Deformation of ambient chemical gradients by sinking spheres

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 Peclet 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 .