  The motion of the electrolyte, comprising of solute ions and solvent
molecules, is a frequently-occurring natural phenomenon. The motion of the
electrolyte leads to the flows of ions and solvent molecules, known as
electrochemical flows. In this study, we establish a general theory to describe
the motion of the electrochemical flows. Our theory provides a different
approach from others to clarify the details of the transport phenomena for the
electrochemical flows. We derive the governing equations in the electrolyte
fluid from mass, charge, momentum, energy, and concentration conservations. In
addition, we normalize the governing equations to derive the dimensionless
parameters, known as Reynolds, Thompson, Peclet, Prandtl and X numbers. The
physical meaning of these parameter numbers in the electrochemical flow is
discussed in detail. A new number, named X number, appears in the Navier-Stokes
equation symbolizing the balance between the inertia force and the electric
force.

Fluid Dynamics;Soft Condensed Matter