Mathematical Model for Isothermal Wire-Coating From a Bath of Giesekus Viscoelastic Fluid

Abstract

A mathematical model of wire-coating based on Giesekus constitutive equation is analyzed under isothermal conditions. It is desired to see the functional dependence of Giesekus model parameters on the important operating variables in the wire-coating process, which include volumetric flow rate (later referred to as flow rate), shear stress at the wire surface (later referred to as shear stress), force required for pulling the wire (later referred to as force), and radius of the coated wire (later referred to as coated wire thickness). To this end, the equation governing the laminar, incompressible, and rectilinear flow is first derived and then solved analytically for the case of vanishing axial pressure gradient. A numerical procedure is described to obtain the solution for the case of nonvanishing pressure gradient. Our results indicate that the magnitude of shear stress and force follow a decreasing trend with increasing Giesekus model parameters in both cases. The flow rate and coated wire thickness decrease on increasing the Giesekus model parameters when there is no imposed pressure gradient. However, in the presence of pressure gradient these variables first decrease with increasing Giesekus model parameters and then follow an increasing trend.