is the ”gold-standard” experiment for measuring surface reactions rates in geochemical and electrochemical systems. In ideal circumstances, described first by Levich, the mass transfer coefficient can be simply related to the intrinsic reaction rate at the surface. However, more recent works show that there are instabilities in the flow at much smaller Reynolds numbers (Re ≈ 10⁴ ) than the expected transition to turbulence (Re ≈ 10⁵ ). Laboratory measurements of mass transfer in a rotating disk experiment use a finite-size disk within a larger container of solution.

Our numerical simulations show that the critical Re for a typical experimental geometry is below 1000, which is much smaller than what is typically used in mass-transfer measurements. We observe the formation of coherent structures in the flow, which might suggest a non-uniform mass transfer at the disk.

Our simulations are finite volume based, using the OpenFOAM toolkit. Our code was validated in a rotor-stator geometry, by comparing with self similar solutions at low Re and with spectral solutions above the critical Re. I will present preliminary results for the flow field in a ”finite-disk” geometry. Here, starting at Re ≈ 800, the instability is initiated at the edge of the disk and propagates to the core of the fluid. Ongoing work is investigating the effects of the instability on the mass transfer at the disk surface.

Figure 1: Velocity magnitude within a slice of the fluid domain lying 0.25R above the top of a spinning disk (radius R). The velocity is highest in the region right above the disk (red). Coherent structures, indicated by variations in the velocity, extend throughout the whole fluid domain and rotate with time at a lower speed than the fluid. The Reynolds number of the flow is about 1000. The black circle indicates the perimeter of the spinning disk.