In a standard galvanic cell, I understand that electrons flow from the anode to the cathode. For example, in a Daniell cell, electrons flow from the Zn anode to the Cu cathode. Before the two half-cells are connected (open circuit), they are each in chemical equilibrium:
$$\require{mhchem} \ce{Zn(s) ⇌ Zn^2+(aq) + 2e^-}$$
$$\require{mhchem} \ce{Cu(s) ⇌ Cu^2+(aq) + 2e^-}$$
This means that in open circuit conditions each electrode will contain a surplus of negative charge. However, the zinc electrode will be more negatively charged because it oxidizes more easily. When the cells are connected via a wire and salt bridge, the electrons will flow from the zinc anode to the copper cathode as they attempt to re-establish new equilibrium positions.
Here is my uncertainty:
When connected, it appears that electrons are flowing from a more negatively charged area (Zn) to a less negatively charged area (Cu). Can the less negatively charged Zn be considered "positive" in relation to the more negative Zn? It seems that instead of a positively charged ion attracting them into the cathode, they travel there because the electron density is less. Is there an error in my logic?
I understand there is an electrochemical potential difference due to a difference in Gibbs free energy--which I have researched--but a quote by a blogger summed up my frustrations perfectly: "To me, this explanation seems to be invoking the "electrochemical potential" as a magic wand that pushes positive ions from the negative to the positive electrode without needing to invoke any electric fields."