Saint-Robert's law. The burning surface recedes faster as chamber pressure rises.
Gas generated at the burning surface balances gas choked through the throat. As the bore grows, Ab and Pc rise.
Local flow area sets the Mach number. The flow is subsonic through the approach, sonic at the throat and supersonic in the exit cone.
Gas cools as it accelerates, which is what the particle color shows.
Momentum thrust from the exhaust, plus a pressure term at the exit plane.
Geometry illustrative. Gas velocities upstream of the nozzle are exaggerated for visibility.