The concentration gradient is linear; i.e. there is a steady drop in the concentration. We can show this in a graph as below:
An electron at any point along the wire will have a higher concentration of delocalised electrons on one side than the other. It will experience a greater repulsion from the side with the higher concentration. This means there will be an overall electric force accelerating the electron in the direction of high to low concentration. Since the concentration gradient is linear, there will be the same strength of force on the electrons all along the wire.
The greater the difference in concentration between each ‘side’ of an electron, i.e. the ‘steeper’ the concentration gradient, the greater the force. The slope of the graph above represents the force on the electrons in the wire.
It is important to appreciate that this is a dynamic situation. The concentration gradient stays the same but individual electrons will be moving ‘down’ the gradient all of the time. The gradient is maintained, so long as the chemical changes inside the battery feed in new electrons at the negative end and capture electrons as they enter the positive end. This keeps the concentration at the negative end high and the concentration at the positive end low.
Have another look at the animation of the simple circuit: