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Non-Faradaic electric currents in the Nernst-Planck equations and 'action at a distance' diffusiophoresis in crossed salt gradients

In the Nernst-Planck equations in two or more dimensions, a non-Faradaic electric current can arise as a consequence of connecting patches with different liquid junction potentials. Whereas this current vanishes for binary electrolytes or one-dimensional problems, it is in general non-vanishing for example in crossed salt gradients. For a suspended colloidal particle, electrophoresis in the corresponding electrostatic potential gradient is generally vectorially misaligned with chemiphoresis in the concentration gradients, and diffusiophoresis (via electrophoresis) can occur in regions where there are no local concentration gradients ('action at a distance'). These phenomena may provide new opportunities to manipulate and sort particles, in microfluidic devices for example.