(Invited) Thoughts on the Viscous Sublayer

Abstract

Years ago people postulated that there is a laminar sublayer near a solid wall in turbulent flow. Murphree (1932) and Levich (1942, 1944) postulated that the turbulence eddies decay only gradually as the solid wall is approached. There are two schools of thought: one says that the eddy diffusivity is proportional to y 3 near the wall; the other says y 4. Which is right? Perhaps there is some truth in both views. It may be that y 4 prevails near the outer limit of the viscous sublayer, adjacent to the outer turbulent flow, but that y3 prevails very close to the wall. It has been thought that this was important only for mass transfer in turbulent flow at high Schmidt numbers, that is, for diffusion coefficients much smaller than the kinematic viscosity. However, it is shown that Nikuradse’s data (1932) for pressure drops (or friction factors) in turbulent pipe flow do not agree with his very careful measurements of profiles of the eddy viscosity. In other words, the viscous sublayer cannot be ignored even in fluid flow. The profile of predicted eddy diffusivity of Wasan, Tien, and Wilke (1963) show regions of y 3 dependence very close to the wall and y dependence in the outer turbulent flow with perhaps a y 4 dependence in the intermediate region. On this diagram, one can identify the thickness of the diffusion layer as a function of the Schmidt number. As is well known, the diffusion layer gets very thin at high Schmidt numbers. Using this profile, one can show that the y 4 dependence will not show up clearly in mass-transfer data at any Schmidt number. Any region of y 4 dependence of the eddy diffusivity is outside the diffusion layer where the concentration does not change (at high Schmidt numbers). These thoughts inspire a method of calculating the profiles of eddy diffusivity and eddy viscosity from consideration of fluctuations themselves. Hopefully this can be a subject of future work.