As the polymer gasifies, the gases collect in bubbles, which move through the melt due to a Marangoni (surface tension gradient) force and to a viscosity gradient force, both of which result from gradients in the temperature of the polymer melt. Both forces drive a bubble in the direction from lower to higher temperatures. Since the temperature is highest toward the surface of the sphere, the radial velocity of the gaseous component is expected to be positive. The velocity of the polymer melt at a given radial location may be positive, reflecting the swelling caused by bubble growth within the sphere, or negative as the melt fills in regions that have lost polymer to gasification. Gas and polymer velocities are needed to determine the barycentric velocity for use in the energy equation.
Standard continuum momentum equations, such as the Navier-Stokes equation for fluids or Darcy's law for porous media, are not used to determine the separate velocities for polymer and gas components. These velocities are determined instead by gasification chemistry and bubble dynamics. A description of the derivation of radial bulk mixture velocities from the bubble submodel is given in section 5.9.