Describing chemical potential in Galvanic cell using Coulomb Force/Electric Potential

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Placing a block of metal in a solution of its ions causes it to go into some kind of dynamic equilibrium such that the metal ions form from atoms and atoms from ions at the same rate. In the first place why does this phenomena occur? Is it something that can be described using Physics?

Assuming its accepted as 'just a phenomena', is it then possible to describe the motion of charges(current flowing) due to connecting two of such cells(of different electrode potentials) using wires and a salt bridge to form a Galvanic cell using electric fields? Is it possible to calculate for example, the electric field due to the electrodes in the wires causing the electrons to move across and such?

Correct me if I'm wrong, but a quick search on the forums seemed to show that in the external circuit, the charges are driven by the electric field due to the battery, while within the battery, its the chemical potential due to the equilibrium in the electrodes that causes charges to move against the electric field within the battery.

So once again is it possible for such motion of charges to be described mathematically or at least, with words?