Pressure corrections for viscoelastic potential flow analysis of capillary instability

Linear stability analysis of the capillary instability of a viscoelastic liquid thread was carried out by Funada and Joseph (2003), who assumed irrotational flow but retained the effect of viscoelasticity (viscoelastic potential flow, VPF). They compared their results with the unapproximated normal mode solution of the linearized fully viscoelastic flow (FVF). The comparison showed that the growth rates from VPF are several times larger than from FVF when the Reynolds number is not large (of the order of 1 or less). Joseph and Wang (2004) presented a method for computing a viscous correction of the irrotational pressure to resolve the discrepancy between the non-zero irrotational shear stress and the zero shear stress boundary condition at a free surface. Here we extend the pressure correction formulation to potential flows of viscoelastic fluids in flows governed by linearized equations, and apply this pressure correction to capillary instability of viscoelastic fluids. The growth rates from this viscoelastic correction of VPF (VCVPF) are in excellent agreement with those from the unapproximated FVF solution.