When you close the switch the needle of the voltmeter moves indicating that a flow of electrons is passing through the cell what happens when you open the switch

That's not enough description to tell us what's going on. 

We need to know what's powering the circuit, what the "cell" is
and how it's configured in the circuit, where the switch is in the
circuit, and what points in the circuit are being touched with the
probes of the voltmeter.

A simple drawing would be an ideal solution to our dilemma.
Given that, we could start work on an answer immediately,
and most likely have it ready for you by next Tuesday.