Vortex-driven chemical species transport near a sharp corner

We investigate how the advection and diffusion dynamics of a single chemical species are affected by Moffatt eddies, a low-Reynolds-number flow pattern emerging near a corner. To this end, we seek scale-free solutions to the 2D diffusion-advection equation to characterize the radial and angular dependence of the concentration field by using Moffatt's velocity profiles. The Lie symmetry method is used to analyze the 2D diffusion advection equation and obtain a similarity ansatz.The equation is then reduced into a 2nd order PDE in spatial variables only. This gives us a basic understanding of the role of advection and diffusion near singularities such as efficiency of chemical signal transport during protrusion formation inside a mesenchymal cell.