Galvanic Cells and Electric Potential In a battery or a galvanic cell, the electric potential of the battery is due to a difference of charges between the two cells like in a capacitor? So it is the electric field due to this separation that is driving the electrons? if yes, why we call it electromotive force of a battery (EMF) ? 
 A: Galvanic cells are driven by a chemical reaction known as a Redox reaction.
Schematically speaking the cell contains a oxidiser $O$ and a reducing agent $R$, separated by a conductive membrane.
When the oxidiser reacts it loses electrons:
$O \to O' + n e^-$ (where $O'$ is the reduced form of $O$)
When the reducing agent reacts it absorbs these electrons:
$R + n e^- \to R'$ (where $R'$ is the oxidised form of $R$)
It's these electrons that cause the potential to arise at the two electrodes and the cell to be able to provide current (a flow of electrons).
The overall Redox reaction is:
$O + R \to O' + R'$
A battery is usually (but not always) a number of the same cells connected in series to obtain the desired output voltage. The reactions take place only when the circuit is closed, so the electrons can flow from cathode to anode.
A typical system is the manganese dioxide ($MnO_2$), zinc ($Zn$) battery in which the oxidiser $MnO_2$ oxidises the $Zn$ metal. These batteries run out when either the oxidiser or reducing agent has been fully consumed in the redox reactions. In galvanic cells chemical energy is converted to electrical energy (when the cell is in use).
Another example of a galvanic (voltaic) cell is the $Zn/CuSO_4$ cell.
At the cathode $Zn$ is oxidised to $ZnSO_4$, while at the anode $CuSO_4$ is reduced to $Cu$. A permeable membrane allows transport of the sulphate ($SO_4^{2-}$) ions, while keeping the oxidation and reduction reactions separated.
The cell potential can be calculated as shown here.
A: The electric field is established only when we connect +ve and -ve of a battery with some resistance between them.
There will be no electric field when the battery is in ideal state. But we need a measure for expressing the power of battery so our physicists introduced EMF, because measuring it with electric field doesn't make sense when battery is ideal.
How current flows in galvonic cells:
The current flows mainly beacuse of the wire connecting them. The wire will have free electrons since it is a conducter. When a wire is connected b/w two different potential chemicals.
The first electron (excess electrons in the ion) transfers from -ve potential liquid to wire and then in wire the electrons flow and it passes one electron to the +ve potential liquid.
This link explains how electrons travel in galvonic cells
Extra Material : Check this to know about how electrons travel in wire
