pressure

The total pressure loss can then be obtained by integrating Eq 6 over the slit length, L, where [P.sub.s] is the solution pressure at the slit entrance and [P.sub.exit] is the solution pressure at the slit exit.

Based on the quasi-static approximation, the pressure of the gas phase can be related to the local solution pressure using Laplace's Eq 13 where the cells are treated as having a uniform radius, R, P is the solution pressure, and [[Gamma].sub.bp] is the surface tension of the gas/polymer interface.

By combining Eqs 12, 13, and 15, an expression relating the gas phase pressure and the solution pressure is derived and given by Eq 16.

Calculating the gas phase pressure for a given solution pressure, requires Eq 16 to be solved iteratively, precluding a closed form solution of Eq 7.

Equations 17 and 18 can be solved using the boundary condition that at the slit exit the solution pressure is given by P(x = L) = [P.sub.exit] = P(i = N).

In equilibrium, the gas phase pressure in the cells, [P.sub.g], is a function of the solution pressure surrounding the cells, P, and the surface energy, [[Gamma].sub.bp], where from Laplace's equation, [P.sub.g] = P + 2[[Gamma].sub.bp]/R.

The model accounts for the fact that gas diffuses into the cells as the solution pressure decreases along the die length such that cell growth during the die flow is driven by both the gas pressure in the cells and the diffusion of gas into the cells.