Mass transfer from small particles suspended in turbulent fluid

Abstract

Small rigid spherical particles are suspended in fluid, and material is being transferred from the surface of each sphere by convection and diffusion. The fluid is in statistically steady turbulent motion maintained by some stirring device. It is assumed that the Péclet number of the flow around a particle is large compared with unity, so that a concentration boundary layer exists at the particle surface, and that the Reynolds number of the flow around the particle is sufficiently small for the velocity distribution near the particle surface to be given by the Stokes equations.

The flow around a particle is a superposition of (a) a streaming flow due to a translational motion of the particle relative to the fluid with a velocity proportional to the density difference, and (b) a flow due to the velocity gradient in the ambient fluid. An expression for the mean transfer rate which is asymptotically exact for large Péclet numbers is obtained in terms of statistical parameters of these two superposed flow fields. As a consequence of the partial suppression of convective transfer by particle rotation, the only relevant parameters are the mean translational velocity of the particle in the direction of the ambient vorticity vector and the mean ambient rate of extension in the direction of the ambient vorticity. The former is shown to be zero in common turbulent flow fields, and an expression for the latter in terms of the mean dissipation rate ε is obtained from the equilibrium theory of the small-scale components of the turbulence. The final non-dimensional expression for the transfer rate is 0·55(a²ε^½/κν^½)^1/3, where a is the particle radius. This is found to agree well with some previously published sets of data for values of $a^2\epsilon^{\frac{1}{2}}/\nu^{\frac{3}{2}}$ less than 10².