Do stirling engines have a pressure gradient across the regenerator?

[Curl]

There is a temperature difference and we know the transition of the working fluid (from the hot chamber to the cold one) is isometric. So either there must be a pressure difference, or the number of molecules must be smaller; however, this can't be the case since eventually all the gas must move over to the other side. So is there a pressure difference? Or is it both constant volume and constant pressure process?

 

[h2oski1326]

What does your Stirling engine look like?

In general, if there is flow through your regenerator (which I suspect there is but cannot confirm without knowing how the engine is configured) there is a pressure difference driving the flow from the pistons in the Stirling engine.