For coextrusion problems, there will be a moving interface between the two materials, in addition to the free surfaces for the outer shape of the extrudate. A moving interface is similar to a free surface, in that its position is computed as part of the solution. A free-surface condition is prescribed along a boundary set, whereas a moving-interface condition is defined along the topological interface between two subdomains. Flow problems must be defined in both subdomains, but the type of flow problem in each (generalized Newtonian, differential viscoelastic, or integral viscoelastic) can be different.
In the absence of surface tension, the position of the steady-state moving interface must be prescribed upstream of the moving interface.
A fixed-interface condition holds along the intersection between subdomain 1 and subdomain 2 when
 | (15–4) |
and
 | (15–5) |
In Equation 15–4 and Equation 15–5, neither the velocity vector nor the surface-force vector is prescribed; only the continuity of these quantities is required. These two conditions replace the dynamic condition (Equation 15–1). These equations do not guarantee that trajectories will not cross the interface; this condition must be added to the system. These equations define a fixed-interface problem, whereas a moving-interface problem occurs when a kinematic condition (Equation 15–2 or Equation 15–3) is added to the system.
For a free surface, the dynamic condition (Equation 15–1) is prescribed as a boundary condition for the momentum equation. For a moving interface, Equation 15–4 and Equation 15–5 are satisfied by the continuity of the velocity's finite-element interpolation across the interface. The pressure is generally not continuous across a moving interface, but the normal force is continuous.
As for free-surface problems, Ansys Polyflow assigns a director 
to each node located on the interface, and the amplitude of
the nodal displacement in the 
direction is called the geometrical degree of freedom
(
).
In a finite-element formulation, it is natural to associate the kinematic
condition (Equation 15–2 or Equation 15–3) with the
variable 
. Let 
denote the shape function associated with the geometrical
degree of freedom. Along the free surface or moving interface, the following
equation must be satisfied:
 | (15–6) |
for steady-state flows, and
 | (15–7) |
for transient flows, where 
denotes the scalar product along the free surface, and
in the absence of upwinding. For consistent SUPG
(streamline-upwind Petrov-Galerkin) schemes,
 | (15–8) |
where 
is the order of the element size.
For 2D flows with a free surface and/or moving interface, it is often a good idea to invoke upwinding on the kinematic equation, as it improves the calculation.
The constitutive relationship in Equation 15–4 does not always hold in the presence of a fluid-fluid interface. It is sometimes necessary to assume that a different fluid velocity exists on each side of the interface, and that a Navier slip model dictates the interaction of one fluid with another.
Consider 
and 
to be the fluid velocity vectors on either side of the
interface. For steady-state flow, immiscibility requirements impose a continuous
normal velocity condition:
 | (15–9) |
while the following kinematic condition is also imposed:
 | (15–10) |
These conditions (Equation 15–9 and Equation 15–10) are sufficient for the normal velocity Dirichlet condition and displacement of the interface.
The constitutive relationship for the tangential velocity can be stated as
 | (15–11) |
where 
is the friction force that fluid 1 exerts on fluid 2,
spawns the subspace of vectors, and
 | (15–12) |
where 
is a Navier coefficient.
Equation 15–9, Equation 15–10, and Equation 15–11 form a set of valid boundary displacement conditions for a fluid-fluid moving interface problem.
Because two velocity vectors must be calculated along the interface, convergence may be more difficult than in the continuous velocity case, and an evolution scheme (on the interface or flow rate) may be required. For robustness reasons, the fluid-fluid slipping method is implemented through a penalty technique.