Potential flows of incompressible fluids admit a pressure (Bernoulli) equation when the divergence of the stress is a gradient as in inviscid fluids, viscous fluids, linear viscoelastic fluids and second-order fluids. We show that the equation balancing drag and acceleration is the same for all these fluids independent of the viscosity or any viscoelastic parameter and that the drag is zero in ...

We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary breakup rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a micr...

Open flow boundaries are often present in viscoelastic flow calculations; their presence is not dictated by the physics of the problem, but rather by the need of truncating the computational domain. Viscoelastic liquids flowing in complex twoand three-dimensional domains are normally modeled by hyperbolic transport equations for the viscoelastic stress or conformation tensor, v · ∇S = F(∇v,S) −...

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 gro...

To understand observations of low Reynolds number mixing and flow transitions in viscoelastic fluids, we study numerically the dynamics of the Oldroyd-B viscoelastic fluid model. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a cellular flow with extensional stagnation points. We find that at O(1) Weissenberg number, these flows l...

The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the existence of a finite stress relaxation time. This present work is motivated by renewed interest in instabilities in polymer flow. The majority of currently...

We have implemented the log-conformation method for two-dimensional viscoelastic flow in COMSOL, a commercial high-level finite element package. The code is verified for an Oldroyd-B fluid flowing past a confined cylinder. We are also able to describe the well-known bistability of the viscoelastic flow in a crossslot geometry for a FENE-CR fluid, and we describe the changes required for perform...

Analysis of the linear theory of capillary instability of threads of Maxwell fluids of diameter D is carried out for the unapproximated normal mode solution and for a solution based on viscoelastic potential flow. The analysis here extends the analysis of viscous potential flow [Int. J. Multiphase Flow 28 (2002) 1459] to viscoelastic fluids of Maxwell type. The analysis is framed in dimensionle...

The understanding of polymeric fluids flows is of essential importance for several industry sectors, including plastic and food processing industries. The rheological response of viscoelastic fluids is quite complex, including combination of viscous and elastic effects and highly non-linear viscous and elastic phenomena. In a previous work we presented a solver for internal viscoelastic fluid f...