Analytical solution for two-phase viscous four-roll-mill flow

Determine an analytical solution for the two-phase viscous mixture flow subject to four-roll-mill body forcing to enable direct assessment of numerical convergence without relying on Richardson extrapolation.

Background

The paper studies a two-phase viscous mixture driven by four-roll-mill forcing and evaluates convergence using Richardson extrapolation because a closed-form reference solution is not available to the authors.

An analytical solution for this configuration would provide a benchmark enabling direct error measurement and validation of numerical methods for co-incompressible two-phase flows.

References

Since we do not know the analytical solution to two-phase viscous flow under four roll mill forcing, we approximate the order of convergence k using Richardson extrapolation:

— Adaptive Mesh Refinement for Two-Phase Viscoelastic Fluid Mixture Models  (2409.19974 - Nagda et al., 2024) in Section: Idealized Four Roll Mill, Subsection Convergence of Newtonian Network