Deformation of ambient chemical gradients by sinking spheres

Abstract

A sphere sinking through a chemical gradient drags fluid with it, deforming the gradient. The sphere leaves a trail of gradient enhancement that persists longer than the velocity disturbance in the Reynolds , Froude and Péclet 102 regime considered here. We quantify the enhancement of the gradient and the diffusive flux in the trail of disturbed chemical left by the passing sphere using a combination of numerical simulations and scaling analyses. When is large and buoyancy forces are negligible, dragged isosurfaces of chemical form a boundary layer of thickness around the sphere with diameter. We derive the scaling from the balance of advection and diffusion in the chemical boundary layer. The sphere displaces a single isosurface of chemical a maximum distance that increases as. Increased flux through the chemical boundary layer moving with the sphere is described by a Sherwood number,. The gradient enhancement trail extends much farther than as displaced isosurfaces slowly return to their original positions through diffusion. In the reference frame of a chemical isosurface moving past the sphere, a new quantity describing the Lagrangian flux is found to scale as. The greater dependence of versus demonstrates the importance of the deformation trail for determining the total flux of chemical in the system. For , buoyancy forces are weak compared to the motion of the sphere and the preceding results are retained. Below , an additional Froude dependence is found and. Buoyancy forces suppress gradient deformation downstream, resulting in and. The productivity of marine plankton - and therefore global carbon and oxygen cycles - depends on the availability of microscale gradients of chemicals. Because most plankton exist in the fluids regime under consideration, this work describes a new mechanism by which sinking particles and plankton can stir weak ambient chemical gradients a distance and increase chemical flux in the trail by a factor of.