Salt solutions with two or more salts generate ion currents analogous to magnetic field lines

A gradient of a single salt in a solution generates an electric field, but not a current. Recent theoretical work by one of us [Phys. Rev. Lett. 24, 248004 (2020)] showed that the Nernst-Planck equations imply that crossed gradients of two or more different salts generate ion currents. These currents in solution have associated non-local electric fields. Particle motion driven by these non-local fields has recently been observed in experiment by Williams et al. [Phys. Rev. Fluids 9, 014201 (2024)]; a phenomenon which was dubbed action-at-a-distance diffusiophoresis. Here we use a magnetostatic analogy to show that in the far-field limit, these non-local currents and electric fields both have the functional form of the magnetic field of a magnetic dipole, decaying as r^(-d) in d = 2 and d = 3 dimensions. These long-ranged electric fields are generated entirely within solutions and have potential practical applications since they can drive both electrophoretic motion of particles, and electro-osmotic flows. The magnetostatic analogy also allows us to import tools and ideas from classical electromagnetism, into the study of multicomponent salt solutions.