Mechanisms of mass transfer to small spheres sinking in turbulence

Abstract

Using laboratory experiments and numerical simulations, we examine the transfer of soluble material from small, spherical particles sinking in homogeneous turbulence at large Péclet number. A theoretical analysis predicts two distinct mechanisms of convective mass transfer: strain due to turbulence and slip due to gravitational settling. Their relative strength is parametrised by the sinking ratio, ${Sr} = w_0 \tau _\eta /a$ , where $w_0$ is the quiescent settling velocity, $a$ is the particle radius and $\tau _\eta$ is the Kolmogorov time scale. This analysis predicts that the topology of the concentration wake changes from a symmetric topology at ${Sr} \ll 1$ to an asymmetric topology at ${Sr} \gg 1$ as the dominant mechanism of mass transfer changes. Particle tracking flow visualisations of small spheres releasing dye in turbulence confirm the existence of this change in mechanism at ${Sr} = O(1)$ . We complement these experiments with numerical simulations of the mass transfer from sinking particles. The transfer rate predicted by the simulation is found to be in good agreement with literature data for mass transfer to turbulent suspensions of solid particles and is consistent with asymptotic expressions for mass transfer in uniform flow when ${Sr} \gg 1$ . A decomposition of the convective fluxes confirms the transition in the transfer mechanism. At ${Sr} = O(1)$ , both mechanisms provide comparable contributions to the transfer rate. Cross-correlation analysis reveals that particle-scale knowledge of both the recent strain and velocity history is required to predict the instantaneous transfer rate. Turbulence-induced particle rotation has a modest suppression effect upon convective transfer by sinking.