Combined boundary singularity method and finite volume method with application to viscous deformation of polymer film in synthesis of sub-micron fibers

Abstract

For sub-micron fiber production involving interaction of melted polymer with flow, the inner sub-domain has the Reynolds number smaller then unity while the outer domain has the Reynolds number exceeding unity. The flow in the inner sub-domain is described by the Stokes equations while the outer flow is described by either the Navier-Stokes equations or Reynolds equations. A combined boundary singularity method (BSM) for the solution of the Stokes equation and finite volume method (FVM) for the solution of the Reynolds equations is developed and applied to the viscous deformation of 2-D tracks by air impinging into polymer film. The proposed FVM-BSM predicts viscous deformation of perturbed surface for the manufacturing process of sub-micron fibers.Sole use of FVM would require highly refined grid and re-meshing of gas flow domain. The FVM-BSM facilitates the advantage of BSM to mesh only the boundary of BSM sub-domain. The advantage of FVM also enables the solving of the Navier-Stokes equations for an arbitrary Reynolds number. In frame of the proposed coupled FVM-BSM approach, the velocity vector field at the boundaries of the low-Reynolds number region in the vicinity of the stagnation point, where deformation occurs, was computed by FVM. This method is used to obtain the deformation of melted pitch for the range of jet impingement angles.