This article addresses the low Weissenberg asymptotic analysis (Newtonian limit) of some macroscopic models of viscoelastic fluid flows in the framework of global weak solutions. We investigate the convergence of the corotational Johnson-Segalman, the FENE-P, the Giesekus and PTT models. Relying on a priori bounds coming from energy or free energy estimates, we first study the weak convergence ...

The use of biological fluids such as saliva and cervical mucus as diagnostics for measurements of health status is becoming increasingly popular in the fields of biology and medecine, particularly given the non-invasiveness and ease of obtaining such fluids [39, 78]. In general, these biological fluids are polymeric, and as a result tend to be viscoelastic. However, as a result of protease and ...

Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number t...

Abstract We report a unique tuneable analogue trend in particle focusing the laminar and weak viscoelastic regime of elasto-inertial flows. observe experimentally that particles circular cross-section microchannels can be tuned to any bandwidths lie between “Segre-Silberberg annulus” centre microcapillary. use direct numerical simulations investigate this phenomenon understand how minute amount...

The recently discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. , Phys. Rev. Lett. vol. 121, 2018, 024502) has offered an explanation for the origin elasto-inertial turbulence that occurs at lower Weissenberg numbers ( $Wi$ ). In support this, we show using weakly nonlinear analysis subcriticality found in Page 125, 2020, 154501) is generic across neutral cur...

Abstract A Taylor–Galerkin finite element time marching scheme is derived to numerically simulate the flow of a compressible and nonisothermal viscoelastic liquid between eccentrically rotating cylinders. Numerical approximations governing constitutive equations are computed over custom refined unstructured grid piecewise linear Galerkin elements. An original extension DEVSS formulation for flu...

A precision-machined cross-slot flow geometry with a shape that has been optimized by numerical simulation of the fluid kinematics is fabricated and used to measure the extensional viscosity of a dilute polymer solution. Full-field birefringence microscopy is used to monitor the evolution and growth of macromolecular anisotropy along the stagnation point streamline, and we observe the formation...

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker-Planck-Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from [1], where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurat...