Gallium does not wet quartz or graphite. I’m pretty sure graphite doesn’t stick to quartz (or not well) especially if smooth. So what if on a round flat plate of polished fused quartz you set a small pile of graphite powder then on top of that you pour liquid gallium to sandwich the graphite between two materials it doesn’t stick to. If you spin the round plate and put a fused quartz lid over it (to prevent spilling out) I believe the graphite will spread out and form a sheet of graphene this way. If not then by the addition of adding a voltage difference (high volts and low milliamperes) between the fused quartz and gallium with opposite polarity or maybe instead with the same polarity. Maybe the electrostatic charges will help the graphene become uniform in addition to the gallium on top spreading it out across the flat fused quartz surface?
Just a thot 2.0